From ebf270b9dd464cad266cde7d215a7ac1ea96c8f2 Mon Sep 17 00:00:00 2001 From: Hamish Hall Date: Sun, 29 Jan 2023 10:00:58 +0000 Subject: [PATCH 1/7] checkpoint --- .ipynb_checkpoints/README-checkpoint.md | 78 + ...Hack-challenge-2023-task1-checkpoint.ipynb | 447 + ...Hack-challenge-2023-task2-checkpoint.ipynb | 448 + ...Hack-challenge-2023-task3-checkpoint.ipynb | 440 + ...Hack-challenge-2023-task4-checkpoint.ipynb | 5037 +++++++++++ ...Hack-challenge-2023-task5-checkpoint.ipynb | 440 + ...Hack-challenge-2023-task6-checkpoint.ipynb | 440 + ...Hack-challenge-2023-task7-checkpoint.ipynb | 440 + ...Hack-challenge-2023-task8-checkpoint.ipynb | 443 + ...Hack-challenge-2023-task9-checkpoint.ipynb | 440 + iQuHack-challenge-2023-task1.ipynb | 1530 +++- iQuHack-challenge-2023-task2.ipynb | 3001 ++++++- iQuHack-challenge-2023-task3.ipynb | 4607 +++++++++- iQuHack-challenge-2023-task4.ipynb | 4650 +++++++++- iQuHack-challenge-2023-task5.ipynb | 3002 ++++++- iQuHack-challenge-2023-task6.ipynb | 7953 ++++++++++++++++- iQuHack-challenge-2023-task8.ipynb | 4629 +++++++++- obj/__entrypoint__.dll | Bin 0 -> 228352 bytes obj/__entrypoint__snippets__.dll | Bin 0 -> 106496 bytes obj/__snippets__.dll | Bin 0 -> 105984 bytes 20 files changed, 37843 insertions(+), 182 deletions(-) create mode 100644 .ipynb_checkpoints/README-checkpoint.md create mode 100644 .ipynb_checkpoints/iQuHack-challenge-2023-task1-checkpoint.ipynb create mode 100644 .ipynb_checkpoints/iQuHack-challenge-2023-task2-checkpoint.ipynb create mode 100644 .ipynb_checkpoints/iQuHack-challenge-2023-task3-checkpoint.ipynb create mode 100644 .ipynb_checkpoints/iQuHack-challenge-2023-task4-checkpoint.ipynb create mode 100644 .ipynb_checkpoints/iQuHack-challenge-2023-task5-checkpoint.ipynb create mode 100644 .ipynb_checkpoints/iQuHack-challenge-2023-task6-checkpoint.ipynb create mode 100644 .ipynb_checkpoints/iQuHack-challenge-2023-task7-checkpoint.ipynb create mode 100644 .ipynb_checkpoints/iQuHack-challenge-2023-task8-checkpoint.ipynb create mode 100644 .ipynb_checkpoints/iQuHack-challenge-2023-task9-checkpoint.ipynb create mode 100644 obj/__entrypoint__.dll create mode 100644 obj/__entrypoint__snippets__.dll create mode 100644 obj/__snippets__.dll diff --git a/.ipynb_checkpoints/README-checkpoint.md b/.ipynb_checkpoints/README-checkpoint.md new file mode 100644 index 0000000..58743d7 --- /dev/null +++ b/.ipynb_checkpoints/README-checkpoint.md @@ -0,0 +1,78 @@ +# Welcome to the Microsoft Challenge @ MIT iQuHACK 2023! + +## Challenge overview + +In this challenge, you will explore optimizing quantum circuits, and more specficially - optimizing quantum oracles. +In each task, you'll be given a quantum oracle that implements a certain classical function (the classical function definition is not included in the task). +You'll need to rewrite the code so that it maintains its correctness, but requires as few resources as possible. + +## Working on the challenge + +* The challenge contains 9 independent tasks. Your team can work on each task independently; tasks are submitted and scored separately. +* You can work on the challenge using a local Quantum Development Kit setup, Azure Quantum hosted notebooks, or qBraid platform. +* You'll need to [create an Azure account and an Azure Quantum workspace](https://aka.ms/iQuHack2023/AQJobSubmit) to evaluate the resources used by your solution, regardless of the platform you're using. +* To work on each task, use the Jupyter notebooks iQuHack-challenge-2023-taskX.ipynb. Each notebook contains the step-by-step instructions for working on the task, including the code that helps you evaluate your solution. +* **You will submit the tasks for challenge using qBraid platform.** + Each task submission is evaluated automatically in two steps. + 1. First, the task correctness is checked by verifying that your code acts the same as the original oracle implementation. If your solution doesn't compile, throws a runtime error, or acts differently from the original oracle implementation, this submission will be ignored. + 2. Second, if the task is logically correct, its resource consumption is evaluated. For this, we submit a resource estimation job for your code, and calculate your score as **(logical algorithmic qubits) * (algorithmic depth)** (see [resource estimation documentation](https://learn.microsoft.com/en-us/azure/quantum/learn-how-the-resource-estimator-works#algorithmic-logical-estimation), [introductory workshop](https://www.twitch.tv/videos/1718264700) or resource estimation samples for the meaning of these parameters). + 3. Your goal is to minimize your score for each task. Your aggregate score in the scoreboard is a sum of ratios (your score for the task) / (the score of the initial oracle implementation for the task) for all tasks. + + +### Tips and tricks for optimizing your quantum programs + +**The score is defined as a product: (logical algorithmic qubits) * (algorithmic depth)** + +* The number of logical qubits after mapping scales proportional to the number of qubits in the circuit. Therefore, reducing the qubits in the circuit always helps, unless it leads to an increase in operations. +* The number of logical cycles depend on the number of Toffoli gates (translated to CCZ), T gates, single-qubit measurements (which you will not be using in this challenge), and rotation gates. Clifford operations do not increase logical cycles. +* Rotation gates are the most expensive ones and should be avoided when possible! (For this challenge, you should be able to avoid them completely, using only reversible computation) +* Multiple-controlled X gates (multiple-controlled Toffoli gates) are decomposed by the resource estimator. The number of cycles is 3 * (n - 1), where n >= 1 is the number of control qubits. +* The concrete formulas to determine the logical qubits and logical cycles (after mapping) from the input program is provided in the paper https://arxiv.org/pdf/2211.07629.pdf + * Number of logical qubits in (D1, page 29) + * Number of logical cycles in (D3, page 30) + + +## Working on qBraid and submitting the tasks +[](https://account.qbraid.com?gitHubUrl=https://github.com/iQuHACK/2023_microsoft.git) +1. If you're working on qBraid, first fork this repository and click the above `Launch on qBraid` button. It will take you to your qBraid Lab with the repository cloned. +2. Once cloned, open terminal (first icon in the **Other** column in Launcher) and `cd` into this repo. Set the repo's remote origin using the git clone url you copied in Step 1, and then create a new branch for your team: +```bash +cd +git remote set-url origin +git branch +git checkout +``` +3. Use the environment manager (**ENVS** tab in the right sidebar) to activate the "Microsoft Q#". click **Activate** to [add a new ipykernel](https://qbraid-qbraid.readthedocs-hosted.com/en/latest/lab/kernels.html#add-remove-kernels) for "Microsoft Q#". + +image + + +4. From the **FILES** tab in the left sidebar, double-click on the `2023_Microsoft_Challenge` directory. + +5. You are now ready to begin hacking! Work with your team to complete the Microsoft Q# Challenge. + + +### qBraid Auto Grader Submission Process To Leaderboard: + +**PLEASE MAKE SURE TO DO THE FOLLOWING BEFORE YOU SUBMIT** + +- Your team name, task #, and a point person's slack name (just in case we need to reach out). +Once you have completed any of the tasks and have added the team name, task # and a point person's slack name, if you are confused). Please got to File (**File** on the top left of the topbar) and click on the `Share notebook` button. +スクリーンショット 2023-01-26 午後4 42 50 + +- Enter `rickyyoung@qbraid.com` and share the file. If it shares successfully, the email should dissapear. Ricky will periodically run the autograder and the leaderboard will be updated accordingly. + +- Then submit the remote project submission form that will show up on the iQuHACK website during the last 8 hours of hacking. The form will ask for a link to your repository and your team members (all of whom have to be remote iQuHACK participants to maintain elligibility). + +## Prizes + +Up to (3) teams with the highest team scores will be chosen as the winners of the Hackathon. +Each member of the winning teams will get a Surface 2 headset. + +## Resources + +* [Introduction to Azure Quantum workshop at MIT iQuHack](https://www.twitch.tv/videos/1718264700), Wednesday, January 25, 2023 +* [The Quantum Katas](https://github.com/Microsoft/QuantumKatas/) - a collection of tutorials and practice problems (chapters "Quantum Oracles and Simple Oracle Algorithms" and "Grover's search algorithm" are a good place to practice your work with marking oracles) +* [Getting started with the resources estimator service](https://learn.microsoft.com/en-us/azure/quantum/quickstart-microsoft-resources-estimator) +* [A deep dive in resource estimation](https://arxiv.org/pdf/2211.07629.pdf) +* [Azure Quantum and Microsoft Quantum Development Kit documentation](https://learn.microsoft.com/azure/quantum/) diff --git a/.ipynb_checkpoints/iQuHack-challenge-2023-task1-checkpoint.ipynb b/.ipynb_checkpoints/iQuHack-challenge-2023-task1-checkpoint.ipynb new file mode 100644 index 0000000..6042c2b --- /dev/null +++ b/.ipynb_checkpoints/iQuHack-challenge-2023-task1-checkpoint.ipynb @@ -0,0 +1,447 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "# MIT iQuHack Microsoft Challenge: Optimizing Quantum Oracles, Task 1\n", + "\n", + "To work on this task,\n", + "1. Use the notebook for this task. Each of the notebooks in the repository has the code of the corresponding task.\n", + "2. Update your team name and Slack ID variables in the next code cell (you can use different Slack IDs for different tasks if different team members work on them, but make sure to use the same team name throughout the Hackathon). Do not change the task variable!\n", + "3. Work on your task in the cell that contains operation `Task1`! Your goal is to rewrite the code so that it maintains its correctness, but requires as few resources as possible. See `evaluate_results` function for details on how your absolute score for the task is calculated.\n", + "4. Submit your task using qBraid. Use the Share Notebook feature on qBraid (See File > Share Notebook) and enter the email rickyyoung@qbraid.com. Once you click submit, if the share notebook feature works correctly, it should show that you receive no errors and the email you entered will disappear. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "Log in to Azure (once per session, don't need to do it if running from Azure workspace)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "!az login" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 1. Write the code" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Run this code cell to import the modules required to work with Q# and Azure\n", + "import qsharp\n", + "from qsharp import azure" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "teamname=\"msft_is_the_best\" # Update this field with your team name\n", + "task=[\"task1\"]\n", + "slack_id=\"myslackid\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# You don't need to run this cell, it defines Q# operations as Python types to keep IntelliSense happy\n", + "Task1_DumpMachineWrapper : qsharp.QSharpCallable = None\n", + "Task1_ResourceEstimationWrapper : qsharp.QSharpCallable = None" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "**The complete code for Task 1 should be in this cell.** \n", + "This cell can include additional open statements and helper operations and functions if your solution needs them. \n", + "If you define helper operations in other cells, they will not be picked up by the grader!" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "open Microsoft.Quantum.Canon;\n", + "open Microsoft.Quantum.Diagnostics;\n", + "\n", + "// Task 1. Warm up with simple bit manipulation\n", + "// (input will contain 3 qubits)\n", + "operation Task1(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " let N = Length(input);\n", + " use aux = Qubit[N - 1];\n", + " within {\n", + " for i in 0 .. N - 2 {\n", + " CNOT(input[i], aux[i]);\n", + " CNOT(input[i + 1], aux[i]);\n", + " }\n", + " } apply {\n", + " Controlled X(aux, target);\n", + " }\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "// Wrapper operation that allows you to observe the effects of the marking oracle by running it on a simulator.\n", + "operation Task1_DumpMachineWrapper() : Unit {\n", + " let N = 3;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " // Prepare an equal superposition of all input states in the input register.\n", + " ApplyToEach(H, input);\n", + " // Apply the oracle.\n", + " Task1(input, target);\n", + " // Print the state of the system after the oracle application.\n", + " DumpMachine();\n", + " ResetAll(input + [target]);\n", + "}\n", + "\n", + "// Wrapper operation that allows to run resource estimation for the task.\n", + "// This operation only allocates the qubits and applies the oracle once, not using any additional gates or measurements.\n", + "operation Task1_ResourceEstimationWrapper() : Unit {\n", + " let N = 3;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " Task1(input, target);\n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 2. Run the code on a simulator to see what it does\n", + "You can also write your own code to explore the effects of the oracle (for example, applying it to different basis states and measuring the results)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Note that in the output of this cell the target qubit corresponds to the rightmost bit\n", + "qsharp.config[\"dump.basisStateLabelingConvention\"]=\"Bitstring\"\n", + "qsharp.config[\"dump.phaseDisplayStyle\"]=\"None\"\n", + "# Uncomment the following line if you want to see only the entries with non-zero amplitudes\n", + "# qsharp.config[\"dump.truncateSmallAmplitudes\"]=True\n", + "Task1_DumpMachineWrapper.simulate()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 3. Evaluate the code using resource estimation" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", + "# If you're using this notebook in qBraid, keep it\n", + "qsharp.azure.connect(\n", + " resourceId=\"...\",\n", + " location=\"...\",\n", + " credential=\"CLI\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "qsharp.azure.target(\"microsoft.estimator\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", + "result = qsharp.azure.execute(Task1_ResourceEstimationWrapper, jobName=\"RE for the task 1\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", + "# result = qsharp.azure.output(\"...\")\n", + "result" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# The function that extracts the relevant resource information from the resource estimation job results and produces your absolute score.\n", + "def evaluate_results(res) : \n", + " width = res['physicalCounts']['breakdown']['algorithmicLogicalQubits']\n", + " depth = res['physicalCounts']['breakdown']['algorithmicLogicalDepth']\n", + " print(f\"Logical algorithmic qubits = {width}\")\n", + " print(f\"Algorithmic depth = {depth}\")\n", + " print(f\"Score = {width * depth}\")\n", + " return width * depth\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "evaluate_results(result)" + ] + } + ], + "metadata": { + "kernel_info": { + "name": "python3" + }, + "kernelspec": { + "display_name": "Python 3 [Default]", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.10" + }, + "nteract": { + "version": "nteract-front-end@1.0.0" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/.ipynb_checkpoints/iQuHack-challenge-2023-task2-checkpoint.ipynb b/.ipynb_checkpoints/iQuHack-challenge-2023-task2-checkpoint.ipynb new file mode 100644 index 0000000..44cc5cd --- /dev/null +++ b/.ipynb_checkpoints/iQuHack-challenge-2023-task2-checkpoint.ipynb @@ -0,0 +1,448 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "# MIT iQuHack Microsoft Challenge: Optimizing Quantum Oracles, Task 2\n", + "\n", + "To work on this task,\n", + "1. Use the notebook for this task. Each of the notebooks in the repository has the code of the corresponding task.\n", + "2. Update your team name and Slack ID variables in the next code cell (you can use different Slack IDs for different tasks if different team members work on them, but make sure to use the same team name throughout the Hackathon). Do not change the task variable!\n", + "3. Work on your task in the cell that contains operation `Task2`! Your goal is to rewrite the code so that it maintains its correctness, but requires as few resources as possible. See `evaluate_results` function for details on how your absolute score for the task is calculated.\n", + "4. Submit your task using qBraid. Use the Share Notebook feature on qBraid (See File > Share Notebook) and enter the email rickyyoung@qbraid.com. Once you click submit, if the share notebook feature works correctly, it should show that you receive no errors and the email you entered will disappear. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "Log in to Azure (once per session, don't need to do it if running from Azure workspace)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "!az login" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 1. Write the code" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Run this code cell to import the modules required to work with Q# and Azure\n", + "import qsharp\n", + "from qsharp import azure" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "teamname=\"msft_is_the_best\" # Update this field with your team name\n", + "task=[\"task2\"]\n", + "slack_id=\"myslackid\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# You don't need to run this cell, it defines Q# operations as Python types to keep IntelliSense happy\n", + "Task2_DumpMachineWrapper : qsharp.QSharpCallable = None\n", + "Task2_ResourceEstimationWrapper : qsharp.QSharpCallable = None" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "**The complete code for Task 2 should be in this cell.** \n", + "This cell can include additional open statements and helper operations and functions if your solution needs them. \n", + "If you define helper operations in other cells, they will not be picked up by the grader!" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "open Microsoft.Quantum.Canon;\n", + "open Microsoft.Quantum.Diagnostics;\n", + "\n", + "// Task 2. Celebrate MIT iQuHack!\n", + "// (input will contain 5 qubits)\n", + "operation Task2(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " ControlledOnInt(13, X)(input, target); // M\n", + " ControlledOnInt( 9, X)(input, target); // I\n", + " ControlledOnInt(20, X)(input, target); // T\n", + "\n", + " ControlledOnInt( 9, X)(input, target); // I\n", + " ControlledOnInt(17, X)(input, target); // Q\n", + " ControlledOnInt(21, X)(input, target); // U\n", + " ControlledOnInt( 8, X)(input, target); // H\n", + " ControlledOnInt( 1, X)(input, target); // A\n", + " ControlledOnInt( 3, X)(input, target); // C\n", + " ControlledOnInt(11, X)(input, target); // K\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "// Wrapper operation that allows you to observe the effects of the marking oracle by running it on a simulator.\n", + "operation Task2_DumpMachineWrapper() : Unit {\n", + " let N = 5;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " // Prepare an equal superposition of all input states in the input register.\n", + " ApplyToEach(H, input);\n", + " // Apply the oracle.\n", + " Task2(input, target);\n", + " // Print the state of the system after the oracle application.\n", + " DumpMachine();\n", + " ResetAll(input + [target]);\n", + "}\n", + "\n", + "// Wrapper operation that allows to run resource estimation for the task.\n", + "// This operation only allocates the qubits and applies the oracle once, not using any additional gates or measurements.\n", + "operation Task2_ResourceEstimationWrapper() : Unit {\n", + " let N = 5;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " Task2(input, target);\n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 2. Run the code on a simulator to see what it does\n", + "You can also write your own code to explore the effects of the oracle (for example, applying it to different basis states and measuring the results)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Note that in the output of this cell the target qubit corresponds to the rightmost bit\n", + "qsharp.config[\"dump.basisStateLabelingConvention\"]=\"Bitstring\"\n", + "qsharp.config[\"dump.phaseDisplayStyle\"]=\"None\"\n", + "# Uncomment the following line if you want to see only the entries with non-zero amplitudes\n", + "# qsharp.config[\"dump.truncateSmallAmplitudes\"]=True\n", + "Task2_DumpMachineWrapper.simulate()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 3. Evaluate the code using resource estimation" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", + "# If you're using this notebook in qBraid, keep it\n", + "qsharp.azure.connect(\n", + " resourceId=\"...\",\n", + " location=\"...\",\n", + " credential=\"CLI\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "qsharp.azure.target(\"microsoft.estimator\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", + "result = qsharp.azure.execute(Task2_ResourceEstimationWrapper, jobName=\"RE for the task 2\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", + "# result = qsharp.azure.output(\"...\")\n", + "result" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# The function that extracts the relevant resource information from the resource estimation job results and produces your absolute score.\n", + "def evaluate_results(res) : \n", + " width = res['physicalCounts']['breakdown']['algorithmicLogicalQubits']\n", + " depth = res['physicalCounts']['breakdown']['algorithmicLogicalDepth']\n", + " print(f\"Logical algorithmic qubits = {width}\")\n", + " print(f\"Algorithmic depth = {depth}\")\n", + " print(f\"Score = {width * depth}\")\n", + " return width * depth\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "evaluate_results(result)" + ] + } + ], + "metadata": { + "kernel_info": { + "name": "python3" + }, + "kernelspec": { + "display_name": "Python 3 [Default]", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.10" + }, + "nteract": { + "version": "nteract-front-end@1.0.0" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/.ipynb_checkpoints/iQuHack-challenge-2023-task3-checkpoint.ipynb b/.ipynb_checkpoints/iQuHack-challenge-2023-task3-checkpoint.ipynb new file mode 100644 index 0000000..77ca776 --- /dev/null +++ b/.ipynb_checkpoints/iQuHack-challenge-2023-task3-checkpoint.ipynb @@ -0,0 +1,440 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "# MIT iQuHack Microsoft Challenge: Optimizing Quantum Oracles, Task 3\n", + "\n", + "To work on this task,\n", + "1. Use the notebook for this task. Each of the notebooks in the repository has the code of the corresponding task.\n", + "2. Update your team name and Slack ID variables in the next code cell (you can use different Slack IDs for different tasks if different team members work on them, but make sure to use the same team name throughout the Hackathon). Do not change the task variable!\n", + "3. Work on your task in the cell that contains operation `Task3`! Your goal is to rewrite the code so that it maintains its correctness, but requires as few resources as possible. See `evaluate_results` function for details on how your absolute score for the task is calculated.\n", + "4. Submit your task using qBraid. Use the Share Notebook feature on qBraid (See File > Share Notebook) and enter the email rickyyoung@qbraid.com. Once you click submit, if the share notebook feature works correctly, it should show that you receive no errors and the email you entered will disappear. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "Log in to Azure (once per session, don't need to do it if running from Azure workspace)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "!az login" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 1. Write the code" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Run this code cell to import the modules required to work with Q# and Azure\n", + "import qsharp\n", + "from qsharp import azure" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "teamname=\"msft_is_the_best\" # Update this field with your team name\n", + "task=[\"task3\"]\n", + "slack_id=\"myslackid\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# You don't need to run this cell, it defines Q# operations as Python types to keep IntelliSense happy\n", + "Task3_DumpMachineWrapper : qsharp.QSharpCallable = None\n", + "Task3_ResourceEstimationWrapper : qsharp.QSharpCallable = None" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "**The complete code for Task 3 should be in this cell.** \n", + "This cell can include additional open statements and helper operations and functions if your solution needs them. \n", + "If you define helper operations in other cells, they will not be picked up by the grader!" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "open Microsoft.Quantum.Canon;\n", + "open Microsoft.Quantum.Diagnostics;\n", + "\n", + "// Task 3. \n", + "// (input will contain 6 qubits)\n", + "operation Task3(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " for i in [7, 11, 13, 14, 19, 21, 22, 25, 26, 28, 35, 37, 38, 41, 42, 44, 49, 50, 52, 56] {\n", + " ControlledOnInt(i, X)(input, target);\n", + " }\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "// Wrapper operation that allows you to observe the effects of the marking oracle by running it on a simulator.\n", + "operation Task3_DumpMachineWrapper() : Unit {\n", + " let N = 6;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " // Prepare an equal superposition of all input states in the input register.\n", + " ApplyToEach(H, input);\n", + " // Apply the oracle.\n", + " Task3(input, target);\n", + " // Print the state of the system after the oracle application.\n", + " DumpMachine();\n", + " ResetAll(input + [target]);\n", + "}\n", + "\n", + "// Wrapper operation that allows to run resource estimation for the task.\n", + "// This operation only allocates the qubits and applies the oracle once, not using any additional gates or measurements.\n", + "operation Task3_ResourceEstimationWrapper() : Unit {\n", + " let N = 6;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " Task3(input, target);\n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 2. Run the code on a simulator to see what it does\n", + "You can also write your own code to explore the effects of the oracle (for example, applying it to different basis states and measuring the results)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Note that in the output of this cell the target qubit corresponds to the rightmost bit\n", + "qsharp.config[\"dump.basisStateLabelingConvention\"]=\"Bitstring\"\n", + "qsharp.config[\"dump.phaseDisplayStyle\"]=\"None\"\n", + "# Uncomment the following line if you want to see only the entries with non-zero amplitudes\n", + "# qsharp.config[\"dump.truncateSmallAmplitudes\"]=True\n", + "Task3_DumpMachineWrapper.simulate()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 3. Evaluate the code using resource estimation" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", + "# If you're using this notebook in qBraid, keep it\n", + "qsharp.azure.connect(\n", + " resourceId=\"...\",\n", + " location=\"...\",\n", + " credential=\"CLI\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "qsharp.azure.target(\"microsoft.estimator\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", + "result = qsharp.azure.execute(Task3_ResourceEstimationWrapper, jobName=\"RE for the task 3\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", + "# result = qsharp.azure.output(\"...\")\n", + "result" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# The function that extracts the relevant resource information from the resource estimation job results and produces your absolute score.\n", + "def evaluate_results(res) : \n", + " width = res['physicalCounts']['breakdown']['algorithmicLogicalQubits']\n", + " depth = res['physicalCounts']['breakdown']['algorithmicLogicalDepth']\n", + " print(f\"Logical algorithmic qubits = {width}\")\n", + " print(f\"Algorithmic depth = {depth}\")\n", + " print(f\"Score = {width * depth}\")\n", + " return width * depth\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "evaluate_results(result)" + ] + } + ], + "metadata": { + "kernel_info": { + "name": "python3" + }, + "kernelspec": { + "display_name": "Python 3 [Default]", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.10" + }, + "nteract": { + "version": "nteract-front-end@1.0.0" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/.ipynb_checkpoints/iQuHack-challenge-2023-task4-checkpoint.ipynb b/.ipynb_checkpoints/iQuHack-challenge-2023-task4-checkpoint.ipynb new file mode 100644 index 0000000..2779048 --- /dev/null +++ b/.ipynb_checkpoints/iQuHack-challenge-2023-task4-checkpoint.ipynb @@ -0,0 +1,5037 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "# MIT iQuHack Microsoft Challenge: Optimizing Quantum Oracles, Task 4\n", + "\n", + "To work on this task,\n", + "1. Use the notebook for this task. Each of the notebooks in the repository has the code of the corresponding task.\n", + "2. Update your team name and Slack ID variables in the next code cell (you can use different Slack IDs for different tasks if different team members work on them, but make sure to use the same team name throughout the Hackathon). Do not change the task variable!\n", + "3. Work on your task in the cell that contains operation `Task4`! Your goal is to rewrite the code so that it maintains its correctness, but requires as few resources as possible. See `evaluate_results` function for details on how your absolute score for the task is calculated.\n", + "4. Submit your task using qBraid. Use the Share Notebook feature on qBraid (See File > Share Notebook) and enter the email rickyyoung@qbraid.com. Once you click submit, if the share notebook feature works correctly, it should show that you receive no errors and the email you entered will disappear. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "Log in to Azure (once per session, don't need to do it if running from Azure workspace)" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\u001b[93mTo sign in, use a web browser to open the page https://microsoft.com/devicelogin and enter the code AXM2895LG to authenticate.\u001b[0m\n", + "[\n", + " {\n", + " \"cloudName\": \"AzureCloud\",\n", + " \"homeTenantId\": \"b4e518fe-3bdc-4371-a4be-7f3d83d7acbd\",\n", + " \"id\": \"7fc54e95-14cf-4a6f-b50e-d6155c241309\",\n", + " \"isDefault\": true,\n", + " \"managedByTenants\": [\n", + " {\n", + " \"tenantId\": \"d0ecd01b-d782-448e-bae0-c3cad0e0543a\"\n", + " },\n", + " {\n", + " \"tenantId\": \"94c4857e-1130-4ab8-8eac-069b40c9db20\"\n", + " },\n", + " {\n", + " \"tenantId\": \"f702a9dc-ae48-4dc7-8f0a-8155a6dfa4e5\"\n", + " }\n", + " ],\n", + " \"name\": \"Azure subscription 1\",\n", + " \"state\": \"Enabled\",\n", + " \"tenantId\": \"b4e518fe-3bdc-4371-a4be-7f3d83d7acbd\",\n", + " \"user\": {\n", + " \"name\": \"hachall@hotmail.com\",\n", + " \"type\": \"user\"\n", + " }\n", + " }\n", + "]\n" + ] + } + ], + "source": [ + "!az login" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 1. Write the code" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Run this code cell to import the modules required to work with Q# and Azure\n", + "import qsharp\n", + "from qsharp import azure" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "teamname=\"schrodingers-duck\" # Update this field with your team name\n", + "task=[\"task4\"]\n", + "slack_id=\"U04L3SFUCQ2\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# You don't need to run this cell, it defines Q# operations as Python types to keep IntelliSense happy\n", + "Task4_DumpMachineWrapper : qsharp.QSharpCallable = None\n", + "Task4_ResourceEstimationWrapper : qsharp.QSharpCallable = None" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "**The complete code for Task 4 should be in this cell.** \n", + "This cell can include additional open statements and helper operations and functions if your solution needs them. \n", + "If you define helper operations in other cells, they will not be picked up by the grader!" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "open Microsoft.Quantum.Canon;\n", + "open Microsoft.Quantum.Diagnostics;\n", + "open Microsoft.Quantum.Arrays;\n", + "\n", + "// Task 4. \n", + "// (input will contain 7 qubits)\n", + "operation original(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " let N = Length(input);\n", + " for i in 0 .. 3 .. 2^N - 1 {\n", + " ControlledOnInt(i, X)(input, target);\n", + " }\n", + "}\n", + "\n", + "operation mod3adder (reg : Qubit[]) : Unit is Adj+Ctl {\n", + " let sum = reg[0];\n", + " let carry = reg[1];\n", + " ControlledOnInt(0, X)([carry], sum);\n", + " ControlledOnInt(0, X)([sum], carry);\n", + "}\n", + "\n", + "operation Task4(input : Qubit[], target : Qubit) : Unit is Adj+Ctl {\n", + " use output = Qubit[2] {\n", + " within {\n", + " for i in 0 .. Length(input) - 1 { // starting from LSB\n", + " if (i % 2 == 0) {\n", + " Controlled mod3adder([input[i]], output);\n", + " } else {\n", + " Controlled Adjoint mod3adder([input[i]], output);\n", + " }\n", + " }\n", + " } apply {\n", + " ControlledOnInt(0, X)(output, target);\n", + " }\n", + "\n", + " }\n", + "}\n", + "\n", + "operation QubitArrayWrapperOperation (op : ((Qubit[], Qubit) => Unit is Adj), qs : Qubit[]) : Unit is Adj { \n", + " op(Most(qs), Tail(qs));\n", + "}\n", + "\n", + "operation TestCompoundGate () : Unit {\n", + " AssertOperationsEqualReferenced(7+1, QubitArrayWrapperOperation(Task4, _), QubitArrayWrapperOperation (original, _));\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "TestCompoundGate();" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "// Wrapper operation that allows you to observe the effects of the marking oracle by running it on a simulator.\n", + "operation Task4_DumpMachineWrapper() : Unit {\n", + " let N = 7;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " // Prepare an equal superposition of all input states in the input register.\n", + " ApplyToEach(H, input);\n", + " // Apply the oracle.\n", + " Task4(input, target);\n", + " // Print the state of the system after the oracle application.\n", + " DumpMachine();\n", + " ResetAll(input + [target]);\n", + "}\n", + "\n", + "// Wrapper operation that allows to run resource estimation for the task.\n", + "// This operation only allocates the qubits and applies the oracle once, not using any additional gates or measurements.\n", + "operation Task4_ResourceEstimationWrapper() : Unit {\n", + " let N = 7;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " Task4(input, target);\n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 2. Run the code on a simulator to see what it does\n", + "You can also write your own code to explore the effects of the oracle (for example, applying it to different basis states and measuring the results)." + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "data": { + "application/x-qsharp-data": 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Qubit IDs0, 1, 2, 3, 4, 5, 6, 7
Basis state (bitstring)AmplitudeMeas. Pr.
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$\\left|1010001100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1010111100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10110000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10110010\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1011010100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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"text/plain": [ + "()" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Note that in the output of this cell the target qubit corresponds to the rightmost bit\n", + "qsharp.config[\"dump.basisStateLabelingConvention\"]=\"Bitstring\"\n", + "qsharp.config[\"dump.phaseDisplayStyle\"]=\"None\"\n", + "# Uncomment the following line if you want to see only the entries with non-zero amplitudes\n", + "qsharp.config[\"dump.truncateSmallAmplitudes\"]=True\n", + "Task4_DumpMachineWrapper.simulate()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 3. Evaluate the code using resource estimation" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "data": { + "application/x-qsharp-data": "\"Connecting to Azure Quantum...\"", + "text/plain": [ + "Connecting to Azure Quantum..." + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Connected to Azure Quantum workspace azure-q in location uksouth.\n" + ] + }, + { + "data": { + "text/plain": [ + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 295782},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 356057},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 2},\n", + " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 200},\n", + " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 200},\n", + " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.qpu.aspen-m-2', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", + "# If you're using this notebook in qBraid, keep it\n", + "qsharp.azure.connect(\n", + " resourceId=\"/subscriptions/7fc54e95-14cf-4a6f-b50e-d6155c241309/resourceGroups/AzureQuantum/providers/Microsoft.Quantum/Workspaces/azure-q\",\n", + " location=\"UK South\",\n", + " credential=\"CLI\")" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loading package Microsoft.Quantum.Providers.Core and dependencies...\n", + "Active target is now microsoft.estimator\n" + ] + }, + { + "data": { + "text/plain": [ + "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qsharp.azure.target(\"microsoft.estimator\")" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Submitting Task4_ResourceEstimationWrapper to target microsoft.estimator...\n", + "Job successfully submitted.\n", + " Job name: RE for the task 4\n", + " Job ID: cf53f47e-8a14-4d2c-b8a2-f6297837511e\n", + "Waiting up to 30 seconds for Azure Quantum job to complete...\n", + "[5:07:17 AM] Current job status: Executing\n", + "[5:07:22 AM] Current job status: Succeeded\n" + ] + } + ], + "source": [ + "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", + "result = qsharp.azure.execute(Task4_ResourceEstimationWrapper, jobName=\"RE for the task 4\")" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "data": { + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":0,\"cczCount\":29,\"measurementCount\":0,\"numQubits\":10,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":87,\"algorithmicLogicalQubits\":30,\"cliffordErrorRate\":0.001,\"logicalDepth\":87,\"numTfactories\":15,\"numTfactoryRuns\":8,\"numTsPerRotation\":null,\"numTstates\":116,\"physicalQubitsForAlgorithm\":7260,\"physicalQubitsForTfactories\":97200,\"requiredLogicalQubitErrorRate\":1.9157088122605365E-07,\"requiredLogicalTstateErrorRate\":4.310344827586207E-06},\"physicalQubits\":104460,\"runtime\":382800},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"93.05 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"1.92e-7\",\"requiredLogicalTstateErrorRate\":\"4.31e-6\",\"runtime\":\"382us 800ns\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 7260 physical qubits to implement the algorithm logic, and 97200 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 87 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 10$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 30$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 0 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 29 CCZ and 0 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 87. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 29 CCZ and 0 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 116 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 15 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{116\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 382us 800ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 116 T states, the 15 copies of the T factory are repeatedly invoked 8 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 7260 are the product of the 30 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 15 in parallel, therefore we need $97200 = 6480 \\\\cdot 15$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 30 logical qubits and the total cycle count 87.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 116.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000019157088122605365)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 4.31e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 30 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or ¬µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "text/html": [ + "\r\n", + "
\r\n", + " \r\n", + " Physical resource estimates\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits104460\r\n", + "

Number of physical qubits

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This value represents the total number of physical qubits, which is the sum of 7260 physical qubits to implement the algorithm logic, and 97200 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

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Runtime382us 800ns\r\n", + "

Total runtime

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This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 87 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

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Logical algorithmic qubits30\r\n", + "

Number of logical qubits for the algorithm after layout

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Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 10\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 30$ logical qubits.

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Algorithmic depth87\r\n", + "

Number of logical cycles for the algorithm

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To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 0 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 29 CCZ and 0 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

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Logical depth87\r\n", + "

Number of logical cycles performed

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This number is usually equal to the logical depth of the algorithm, which is 87. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

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Number of T states116\r\n", + "

Number of T states consumed by the algorithm

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To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 29 CCZ and 0 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

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Number of T factories15\r\n", + "

Number of T factories capable of producing the demanded 116 T states during the algorithm's runtime

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The total number of T factories 15 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{116\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 382us 800ns\\;\\text{algorithm runtime}}\\right\\rceil\\)

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Number of T factory invocations8\r\n", + "

Number of times all T factories are invoked

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In order to prepare the 116 T states, the 15 copies of the T factory are repeatedly invoked 8 times.

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Physical algorithmic qubits7260\r\n", + "

Number of physical qubits for the algorithm after layout

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The 7260 are the product of the 30 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.

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Physical T factory qubits97200\r\n", + "

Number of physical qubits for the T factories

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Each T factory requires 6480 physical qubits and we run 15 in parallel, therefore we need $97200 = 6480 \\cdot 15$ qubits.

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Required logical qubit error rate1.92e-7\r\n", + "

The minimum logical qubit error rate required to run the algorithm within the error budget

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The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 30 logical qubits and the total cycle count 87.

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Required logical T state error rate4.31e-6\r\n", + "

The minimum T state error rate required for distilled T states

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The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 116.

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Number of T states per rotationNo rotations in algorithm\r\n", + "

Number of T states to implement a rotation with an arbitrary angle

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The number of T states to implement a rotation with an arbitrary angle is \\(\\lceil 0.53 \\log_2(0 / 0) + 5.3\\rceil\\) [arXiv:2203.10064]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.

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\r\n", + " \r\n", + " Logical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
QEC schemesurface_code\r\n", + "

Name of QEC scheme

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You can load pre-defined QEC schemes by using the name surface_code or floquet_code. The latter only works with Majorana qubits.

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Code distance11\r\n", + "

Required code distance for error correction

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The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000019157088122605365)}{\\log(0.01/0.001)} - 1\\)

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Physical qubits242\r\n", + "

Number of physical qubits per logical qubit

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The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.

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Logical cycle time4us 400ns\r\n", + "

Duration of a logical cycle in nanoseconds

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The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.

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Logical qubit error rate3.00e-8\r\n", + "

Logical qubit error rate

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The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{11 + 1}{2}$

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Crossing prefactor0.03\r\n", + "

Crossing prefactor used in QEC scheme

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The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.

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Error correction threshold0.01\r\n", + "

Error correction threshold used in QEC scheme

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The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.

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Logical cycle time formula(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\r\n", + "

QEC scheme formula used to compute logical cycle time

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This is the formula that is used to compute the logical cycle time 4us 400ns.

\n", + "\r\n", + "
Physical qubits formula2 * codeDistance * codeDistance\r\n", + "

QEC scheme formula used to compute number of physical qubits per logical qubit

\n", + "\r\n", + "
\r\n", + "

This is the formula that is used to compute the number of physical qubits per logical qubits 242.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " T factory parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits6480\r\n", + "

Number of physical qubits for a single T factory

\n", + "\r\n", + "
\r\n", + "

This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.

\n", + "\r\n", + "
Runtime46us 800ns\r\n", + "

Runtime of a single T factory

\n", + "\r\n", + "
\r\n", + "

The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.

\n", + "\r\n", + "
Number of output T states per run1\r\n", + "

Number of output T states produced in a single run of T factory

\n", + "\r\n", + "
\r\n", + "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.

\n", + "\r\n", + "
Number of input T states per run30\r\n", + "

Number of physical input T states consumed in a single run of a T factory

\n", + "\r\n", + "
\r\n", + "

This value includes the physical input T states of all copies of the distillation unit in the first round.

\n", + "\r\n", + "
Distillation rounds1\r\n", + "

The number of distillation rounds

\n", + "\r\n", + "
\r\n", + "

This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.

\n", + "\r\n", + "
Distillation units per round2\r\n", + "

The number of units in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the number of copies for the distillation units per round.

\n", + "\r\n", + "
Distillation units15-to-1 space efficient logical\r\n", + "

The types of distillation units

\n", + "\r\n", + "
\r\n", + "

These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.

\n", + "\r\n", + "
Distillation code distances9\r\n", + "

The code distance in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.

\n", + "\r\n", + "
Number of physical qubits per round6480\r\n", + "

The number of physical qubits used in each round of distillation

\n", + "\r\n", + "
\r\n", + "

The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.

\n", + "\r\n", + "
Runtime per round46us 800ns\r\n", + "

The runtime of each distillation round

\n", + "\r\n", + "
\r\n", + "

The runtime of the T factory is the sum of the runtimes in all rounds.

\n", + "\r\n", + "
Logical T state error rate2.17e-6\r\n", + "

Logical T state error rate

\n", + "\r\n", + "
\r\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 4.31e-6.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Pre-layout logical resources\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Logical qubits (pre-layout)10\r\n", + "

Number of logical qubits in the input quantum program

\n", + "\r\n", + "
\r\n", + "

We determine 30 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", + "\r\n", + "
T gates0\r\n", + "

Number of T gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.

\n", + "\r\n", + "
Rotation gates0\r\n", + "

Number of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.

\n", + "\r\n", + "
Rotation depth0\r\n", + "

Depth of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.

\n", + "\r\n", + "
CCZ gates29\r\n", + "

Number of CCZ-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCZ gates.

\n", + "\r\n", + "
CCiX gates0\r\n", + "

Number of CCiX-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCiX gates, which applies \\(-iX\\) controlled on two control qubits [1212.5069].

\n", + "\r\n", + "
Measurement operations0\r\n", + "

Number of single qubit measurements in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Assumed error budget\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Total error budget1.00e-3\r\n", + "

Total error budget for the algorithm

\n", + "\r\n", + "
\r\n", + "

The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget \\(\\epsilon = \\epsilon_{\\log} + \\epsilon_{\\rm dis} + \\epsilon_{\\rm syn}\\) is uniformly distributed and applies to errors \\(\\epsilon_{\\log}\\) to implement logical qubits, an error budget \\(\\epsilon_{\\rm dis}\\) to produce T states through distillation, and an error budget \\(\\epsilon_{\\rm syn}\\) to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets \\(\\epsilon_{\\rm dis}\\) and \\(\\epsilon_{\\rm syn}\\) are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.

\n", + "\r\n", + "
Logical error probability5.00e-4\r\n", + "

Probability of at least one logical error

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
T distillation error probability5.00e-4\r\n", + "

Probability of at least one faulty T distillation

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
Rotation synthesis error probability0.00e0\r\n", + "

Probability of at least one failed rotation synthesis

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Physical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Qubit namequbit_gate_ns_e3\r\n", + "

Some descriptive name for the qubit model

\n", + "\r\n", + "
\r\n", + "

You can load pre-defined qubit parameters by using the names qubit_gate_ns_e3, qubit_gate_ns_e4, qubit_gate_us_e3, qubit_gate_us_e4, qubit_maj_ns_e4, or qubit_maj_ns_e6. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).

\n", + "\r\n", + "
Instruction setGateBased\r\n", + "

Underlying qubit technology (gate-based or Majorana)

\n", + "\r\n", + "
\r\n", + "

When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either gate-based or Majorana. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.

\n", + "\r\n", + "
Single-qubit measurement time100 ns\r\n", + "

Operation time for single-qubit measurement (t_meas) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.

\n", + "\r\n", + "
Single-qubit gate time50 ns\r\n", + "

Operation time for single-qubit gate (t_gate) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.

\n", + "\r\n", + "
Two-qubit gate time50 ns\r\n", + "

Operation time for two-qubit gate in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.

\n", + "\r\n", + "
T gate time50 ns\r\n", + "

Operation time for a T gate

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to execute a T gate.

\n", + "\r\n", + "
Single-qubit measurement error rate0.001\r\n", + "

Error rate for single-qubit measurement

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit measurement in the Pauli basis may fail.

\n", + "\r\n", + "
Single-qubit error rate0.001\r\n", + "

Error rate for single-qubit Clifford gate (p)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.

\n", + "\r\n", + "
Two-qubit error rate0.001\r\n", + "

Error rate for two-qubit Clifford gate

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.

\n", + "\r\n", + "
T gate error rate0.001\r\n", + "

Error rate to prepare single-qubit T state or apply a T gate (p_T)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which executing a single T gate may fail.

\n", + "\r\n", + "
\n", + "
\r\n", + " Assumptions\r\n", + "
    \n", + "

  • More details on the following lists of assumptions can be found in the paper Accessing requirements for scaling quantum computers and their applications.

    \n", + "
    • \n", + "

  • Uniform independent physical noise. We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.

    \n", + "
    • \n", + "

  • Efficient classical computation. We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.

    \n", + "
    • \n", + "

  • Extraction circuits for planar quantum ISA. We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).

    \n", + "
    • \n", + "

  • Uniform independent logical noise. We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.

    \n", + "
    • \n", + "

  • Negligible Clifford costs for synthesis. We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.

    \n", + "
    • \n", + "

  • Smooth magic state consumption rate. We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.

    \n", + "
    • \n", + "
\n" + ], + "text/plain": [ + "{'errorBudget': {'logical': 0.0005, 'rotations': 0.0, 'tstates': 0.0005},\n", + " 'jobParams': {'errorBudget': 0.001,\n", + " 'qecScheme': {'crossingPrefactor': 0.03,\n", + " 'errorCorrectionThreshold': 0.01,\n", + " 'logicalCycleTime': '(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance',\n", + " 'name': 'surface_code',\n", + " 'physicalQubitsPerLogicalQubit': '2 * codeDistance * codeDistance'},\n", + " 'qubitParams': {'instructionSet': 'GateBased',\n", + " 'name': 'qubit_gate_ns_e3',\n", + " 'oneQubitGateErrorRate': 0.001,\n", + " 'oneQubitGateTime': '50 ns',\n", + " 'oneQubitMeasurementErrorRate': 0.001,\n", + " 'oneQubitMeasurementTime': '100 ns',\n", + " 'tGateErrorRate': 0.001,\n", + " 'tGateTime': '50 ns',\n", + " 'twoQubitGateErrorRate': 0.001,\n", + " 'twoQubitGateTime': '50 ns'}},\n", + " 'logicalCounts': {'ccixCount': 0,\n", + " 'cczCount': 29,\n", + " 'measurementCount': 0,\n", + " 'numQubits': 10,\n", + " 'rotationCount': 0,\n", + " 'rotationDepth': 0,\n", + " 'tCount': 0},\n", + " 'logicalQubit': {'codeDistance': 11,\n", + " 'logicalCycleTime': 4400.0,\n", + " 'logicalErrorRate': 3.000000000000002e-08,\n", + " 'physicalQubits': 242},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 87,\n", + " 'algorithmicLogicalQubits': 30,\n", + " 'cliffordErrorRate': 0.001,\n", + " 'logicalDepth': 87,\n", + " 'numTfactories': 15,\n", + " 'numTfactoryRuns': 8,\n", + " 'numTsPerRotation': None,\n", + " 'numTstates': 116,\n", + " 'physicalQubitsForAlgorithm': 7260,\n", + " 'physicalQubitsForTfactories': 97200,\n", + " 'requiredLogicalQubitErrorRate': 1.9157088122605365e-07,\n", + " 'requiredLogicalTstateErrorRate': 4.310344827586207e-06},\n", + " 'physicalQubits': 104460,\n", + " 'runtime': 382800},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", + " 'errorBudget': '1.00e-3',\n", + " 'errorBudgetLogical': '5.00e-4',\n", + " 'errorBudgetRotations': '0.00e0',\n", + " 'errorBudgetTstates': '5.00e-4',\n", + " 'logicalCycleTime': '4us 400ns',\n", + " 'logicalErrorRate': '3.00e-8',\n", + " 'numTsPerRotation': 'No rotations in algorithm',\n", + " 'numUnitsPerRound': '2',\n", + " 'physicalQubitsForTfactoriesPercentage': '93.05 %',\n", + " 'physicalQubitsPerRound': '6480',\n", + " 'requiredLogicalQubitErrorRate': '1.92e-7',\n", + " 'requiredLogicalTstateErrorRate': '4.31e-6',\n", + " 'runtime': '382us 800ns',\n", + " 'tfactoryRuntime': '46us 800ns',\n", + " 'tfactoryRuntimePerRound': '46us 800ns',\n", + " 'tstateLogicalErrorRate': '2.17e-6',\n", + " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", + " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", + " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", + " '**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.',\n", + " '**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).',\n", + " '**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.',\n", + " '**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.',\n", + " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", + " 'groups': [{'alwaysVisible': True,\n", + " 'entries': [{'description': 'Number of physical qubits',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 7260 physical qubits to implement the algorithm logic, and 97200 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'physicalCounts/physicalQubits'},\n", + " {'description': 'Total runtime',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 87 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/runtime'}],\n", + " 'title': 'Physical resource estimates'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 10$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 30$ logical qubits.',\n", + " 'label': 'Logical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", + " {'description': 'Number of logical cycles for the algorithm',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 0 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 29 CCZ and 0 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'label': 'Algorithmic depth',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", + " {'description': 'Number of logical cycles performed',\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 87. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'label': 'Logical depth',\n", + " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", + " {'description': 'Number of T states consumed by the algorithm',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 29 CCZ and 0 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'label': 'Number of T states',\n", + " 'path': 'physicalCounts/breakdown/numTstates'},\n", + " {'description': \"Number of T factories capable of producing the demanded 116 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 15 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{116\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 382us 800ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " 'label': 'Number of T factories',\n", + " 'path': 'physicalCounts/breakdown/numTfactories'},\n", + " {'description': 'Number of times all T factories are invoked',\n", + " 'explanation': 'In order to prepare the 116 T states, the 15 copies of the T factory are repeatedly invoked 8 times.',\n", + " 'label': 'Number of T factory invocations',\n", + " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", + " {'description': 'Number of physical qubits for the algorithm after layout',\n", + " 'explanation': 'The 7260 are the product of the 30 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.',\n", + " 'label': 'Physical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", + " {'description': 'Number of physical qubits for the T factories',\n", + " 'explanation': 'Each T factory requires 6480 physical qubits and we run 15 in parallel, therefore we need $97200 = 6480 \\\\cdot 15$ qubits.',\n", + " 'label': 'Physical T factory qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", + " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 30 logical qubits and the total cycle count 87.',\n", + " 'label': 'Required logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", + " {'description': 'The minimum T state error rate required for distilled T states',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 116.',\n", + " 'label': 'Required logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", + " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", + " 'explanation': 'The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.',\n", + " 'label': 'Number of T states per rotation',\n", + " 'path': 'physicalCountsFormatted/numTsPerRotation'}],\n", + " 'title': 'Resource estimates breakdown'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Name of QEC scheme',\n", + " 'explanation': 'You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.',\n", + " 'label': 'QEC scheme',\n", + " 'path': 'jobParams/qecScheme/name'},\n", + " {'description': 'Required code distance for error correction',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000019157088122605365)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'label': 'Code distance',\n", + " 'path': 'logicalQubit/codeDistance'},\n", + " {'description': 'Number of physical qubits per logical qubit',\n", + " 'explanation': 'The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'logicalQubit/physicalQubits'},\n", + " {'description': 'Duration of a logical cycle in nanoseconds',\n", + " 'explanation': 'The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.',\n", + " 'label': 'Logical cycle time',\n", + " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", + " {'description': 'Logical qubit error rate',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$',\n", + " 'label': 'Logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", + " {'description': 'Crossing prefactor used in QEC scheme',\n", + " 'explanation': 'The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.',\n", + " 'label': 'Crossing prefactor',\n", + " 'path': 'jobParams/qecScheme/crossingPrefactor'},\n", + " {'description': 'Error correction threshold used in QEC scheme',\n", + " 'explanation': 'The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.',\n", + " 'label': 'Error correction threshold',\n", + " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", + " {'description': 'QEC scheme formula used to compute logical cycle time',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 4us 400ns.',\n", + " 'label': 'Logical cycle time formula',\n", + " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", + " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 242.',\n", + " 'label': 'Physical qubits formula',\n", + " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", + " 'title': 'Logical qubit parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of physical qubits for a single T factory',\n", + " 'explanation': 'This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'tfactory/physicalQubits'},\n", + " {'description': 'Runtime of a single T factory',\n", + " 'explanation': 'The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", + " {'description': 'Number of output T states produced in a single run of T factory',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.',\n", + " 'label': 'Number of output T states per run',\n", + " 'path': 'tfactory/numTstates'},\n", + " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", + " 'explanation': 'This value includes the physical input T states of all copies of the distillation unit in the first round.',\n", + " 'label': 'Number of input T states per run',\n", + " 'path': 'tfactory/numInputTstates'},\n", + " {'description': 'The number of distillation rounds',\n", + " 'explanation': 'This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.',\n", + " 'label': 'Distillation rounds',\n", + " 'path': 'tfactory/numRounds'},\n", + " {'description': 'The number of units in each round of distillation',\n", + " 'explanation': 'This is the number of copies for the distillation units per round.',\n", + " 'label': 'Distillation units per round',\n", + " 'path': 'physicalCountsFormatted/numUnitsPerRound'},\n", + " {'description': 'The types of distillation units',\n", + " 'explanation': 'These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.',\n", + " 'label': 'Distillation units',\n", + " 'path': 'physicalCountsFormatted/unitNamePerRound'},\n", + " {'description': 'The code distance in each round of distillation',\n", + " 'explanation': 'This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.',\n", + " 'label': 'Distillation code distances',\n", + " 'path': 'physicalCountsFormatted/codeDistancePerRound'},\n", + " {'description': 'The number of physical qubits used in each round of distillation',\n", + " 'explanation': 'The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.',\n", + " 'label': 'Number of physical qubits per round',\n", + " 'path': 'physicalCountsFormatted/physicalQubitsPerRound'},\n", + " {'description': 'The runtime of each distillation round',\n", + " 'explanation': 'The runtime of the T factory is the sum of the runtimes in all rounds.',\n", + " 'label': 'Runtime per round',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", + " {'description': 'Logical T state error rate',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 4.31e-6.',\n", + " 'label': 'Logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", + " 'title': 'T factory parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", + " 'explanation': 'We determine 30 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'label': 'Logical qubits (pre-layout)',\n", + " 'path': 'logicalCounts/numQubits'},\n", + " {'description': 'Number of T gates in the input quantum program',\n", + " 'explanation': 'This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.',\n", + " 'label': 'T gates',\n", + " 'path': 'logicalCounts/tCount'},\n", + " {'description': 'Number of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.',\n", + " 'label': 'Rotation gates',\n", + " 'path': 'logicalCounts/rotationCount'},\n", + " {'description': 'Depth of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.',\n", + " 'label': 'Rotation depth',\n", + " 'path': 'logicalCounts/rotationDepth'},\n", + " {'description': 'Number of CCZ-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCZ gates.',\n", + " 'label': 'CCZ gates',\n", + " 'path': 'logicalCounts/cczCount'},\n", + " {'description': 'Number of CCiX-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].',\n", + " 'label': 'CCiX gates',\n", + " 'path': 'logicalCounts/ccixCount'},\n", + " {'description': 'Number of single qubit measurements in the input quantum program',\n", + " 'explanation': 'This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.',\n", + " 'label': 'Measurement operations',\n", + " 'path': 'logicalCounts/measurementCount'}],\n", + " 'title': 'Pre-layout logical resources'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Total error budget for the algorithm',\n", + " 'explanation': \"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\n", + " 'label': 'Total error budget',\n", + " 'path': 'physicalCountsFormatted/errorBudget'},\n", + " {'description': 'Probability of at least one logical error',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'Logical error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetLogical'},\n", + " {'description': 'Probability of at least one faulty T distillation',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'T distillation error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetTstates'},\n", + " {'description': 'Probability of at least one failed rotation synthesis',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3.',\n", + " 'label': 'Rotation synthesis error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetRotations'}],\n", + " 'title': 'Assumed error budget'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Some descriptive name for the qubit model',\n", + " 'explanation': 'You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).',\n", + " 'label': 'Qubit name',\n", + " 'path': 'jobParams/qubitParams/name'},\n", + " {'description': 'Underlying qubit technology (gate-based or Majorana)',\n", + " 'explanation': 'When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.',\n", + " 'label': 'Instruction set',\n", + " 'path': 'jobParams/qubitParams/instructionSet'},\n", + " {'description': 'Operation time for single-qubit measurement (t_meas) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.',\n", + " 'label': 'Single-qubit measurement time',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementTime'},\n", + " {'description': 'Operation time for single-qubit gate (t_gate) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.',\n", + " 'label': 'Single-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateTime'},\n", + " {'description': 'Operation time for two-qubit gate in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.',\n", + " 'label': 'Two-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateTime'},\n", + " {'description': 'Operation time for a T gate',\n", + " 'explanation': 'This is the operation time in nanoseconds to execute a T gate.',\n", + " 'label': 'T gate time',\n", + " 'path': 'jobParams/qubitParams/tGateTime'},\n", + " {'description': 'Error rate for single-qubit measurement',\n", + " 'explanation': 'This is the probability in which a single-qubit measurement in the Pauli basis may fail.',\n", + " 'label': 'Single-qubit measurement error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementErrorRate'},\n", + " {'description': 'Error rate for single-qubit Clifford gate (p)',\n", + " 'explanation': 'This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.',\n", + " 'label': 'Single-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateErrorRate'},\n", + " {'description': 'Error rate for two-qubit Clifford gate',\n", + " 'explanation': 'This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.',\n", + " 'label': 'Two-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateErrorRate'},\n", + " {'description': 'Error rate to prepare single-qubit T state or apply a T gate (p_T)',\n", + " 'explanation': 'This is the probability in which executing a single T gate may fail.',\n", + " 'label': 'T gate error rate',\n", + " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", + " 'title': 'Physical qubit parameters'}]},\n", + " 'status': 'success',\n", + " 'tfactory': {'codeDistancePerRound': [9],\n", + " 'logicalErrorRate': 2.165000000000001e-06,\n", + " 'numInputTstates': 30,\n", + " 'numRounds': 1,\n", + " 'numTstates': 1,\n", + " 'numUnitsPerRound': [2],\n", + " 'physicalQubits': 6480,\n", + " 'physicalQubitsPerRound': [6480],\n", + " 'runtime': 46800.0,\n", + " 'runtimePerRound': [46800.0],\n", + " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" + ] + }, + "execution_count": 47, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", + "# result = qsharp.azure.output(\"...\")\n", + "result" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# The function that extracts the relevant resource information from the resource estimation job results and produces your absolute score.\n", + "def evaluate_results(res) : \n", + " width = res['physicalCounts']['breakdown']['algorithmicLogicalQubits']\n", + " depth = res['physicalCounts']['breakdown']['algorithmicLogicalDepth']\n", + " print(f\"Logical algorithmic qubits = {width}\")\n", + " print(f\"Algorithmic depth = {depth}\")\n", + " print(f\"Score = {width * depth}\")\n", + " return width * depth\n" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Logical algorithmic qubits = 30\n", + "Algorithmic depth = 87\n", + "Score = 2610\n" + ] + }, + { + "data": { + "text/plain": [ + "2610" + ] + }, + "execution_count": 49, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "evaluate_results(result)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernel_info": { + "name": "python3" + }, + "kernelspec": { + "display_name": "Python 3 [Q#]", + "language": "python", + "name": "python3_qsharp_b54crn" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.10" + }, + "nteract": { + "version": "nteract-front-end@1.0.0" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/.ipynb_checkpoints/iQuHack-challenge-2023-task5-checkpoint.ipynb b/.ipynb_checkpoints/iQuHack-challenge-2023-task5-checkpoint.ipynb new file mode 100644 index 0000000..85e5038 --- /dev/null +++ b/.ipynb_checkpoints/iQuHack-challenge-2023-task5-checkpoint.ipynb @@ -0,0 +1,440 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "# MIT iQuHack Microsoft Challenge: Optimizing Quantum Oracles, Task 5\n", + "\n", + "To work on this task,\n", + "1. Use the notebook for this task. Each of the notebooks in the repository has the code of the corresponding task.\n", + "2. Update your team name and Slack ID variables in the next code cell (you can use different Slack IDs for different tasks if different team members work on them, but make sure to use the same team name throughout the Hackathon). Do not change the task variable!\n", + "3. Work on your task in the cell that contains operation `Task5`! Your goal is to rewrite the code so that it maintains its correctness, but requires as few resources as possible. See `evaluate_results` function for details on how your absolute score for the task is calculated.\n", + "4. Submit your task using qBraid. Use the Share Notebook feature on qBraid (See File > Share Notebook) and enter the email rickyyoung@qbraid.com. Once you click submit, if the share notebook feature works correctly, it should show that you receive no errors and the email you entered will disappear. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "Log in to Azure (once per session, don't need to do it if running from Azure workspace)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "!az login" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 1. Write the code" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Run this code cell to import the modules required to work with Q# and Azure\n", + "import qsharp\n", + "from qsharp import azure" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "teamname=\"msft_is_the_best\" # Update this field with your team name\n", + "task=[\"task5\"]\n", + "slack_id=\"myslackid\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# You don't need to run this cell, it defines Q# operations as Python types to keep IntelliSense happy\n", + "Task5_DumpMachineWrapper : qsharp.QSharpCallable = None\n", + "Task5_ResourceEstimationWrapper : qsharp.QSharpCallable = None" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "**The complete code for Task 5 should be in this cell.** \n", + "This cell can include additional open statements and helper operations and functions if your solution needs them. \n", + "If you define helper operations in other cells, they will not be picked up by the grader!" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "open Microsoft.Quantum.Canon;\n", + "open Microsoft.Quantum.Diagnostics;\n", + "\n", + "// Task 5. \n", + "// (input will contain 6 qubits)\n", + "operation Task5(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " for i in [0, 9, 18, 21, 27, 36, 42, 45, 54, 63] {\n", + " ControlledOnInt(i, X)(input, target);\n", + " }\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "// Wrapper operation that allows you to observe the effects of the marking oracle by running it on a simulator.\n", + "operation Task5_DumpMachineWrapper() : Unit {\n", + " let N = 6;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " // Prepare an equal superposition of all input states in the input register.\n", + " ApplyToEach(H, input);\n", + " // Apply the oracle.\n", + " Task5(input, target);\n", + " // Print the state of the system after the oracle application.\n", + " DumpMachine();\n", + " ResetAll(input + [target]);\n", + "}\n", + "\n", + "// Wrapper operation that allows to run resource estimation for the task.\n", + "// This operation only allocates the qubits and applies the oracle once, not using any additional gates or measurements.\n", + "operation Task5_ResourceEstimationWrapper() : Unit {\n", + " let N = 6;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " Task5(input, target);\n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 2. Run the code on a simulator to see what it does\n", + "You can also write your own code to explore the effects of the oracle (for example, applying it to different basis states and measuring the results)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Note that in the output of this cell the target qubit corresponds to the rightmost bit\n", + "qsharp.config[\"dump.basisStateLabelingConvention\"]=\"Bitstring\"\n", + "qsharp.config[\"dump.phaseDisplayStyle\"]=\"None\"\n", + "# Uncomment the following line if you want to see only the entries with non-zero amplitudes\n", + "qsharp.config[\"dump.truncateSmallAmplitudes\"]=True\n", + "Task5_DumpMachineWrapper.simulate()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 3. Evaluate the code using resource estimation" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", + "# If you're using this notebook in qBraid, keep it\n", + "qsharp.azure.connect(\n", + " resourceId=\"...\",\n", + " location=\"...\",\n", + " credential=\"CLI\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "qsharp.azure.target(\"microsoft.estimator\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", + "result = qsharp.azure.execute(Task5_ResourceEstimationWrapper, jobName=\"RE for the task 5\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", + "# result = qsharp.azure.output(\"...\")\n", + "result" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# The function that extracts the relevant resource information from the resource estimation job results and produces your absolute score.\n", + "def evaluate_results(res) : \n", + " width = res['physicalCounts']['breakdown']['algorithmicLogicalQubits']\n", + " depth = res['physicalCounts']['breakdown']['algorithmicLogicalDepth']\n", + " print(f\"Logical algorithmic qubits = {width}\")\n", + " print(f\"Algorithmic depth = {depth}\")\n", + " print(f\"Score = {width * depth}\")\n", + " return width * depth\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "evaluate_results(result)" + ] + } + ], + "metadata": { + "kernel_info": { + "name": "python3" + }, + "kernelspec": { + "display_name": "Python 3 [Default]", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.10" + }, + "nteract": { + "version": "nteract-front-end@1.0.0" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/.ipynb_checkpoints/iQuHack-challenge-2023-task6-checkpoint.ipynb b/.ipynb_checkpoints/iQuHack-challenge-2023-task6-checkpoint.ipynb new file mode 100644 index 0000000..4d2f2c8 --- /dev/null +++ b/.ipynb_checkpoints/iQuHack-challenge-2023-task6-checkpoint.ipynb @@ -0,0 +1,440 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "# MIT iQuHack Microsoft Challenge: Optimizing Quantum Oracles, Task 6\n", + "\n", + "To work on this task,\n", + "1. Use the notebook for this task. Each of the notebooks in the repository has the code of the corresponding task.\n", + "2. Update your team name and Slack ID variables in the next code cell (you can use different Slack IDs for different tasks if different team members work on them, but make sure to use the same team name throughout the Hackathon). Do not change the task variable!\n", + "3. Work on your task in the cell that contains operation `Task6`! Your goal is to rewrite the code so that it maintains its correctness, but requires as few resources as possible. See `evaluate_results` function for details on how your absolute score for the task is calculated.\n", + "4. Submit your task using qBraid. Use the Share Notebook feature on qBraid (See File > Share Notebook) and enter the email rickyyoung@qbraid.com. Once you click submit, if the share notebook feature works correctly, it should show that you receive no errors and the email you entered will disappear. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "Log in to Azure (once per session, don't need to do it if running from Azure workspace)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "!az login" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 1. Write the code" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Run this code cell to import the modules required to work with Q# and Azure\n", + "import qsharp\n", + "from qsharp import azure" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "teamname=\"msft_is_the_best\" # Update this field with your team name\n", + "task=[\"task6\"]\n", + "slack_id=\"myslackid\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# You don't need to run this cell, it defines Q# operations as Python types to keep IntelliSense happy\n", + "Task6_DumpMachineWrapper : qsharp.QSharpCallable = None\n", + "Task6_ResourceEstimationWrapper : qsharp.QSharpCallable = None" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "**The complete code for Task 6 should be in this cell.** \n", + "This cell can include additional open statements and helper operations and functions if your solution needs them. \n", + "If you define helper operations in other cells, they will not be picked up by the grader!" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "open Microsoft.Quantum.Canon;\n", + "open Microsoft.Quantum.Diagnostics;\n", + "\n", + "// Task 6. \n", + "// (input will contain 8 qubits)\n", + "operation Task6(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " for i in [144, 145, 148, 149, 152, 153, 156, 157, 208, 209, 212, 213, 216, 217, 220, 221] {\n", + " ControlledOnInt(i, X)(input, target);\n", + " }\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "// Wrapper operation that allows you to observe the effects of the marking oracle by running it on a simulator.\n", + "operation Task6_DumpMachineWrapper() : Unit {\n", + " let N = 8;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " // Prepare an equal superposition of all input states in the input register.\n", + " ApplyToEach(H, input);\n", + " // Apply the oracle.\n", + " Task6(input, target);\n", + " // Print the state of the system after the oracle application.\n", + " DumpMachine();\n", + " ResetAll(input + [target]);\n", + "}\n", + "\n", + "// Wrapper operation that allows to run resource estimation for the task.\n", + "// This operation only allocates the qubits and applies the oracle once, not using any additional gates or measurements.\n", + "operation Task6_ResourceEstimationWrapper() : Unit {\n", + " let N = 8;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " Task6(input, target);\n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 2. Run the code on a simulator to see what it does\n", + "You can also write your own code to explore the effects of the oracle (for example, applying it to different basis states and measuring the results)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Note that in the output of this cell the target qubit corresponds to the rightmost bit\n", + "qsharp.config[\"dump.basisStateLabelingConvention\"]=\"Bitstring\"\n", + "qsharp.config[\"dump.phaseDisplayStyle\"]=\"None\"\n", + "# Uncomment the following line if you want to see only the entries with non-zero amplitudes\n", + "qsharp.config[\"dump.truncateSmallAmplitudes\"]=True\n", + "Task6_DumpMachineWrapper.simulate()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 3. Evaluate the code using resource estimation" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", + "# If you're using this notebook in qBraid, keep it\n", + "qsharp.azure.connect(\n", + " resourceId=\"...\",\n", + " location=\"...\",\n", + " credential=\"CLI\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "qsharp.azure.target(\"microsoft.estimator\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", + "result = qsharp.azure.execute(Task6_ResourceEstimationWrapper, jobName=\"RE for the task 6\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", + "# result = qsharp.azure.output(\"...\")\n", + "result" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# The function that extracts the relevant resource information from the resource estimation job results and produces your absolute score.\n", + "def evaluate_results(res) : \n", + " width = res['physicalCounts']['breakdown']['algorithmicLogicalQubits']\n", + " depth = res['physicalCounts']['breakdown']['algorithmicLogicalDepth']\n", + " print(f\"Logical algorithmic qubits = {width}\")\n", + " print(f\"Algorithmic depth = {depth}\")\n", + " print(f\"Score = {width * depth}\")\n", + " return width * depth\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "evaluate_results(result)" + ] + } + ], + "metadata": { + "kernel_info": { + "name": "python3" + }, + "kernelspec": { + "display_name": "Python 3 [Default]", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.10" + }, + "nteract": { + "version": "nteract-front-end@1.0.0" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/.ipynb_checkpoints/iQuHack-challenge-2023-task7-checkpoint.ipynb b/.ipynb_checkpoints/iQuHack-challenge-2023-task7-checkpoint.ipynb new file mode 100644 index 0000000..2670c29 --- /dev/null +++ b/.ipynb_checkpoints/iQuHack-challenge-2023-task7-checkpoint.ipynb @@ -0,0 +1,440 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "# MIT iQuHack Microsoft Challenge: Optimizing Quantum Oracles, Task 7\n", + "\n", + "To work on this task,\n", + "1. Use the notebook for this task. Each of the notebooks in the repository has the code of the corresponding task.\n", + "2. Update your team name and Slack ID variables in the next code cell (you can use different Slack IDs for different tasks if different team members work on them, but make sure to use the same team name throughout the Hackathon). Do not change the task variable!\n", + "3. Work on your task in the cell that contains operation `Task7`! Your goal is to rewrite the code so that it maintains its correctness, but requires as few resources as possible. See `evaluate_results` function for details on how your absolute score for the task is calculated.\n", + "4. Submit your task using qBraid. Use the Share Notebook feature on qBraid (See File > Share Notebook) and enter the email rickyyoung@qbraid.com. Once you click submit, if the share notebook feature works correctly, it should show that you receive no errors and the email you entered will disappear. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "Log in to Azure (once per session, don't need to do it if running from Azure workspace)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "!az login" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 1. Write the code" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Run this code cell to import the modules required to work with Q# and Azure\n", + "import qsharp\n", + "from qsharp import azure" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "teamname=\"msft_is_the_best\" # Update this field with your team name\n", + "task=[\"task7\"]\n", + "slack_id=\"myslackid\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# You don't need to run this cell, it defines Q# operations as Python types to keep IntelliSense happy\n", + "Task7_DumpMachineWrapper : qsharp.QSharpCallable = None\n", + "Task7_ResourceEstimationWrapper : qsharp.QSharpCallable = None" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "**The complete code for Task 7 should be in this cell.** \n", + "This cell can include additional open statements and helper operations and functions if your solution needs them. \n", + "If you define helper operations in other cells, they will not be picked up by the grader!" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "open Microsoft.Quantum.Canon;\n", + "open Microsoft.Quantum.Diagnostics;\n", + "\n", + "// Task 7. \n", + "// (input will contain 7 qubits)\n", + "operation Task7(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " for i in [9,18,19,25,36,37,38,39,41,50,51,57,72,73,74,75,76,77,78,79,82,83,89,100,101,102,103,105,114,115,121] {\n", + " ControlledOnInt(i, X)(input, target);\n", + " }\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "// Wrapper operation that allows you to observe the effects of the marking oracle by running it on a simulator.\n", + "operation Task7_DumpMachineWrapper() : Unit {\n", + " let N = 7;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " // Prepare an equal superposition of all input states in the input register.\n", + " ApplyToEach(H, input);\n", + " // Apply the oracle.\n", + " Task7(input, target);\n", + " // Print the state of the system after the oracle application.\n", + " DumpMachine();\n", + " ResetAll(input + [target]);\n", + "}\n", + "\n", + "// Wrapper operation that allows to run resource estimation for the task.\n", + "// This operation only allocates the qubits and applies the oracle once, not using any additional gates or measurements.\n", + "operation Task7_ResourceEstimationWrapper() : Unit {\n", + " let N = 7;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " Task7(input, target);\n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 2. Run the code on a simulator to see what it does\n", + "You can also write your own code to explore the effects of the oracle (for example, applying it to different basis states and measuring the results)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Note that in the output of this cell the target qubit corresponds to the rightmost bit\n", + "qsharp.config[\"dump.basisStateLabelingConvention\"]=\"Bitstring\"\n", + "qsharp.config[\"dump.phaseDisplayStyle\"]=\"None\"\n", + "# Uncomment the following line if you want to see only the entries with non-zero amplitudes\n", + "qsharp.config[\"dump.truncateSmallAmplitudes\"]=True\n", + "Task7_DumpMachineWrapper.simulate()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 3. Evaluate the code using resource estimation" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", + "# If you're using this notebook in qBraid, keep it\n", + "qsharp.azure.connect(\n", + " resourceId=\"...\",\n", + " location=\"...\",\n", + " credential=\"CLI\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "qsharp.azure.target(\"microsoft.estimator\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", + "result = qsharp.azure.execute(Task7_ResourceEstimationWrapper, jobName=\"RE for the task 7\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", + "# result = qsharp.azure.output(\"...\")\n", + "result" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# The function that extracts the relevant resource information from the resource estimation job results and produces your absolute score.\n", + "def evaluate_results(res) : \n", + " width = res['physicalCounts']['breakdown']['algorithmicLogicalQubits']\n", + " depth = res['physicalCounts']['breakdown']['algorithmicLogicalDepth']\n", + " print(f\"Logical algorithmic qubits = {width}\")\n", + " print(f\"Algorithmic depth = {depth}\")\n", + " print(f\"Score = {width * depth}\")\n", + " return width * depth\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "evaluate_results(result)" + ] + } + ], + "metadata": { + "kernel_info": { + "name": "python3" + }, + "kernelspec": { + "display_name": "Python 3 [Default]", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.10" + }, + "nteract": { + "version": "nteract-front-end@1.0.0" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/.ipynb_checkpoints/iQuHack-challenge-2023-task8-checkpoint.ipynb b/.ipynb_checkpoints/iQuHack-challenge-2023-task8-checkpoint.ipynb new file mode 100644 index 0000000..a84b05a --- /dev/null +++ b/.ipynb_checkpoints/iQuHack-challenge-2023-task8-checkpoint.ipynb @@ -0,0 +1,443 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "# MIT iQuHack Microsoft Challenge: Optimizing Quantum Oracles, Task 8\n", + "\n", + "To work on this task,\n", + "1. Use the notebook for this task. Each of the notebooks in the repository has the code of the corresponding task.\n", + "2. Update your team name and Slack ID variables in the next code cell (you can use different Slack IDs for different tasks if different team members work on them, but make sure to use the same team name throughout the Hackathon). Do not change the task variable!\n", + "3. Work on your task in the cell that contains operation `Task8`! Your goal is to rewrite the code so that it maintains its correctness, but requires as few resources as possible. See `evaluate_results` function for details on how your absolute score for the task is calculated.\n", + "4. Submit your task using qBraid. Use the Share Notebook feature on qBraid (See File > Share Notebook) and enter the email rickyyoung@qbraid.com. Once you click submit, if the share notebook feature works correctly, it should show that you receive no errors and the email you entered will disappear. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "Log in to Azure (once per session, don't need to do it if running from Azure workspace)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "!az login" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 1. Write the code" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Run this code cell to import the modules required to work with Q# and Azure\n", + "import qsharp\n", + "from qsharp import azure" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "teamname=\"msft_is_the_best\" # Update this field with your team name\n", + "task=[\"task8\"]\n", + "slack_id=\"myslackid\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# You don't need to run this cell, it defines Q# operations as Python types to keep IntelliSense happy\n", + "Task8_DumpMachineWrapper : qsharp.QSharpCallable = None\n", + "Task8_ResourceEstimationWrapper : qsharp.QSharpCallable = None" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "**The complete code for Task 8 should be in this cell.** \n", + "This cell can include additional open statements and helper operations and functions if your solution needs them. \n", + "If you define helper operations in other cells, they will not be picked up by the grader!" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "open Microsoft.Quantum.Canon;\n", + "open Microsoft.Quantum.Diagnostics;\n", + "\n", + "// Task 8. \n", + "// (input will contain 7 qubits)\n", + "operation Task8(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " for i in [15,23,27,29,30,31,39,43, 45,46,47,51,53,54,55,57, \n", + " 58,59,60,61,62,63,71,75, 77,78,79,83,85,86,87,89,\n", + " 90,91,92,93,94,95,99,101, 102,103,105,106,107,108,109,110,\n", + " 111,113,114,115,116,117,118,119, 120,121,122,123,124,125,126,127] {\n", + " ControlledOnInt(i, X)(input, target);\n", + " }\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "// Wrapper operation that allows you to observe the effects of the marking oracle by running it on a simulator.\n", + "operation Task8_DumpMachineWrapper() : Unit {\n", + " let N = 7;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " // Prepare an equal superposition of all input states in the input register.\n", + " ApplyToEach(H, input);\n", + " // Apply the oracle.\n", + " Task8(input, target);\n", + " // Print the state of the system after the oracle application.\n", + " DumpMachine();\n", + " ResetAll(input + [target]);\n", + "}\n", + "\n", + "// Wrapper operation that allows to run resource estimation for the task.\n", + "// This operation only allocates the qubits and applies the oracle once, not using any additional gates or measurements.\n", + "operation Task8_ResourceEstimationWrapper() : Unit {\n", + " let N = 7;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " Task8(input, target);\n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 2. Run the code on a simulator to see what it does\n", + "You can also write your own code to explore the effects of the oracle (for example, applying it to different basis states and measuring the results)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Note that in the output of this cell the target qubit corresponds to the rightmost bit\n", + "qsharp.config[\"dump.basisStateLabelingConvention\"]=\"Bitstring\"\n", + "qsharp.config[\"dump.phaseDisplayStyle\"]=\"None\"\n", + "# Uncomment the following line if you want to see only the entries with non-zero amplitudes\n", + "qsharp.config[\"dump.truncateSmallAmplitudes\"]=True\n", + "Task8_DumpMachineWrapper.simulate()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 3. Evaluate the code using resource estimation" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", + "# If you're using this notebook in qBraid, keep it\n", + "qsharp.azure.connect(\n", + " resourceId=\"...\",\n", + " location=\"...\",\n", + " credential=\"CLI\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "qsharp.azure.target(\"microsoft.estimator\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", + "result = qsharp.azure.execute(Task8_ResourceEstimationWrapper, jobName=\"RE for the task 8\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", + "# result = qsharp.azure.output(\"...\")\n", + "result" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# The function that extracts the relevant resource information from the resource estimation job results and produces your absolute score.\n", + "def evaluate_results(res) : \n", + " width = res['physicalCounts']['breakdown']['algorithmicLogicalQubits']\n", + " depth = res['physicalCounts']['breakdown']['algorithmicLogicalDepth']\n", + " print(f\"Logical algorithmic qubits = {width}\")\n", + " print(f\"Algorithmic depth = {depth}\")\n", + " print(f\"Score = {width * depth}\")\n", + " return width * depth\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "evaluate_results(result)" + ] + } + ], + "metadata": { + "kernel_info": { + "name": "python3" + }, + "kernelspec": { + "display_name": "Python 3 [Default]", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.10" + }, + "nteract": { + "version": "nteract-front-end@1.0.0" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/.ipynb_checkpoints/iQuHack-challenge-2023-task9-checkpoint.ipynb b/.ipynb_checkpoints/iQuHack-challenge-2023-task9-checkpoint.ipynb new file mode 100644 index 0000000..eea076e --- /dev/null +++ b/.ipynb_checkpoints/iQuHack-challenge-2023-task9-checkpoint.ipynb @@ -0,0 +1,440 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "# MIT iQuHack Microsoft Challenge: Optimizing Quantum Oracles, Task 9\n", + "\n", + "To work on this task,\n", + "1. Use the notebook for this task. Each of the notebooks in the repository has the code of the corresponding task.\n", + "2. Update your team name and Slack ID variables in the next code cell (you can use different Slack IDs for different tasks if different team members work on them, but make sure to use the same team name throughout the Hackathon). Do not change the task variable!\n", + "3. Work on your task in the cell that contains operation `Task9`! Your goal is to rewrite the code so that it maintains its correctness, but requires as few resources as possible. See `evaluate_results` function for details on how your absolute score for the task is calculated.\n", + "4. Submit your task using qBraid. Use the Share Notebook feature on qBraid (See File > Share Notebook) and enter the email rickyyoung@qbraid.com. Once you click submit, if the share notebook feature works correctly, it should show that you receive no errors and the email you entered will disappear. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "Log in to Azure (once per session, don't need to do it if running from Azure workspace)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "!az login" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 1. Write the code" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Run this code cell to import the modules required to work with Q# and Azure\n", + "import qsharp\n", + "from qsharp import azure" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "teamname=\"msft_is_the_best\" # Update this field with your team name\n", + "task=[\"task9\"]\n", + "slack_id=\"myslackid\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# You don't need to run this cell, it defines Q# operations as Python types to keep IntelliSense happy\n", + "Task9_DumpMachineWrapper : qsharp.QSharpCallable = None\n", + "Task9_ResourceEstimationWrapper : qsharp.QSharpCallable = None" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "**The complete code for Task 9 should be in this cell.** \n", + "This cell can include additional open statements and helper operations and functions if your solution needs them. \n", + "If you define helper operations in other cells, they will not be picked up by the grader!" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "open Microsoft.Quantum.Canon;\n", + "open Microsoft.Quantum.Diagnostics;\n", + "\n", + "// Task 9. \n", + "// (input will contain 8 qubits)\n", + "operation Task9(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " for i in [31,46,61,76,91,106,121,136,151,166,181,196,211,226,241] {\n", + " ControlledOnInt(i, X)(input, target);\n", + " }\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "// Wrapper operation that allows you to observe the effects of the marking oracle by running it on a simulator.\n", + "operation Task9_DumpMachineWrapper() : Unit {\n", + " let N = 8;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " // Prepare an equal superposition of all input states in the input register.\n", + " ApplyToEach(H, input);\n", + " // Apply the oracle.\n", + " Task9(input, target);\n", + " // Print the state of the system after the oracle application.\n", + " DumpMachine();\n", + " ResetAll(input + [target]);\n", + "}\n", + "\n", + "// Wrapper operation that allows to run resource estimation for the task.\n", + "// This operation only allocates the qubits and applies the oracle once, not using any additional gates or measurements.\n", + "operation Task9_ResourceEstimationWrapper() : Unit {\n", + " let N = 8;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " Task9(input, target);\n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 2. Run the code on a simulator to see what it does\n", + "You can also write your own code to explore the effects of the oracle (for example, applying it to different basis states and measuring the results)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Note that in the output of this cell the target qubit corresponds to the rightmost bit\n", + "qsharp.config[\"dump.basisStateLabelingConvention\"]=\"Bitstring\"\n", + "qsharp.config[\"dump.phaseDisplayStyle\"]=\"None\"\n", + "# Uncomment the following line if you want to see only the entries with non-zero amplitudes\n", + "qsharp.config[\"dump.truncateSmallAmplitudes\"]=True\n", + "Task9_DumpMachineWrapper.simulate()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 3. Evaluate the code using resource estimation" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", + "# If you're using this notebook in qBraid, keep it\n", + "qsharp.azure.connect(\n", + " resourceId=\"...\",\n", + " location=\"...\",\n", + " credential=\"CLI\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "qsharp.azure.target(\"microsoft.estimator\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", + "result = qsharp.azure.execute(Task9_ResourceEstimationWrapper, jobName=\"RE for the task 9\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", + "# result = qsharp.azure.output(\"...\")\n", + "result" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# The function that extracts the relevant resource information from the resource estimation job results and produces your absolute score.\n", + "def evaluate_results(res) : \n", + " width = res['physicalCounts']['breakdown']['algorithmicLogicalQubits']\n", + " depth = res['physicalCounts']['breakdown']['algorithmicLogicalDepth']\n", + " print(f\"Logical algorithmic qubits = {width}\")\n", + " print(f\"Algorithmic depth = {depth}\")\n", + " print(f\"Score = {width * depth}\")\n", + " return width * depth\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "evaluate_results(result)" + ] + } + ], + "metadata": { + "kernel_info": { + "name": "python3" + }, + "kernelspec": { + "display_name": "Python 3 [Default]", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.10" + }, + "nteract": { + "version": "nteract-front-end@1.0.0" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/iQuHack-challenge-2023-task1.ipynb b/iQuHack-challenge-2023-task1.ipynb index 6042c2b..6899603 100644 --- a/iQuHack-challenge-2023-task1.ipynb +++ b/iQuHack-challenge-2023-task1.ipynb @@ -34,7 +34,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "collapsed": false, "jupyter": { @@ -47,7 +47,41 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\u001b[93mTo sign in, use a web browser to open the page https://microsoft.com/devicelogin and enter the code RGGYKHPB3 to authenticate.\u001b[0m\n", + "[\n", + " {\n", + " \"cloudName\": \"AzureCloud\",\n", + " \"homeTenantId\": \"b4e518fe-3bdc-4371-a4be-7f3d83d7acbd\",\n", + " \"id\": \"7fc54e95-14cf-4a6f-b50e-d6155c241309\",\n", + " \"isDefault\": true,\n", + " \"managedByTenants\": [\n", + " {\n", + " \"tenantId\": \"d0ecd01b-d782-448e-bae0-c3cad0e0543a\"\n", + " },\n", + " {\n", + " \"tenantId\": \"94c4857e-1130-4ab8-8eac-069b40c9db20\"\n", + " },\n", + " {\n", + " \"tenantId\": \"f702a9dc-ae48-4dc7-8f0a-8155a6dfa4e5\"\n", + " }\n", + " ],\n", + " \"name\": \"Azure subscription 1\",\n", + " \"state\": \"Enabled\",\n", + " \"tenantId\": \"b4e518fe-3bdc-4371-a4be-7f3d83d7acbd\",\n", + " \"user\": {\n", + " \"name\": \"hachall@hotmail.com\",\n", + " \"type\": \"user\"\n", + " }\n", + " }\n", + "]\n" + ] + } + ], "source": [ "!az login" ] @@ -67,7 +101,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "collapsed": false, "jupyter": { @@ -90,6 +124,13 @@ { "cell_type": "code", "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 2, "metadata": { "collapsed": false, "jupyter": { @@ -104,14 +145,14 @@ }, "outputs": [], "source": [ - "teamname=\"msft_is_the_best\" # Update this field with your team name\n", - "task=[\"task1\"]\n", - "slack_id=\"myslackid\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + "teamname=\"schrodingers-duck\" # Update this field with your team name\n", + "task=[\"task6\"]\n", + "slack_id=\"U04L3SFUCQ2\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": { "collapsed": false, "jupyter": { @@ -148,7 +189,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 19, "metadata": { "collapsed": false, "jupyter": { @@ -169,10 +210,11 @@ "%%qsharp\n", "open Microsoft.Quantum.Canon;\n", "open Microsoft.Quantum.Diagnostics;\n", + "open Microsoft.Quantum.Arrays;\n", "\n", "// Task 1. Warm up with simple bit manipulation\n", "// (input will contain 3 qubits)\n", - "operation Task1(input : Qubit[], target : Qubit) : Unit is Adj {\n", + "operation original(input : Qubit[], target : Qubit) : Unit is Adj {\n", " let N = Length(input);\n", " use aux = Qubit[N - 1];\n", " within {\n", @@ -183,12 +225,37 @@ " } apply {\n", " Controlled X(aux, target);\n", " }\n", + "}\n", + "\n", + "operation Task1(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " CNOT(input[1], input[0]);\n", + " CNOT(input[1], input[2]);\n", + " CCNOT(input[0], input[2], target);\n", + " CNOT(input[1], input[0]);\n", + " CNOT(input[1], input[2]);\n", + "}\n", + "\n", + "operation QubitArrayWrapperOperation (op : ((Qubit[], Qubit) => Unit is Adj), qs : Qubit[]) : Unit is Adj { \n", + " op(Most(qs), Tail(qs));\n", + "}\n", + "\n", + "operation TestCompoundGate () : Unit {\n", + " AssertOperationsEqualReferenced(3+1, QubitArrayWrapperOperation(Task1, _), QubitArrayWrapperOperation (original, _));\n", "}" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 20, + "metadata": {}, + "outputs": [], + "source": [ + "TestCompoundGate();" + ] + }, + { + "cell_type": "code", + "execution_count": 21, "metadata": { "collapsed": false, "jupyter": { @@ -245,7 +312,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 22, "metadata": { "collapsed": false, "jupyter": { @@ -258,13 +325,260 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1,2,3],\"n_qubits\":4,\"amplitudes\":{\"0\":{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},\"1\":{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},\"2\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"3\":{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},\"4\":{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},\"5\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"6\":{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},\"7\":{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},\"8\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"9\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"10\":{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},\"11\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"12\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"13\":{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},\"14\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"15\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0}}}", + "text/html": [ + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + "
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" + ], + "text/plain": [ + "|0000⟩\t0.35355339059327384 + 0𝑖\n", + "|0010⟩\t0.35355339059327384 + 0𝑖\n", + "|0101⟩\t0.35355339059327384 + 0𝑖\n", + "|0110⟩\t0.35355339059327384 + 0𝑖\n", + "|1000⟩\t0.35355339059327384 + 0𝑖\n", + "|1011⟩\t0.35355339059327384 + 0𝑖\n", + "|1100⟩\t0.35355339059327384 + 0𝑖\n", + "|1110⟩\t0.35355339059327384 + 0𝑖" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "()" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# Note that in the output of this cell the target qubit corresponds to the rightmost bit\n", "qsharp.config[\"dump.basisStateLabelingConvention\"]=\"Bitstring\"\n", "qsharp.config[\"dump.phaseDisplayStyle\"]=\"None\"\n", "# Uncomment the following line if you want to see only the entries with non-zero amplitudes\n", - "# qsharp.config[\"dump.truncateSmallAmplitudes\"]=True\n", + "qsharp.config[\"dump.truncateSmallAmplitudes\"]=True\n", "Task1_DumpMachineWrapper.simulate()" ] }, @@ -283,7 +597,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 23, "metadata": { "collapsed": false, "jupyter": { @@ -296,19 +610,68 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "\"Connecting to Azure Quantum...\"", + "text/plain": [ + "Connecting to Azure Quantum..." + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Connected to Azure Quantum workspace azure-q in location uksouth.\n" + ] + }, + { + "data": { + "text/plain": [ + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 165633},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 398028},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 2},\n", + " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 180},\n", + " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 180},\n", + " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.qpu.aspen-m-2', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", "# If you're using this notebook in qBraid, keep it\n", "qsharp.azure.connect(\n", - " resourceId=\"...\",\n", - " location=\"...\",\n", + " resourceId=\"/subscriptions/7fc54e95-14cf-4a6f-b50e-d6155c241309/resourceGroups/AzureQuantum/providers/Microsoft.Quantum/Workspaces/azure-q\",\n", + " location=\"UK South\",\n", " credential=\"CLI\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 24, "metadata": { "collapsed": false, "jupyter": { @@ -321,14 +684,33 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loading package Microsoft.Quantum.Providers.Core and dependencies...\n", + "Active target is now microsoft.estimator\n" + ] + }, + { + "data": { + "text/plain": [ + "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "qsharp.azure.target(\"microsoft.estimator\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 25, "metadata": { "collapsed": false, "jupyter": { @@ -341,7 +723,21 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Submitting Task1_ResourceEstimationWrapper to target microsoft.estimator...\n", + "Job successfully submitted.\n", + " Job name: RE for the task 1\n", + " Job ID: 8dfa4a14-f799-49f9-98b5-d62cd808a86f\n", + "Waiting up to 30 seconds for Azure Quantum job to complete...\n", + "[9:45:41 AM] Current job status: Executing\n", + "[9:45:46 AM] Current job status: Succeeded\n" + ] + } + ], "source": [ "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", "result = qsharp.azure.execute(Task1_ResourceEstimationWrapper, jobName=\"RE for the task 1\")" @@ -349,7 +745,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 26, "metadata": { "collapsed": false, "jupyter": { @@ -362,7 +758,1051 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":0,\"cczCount\":1,\"measurementCount\":0,\"numQubits\":4,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":9,\"logicalCycleTime\":3600.0,\"logicalErrorRate\":3.0000000000000015E-07,\"physicalQubits\":162},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":3,\"algorithmicLogicalQubits\":15,\"cliffordErrorRate\":0.001,\"logicalDepth\":13,\"numTfactories\":4,\"numTfactoryRuns\":1,\"numTsPerRotation\":null,\"numTstates\":4,\"physicalQubitsForAlgorithm\":2430,\"physicalQubitsForTfactories\":15680,\"requiredLogicalQubitErrorRate\":2.564102564102564E-06,\"requiredLogicalTstateErrorRate\":0.000125},\"physicalQubits\":18110,\"runtime\":46800},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"7\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"3us 600ns\",\"logicalErrorRate\":\"3.00e-7\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"86.58 %\",\"physicalQubitsPerRound\":\"3920\",\"requiredLogicalQubitErrorRate\":\"2.56e-6\",\"requiredLogicalTstateErrorRate\":\"1.25e-4\",\"runtime\":\"46us 800ns\",\"tfactoryRuntime\":\"36us 400ns\",\"tfactoryRuntimePerRound\":\"36us 400ns\",\"tstateLogicalErrorRate\":\"2.13e-5\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 2430 physical qubits to implement the algorithm logic, and 15680 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 3 logical cycles to run the algorithm. If however the duration of a single T factory (here: 36us 400ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 4$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 15$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 0 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 1 CCZ and 0 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 3. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 1 CCZ and 0 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 4 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 4 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{4\\\\;\\\\text{T states} \\\\cdot 36us 400ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 46us 800ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 4 T states, the 4 copies of the T factory are repeatedly invoked 1 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 2430 are the product of the 15 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 3920 physical qubits and we run 4 in parallel, therefore we need $15680 = 3920 \\\\cdot 4$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 15 logical qubits and the total cycle count 13.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 4.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.000002564102564102564)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{9 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 3us 600ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 162.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.13e-5.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-4.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 15 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or ¬µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[7],\"logicalErrorRate\":2.133500000000001E-05,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":3920,\"physicalQubitsPerRound\":[3920],\"runtime\":36400.0,\"runtimePerRound\":[36400.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "text/html": [ + "\r\n", + "
\r\n", + " \r\n", + " Physical resource estimates\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits18110\r\n", + "

Number of physical qubits

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\r\n", + "

This value represents the total number of physical qubits, which is the sum of 2430 physical qubits to implement the algorithm logic, and 15680 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

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Runtime46us 800ns\r\n", + "

Total runtime

\n", + "\r\n", + "
\r\n", + "

This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 3 logical cycles to run the algorithm. If however the duration of a single T factory (here: 36us 400ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

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\r\n", + " \r\n", + " Resource estimates breakdown\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Logical algorithmic qubits15\r\n", + "

Number of logical qubits for the algorithm after layout

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\r\n", + "

Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 4\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 15$ logical qubits.

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Algorithmic depth3\r\n", + "

Number of logical cycles for the algorithm

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To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 0 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 1 CCZ and 0 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

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Logical depth13\r\n", + "

Number of logical cycles performed

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This number is usually equal to the logical depth of the algorithm, which is 3. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

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Number of T states4\r\n", + "

Number of T states consumed by the algorithm

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To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 1 CCZ and 0 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

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Number of T factories4\r\n", + "

Number of T factories capable of producing the demanded 4 T states during the algorithm's runtime

\n", + "\r\n", + "
\r\n", + "

The total number of T factories 4 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{4\\;\\text{T states} \\cdot 36us 400ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 46us 800ns\\;\\text{algorithm runtime}}\\right\\rceil\\)

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Number of T factory invocations1\r\n", + "

Number of times all T factories are invoked

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\r\n", + "

In order to prepare the 4 T states, the 4 copies of the T factory are repeatedly invoked 1 times.

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Physical algorithmic qubits2430\r\n", + "

Number of physical qubits for the algorithm after layout

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\r\n", + "

The 2430 are the product of the 15 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.

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Physical T factory qubits15680\r\n", + "

Number of physical qubits for the T factories

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\r\n", + "

Each T factory requires 3920 physical qubits and we run 4 in parallel, therefore we need $15680 = 3920 \\cdot 4$ qubits.

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Required logical qubit error rate2.56e-6\r\n", + "

The minimum logical qubit error rate required to run the algorithm within the error budget

\n", + "\r\n", + "
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The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 15 logical qubits and the total cycle count 13.

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Required logical T state error rate1.25e-4\r\n", + "

The minimum T state error rate required for distilled T states

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\r\n", + "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 4.

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Number of T states per rotationNo rotations in algorithm\r\n", + "

Number of T states to implement a rotation with an arbitrary angle

\n", + "\r\n", + "
\r\n", + "

The number of T states to implement a rotation with an arbitrary angle is \\(\\lceil 0.53 \\log_2(0 / 0) + 5.3\\rceil\\) [arXiv:2203.10064]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.

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\r\n", + " \r\n", + " Logical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
QEC schemesurface_code\r\n", + "

Name of QEC scheme

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\r\n", + "

You can load pre-defined QEC schemes by using the name surface_code or floquet_code. The latter only works with Majorana qubits.

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Code distance9\r\n", + "

Required code distance for error correction

\n", + "\r\n", + "
\r\n", + "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.000002564102564102564)}{\\log(0.01/0.001)} - 1\\)

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Physical qubits162\r\n", + "

Number of physical qubits per logical qubit

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\r\n", + "

The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.

\n", + "\r\n", + "
Logical cycle time3us 600ns\r\n", + "

Duration of a logical cycle in nanoseconds

\n", + "\r\n", + "
\r\n", + "

The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.

\n", + "\r\n", + "
Logical qubit error rate3.00e-7\r\n", + "

Logical qubit error rate

\n", + "\r\n", + "
\r\n", + "

The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{9 + 1}{2}$

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Crossing prefactor0.03\r\n", + "

Crossing prefactor used in QEC scheme

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\r\n", + "

The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.

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Error correction threshold0.01\r\n", + "

Error correction threshold used in QEC scheme

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The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.

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Logical cycle time formula(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\r\n", + "

QEC scheme formula used to compute logical cycle time

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\r\n", + "

This is the formula that is used to compute the logical cycle time 3us 600ns.

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Physical qubits formula2 * codeDistance * codeDistance\r\n", + "

QEC scheme formula used to compute number of physical qubits per logical qubit

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\r\n", + "

This is the formula that is used to compute the number of physical qubits per logical qubits 162.

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Physical qubits3920\r\n", + "

Number of physical qubits for a single T factory

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This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.

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Runtime36us 400ns\r\n", + "

Runtime of a single T factory

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The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.

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Number of output T states per run1\r\n", + "

Number of output T states produced in a single run of T factory

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\r\n", + "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.13e-5.

\n", + "\r\n", + "
Number of input T states per run30\r\n", + "

Number of physical input T states consumed in a single run of a T factory

\n", + "\r\n", + "
\r\n", + "

This value includes the physical input T states of all copies of the distillation unit in the first round.

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Distillation rounds1\r\n", + "

The number of distillation rounds

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\r\n", + "

This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.

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Distillation units per round2\r\n", + "

The number of units in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the number of copies for the distillation units per round.

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Distillation units15-to-1 space efficient logical\r\n", + "

The types of distillation units

\n", + "\r\n", + "
\r\n", + "

These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.

\n", + "\r\n", + "
Distillation code distances7\r\n", + "

The code distance in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.

\n", + "\r\n", + "
Number of physical qubits per round3920\r\n", + "

The number of physical qubits used in each round of distillation

\n", + "\r\n", + "
\r\n", + "

The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.

\n", + "\r\n", + "
Runtime per round36us 400ns\r\n", + "

The runtime of each distillation round

\n", + "\r\n", + "
\r\n", + "

The runtime of the T factory is the sum of the runtimes in all rounds.

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Logical T state error rate2.13e-5\r\n", + "

Logical T state error rate

\n", + "\r\n", + "
\r\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-4.

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\r\n", + " \r\n", + " Pre-layout logical resources\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Logical qubits (pre-layout)4\r\n", + "

Number of logical qubits in the input quantum program

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\r\n", + "

We determine 15 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

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T gates0\r\n", + "

Number of T gates in the input quantum program

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\r\n", + "

This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.

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Rotation gates0\r\n", + "

Number of rotation gates in the input quantum program

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\r\n", + "

This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.

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Rotation depth0\r\n", + "

Depth of rotation gates in the input quantum program

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\r\n", + "

This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.

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CCZ gates1\r\n", + "

Number of CCZ-gates in the input quantum program

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\r\n", + "

This is the number of CCZ gates.

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CCiX gates0\r\n", + "

Number of CCiX-gates in the input quantum program

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This is the number of CCiX gates, which applies \\(-iX\\) controlled on two control qubits [1212.5069].

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Measurement operations0\r\n", + "

Number of single qubit measurements in the input quantum program

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This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.

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\r\n", + " \r\n", + " Assumed error budget\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Total error budget1.00e-3\r\n", + "

Total error budget for the algorithm

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The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget \\(\\epsilon = \\epsilon_{\\log} + \\epsilon_{\\rm dis} + \\epsilon_{\\rm syn}\\) is uniformly distributed and applies to errors \\(\\epsilon_{\\log}\\) to implement logical qubits, an error budget \\(\\epsilon_{\\rm dis}\\) to produce T states through distillation, and an error budget \\(\\epsilon_{\\rm syn}\\) to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets \\(\\epsilon_{\\rm dis}\\) and \\(\\epsilon_{\\rm syn}\\) are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.

\n", + "\r\n", + "
Logical error probability5.00e-4\r\n", + "

Probability of at least one logical error

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
T distillation error probability5.00e-4\r\n", + "

Probability of at least one faulty T distillation

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
Rotation synthesis error probability0.00e0\r\n", + "

Probability of at least one failed rotation synthesis

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Physical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Qubit namequbit_gate_ns_e3\r\n", + "

Some descriptive name for the qubit model

\n", + "\r\n", + "
\r\n", + "

You can load pre-defined qubit parameters by using the names qubit_gate_ns_e3, qubit_gate_ns_e4, qubit_gate_us_e3, qubit_gate_us_e4, qubit_maj_ns_e4, or qubit_maj_ns_e6. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).

\n", + "\r\n", + "
Instruction setGateBased\r\n", + "

Underlying qubit technology (gate-based or Majorana)

\n", + "\r\n", + "
\r\n", + "

When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either gate-based or Majorana. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.

\n", + "\r\n", + "
Single-qubit measurement time100 ns\r\n", + "

Operation time for single-qubit measurement (t_meas) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.

\n", + "\r\n", + "
Single-qubit gate time50 ns\r\n", + "

Operation time for single-qubit gate (t_gate) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.

\n", + "\r\n", + "
Two-qubit gate time50 ns\r\n", + "

Operation time for two-qubit gate in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.

\n", + "\r\n", + "
T gate time50 ns\r\n", + "

Operation time for a T gate

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to execute a T gate.

\n", + "\r\n", + "
Single-qubit measurement error rate0.001\r\n", + "

Error rate for single-qubit measurement

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit measurement in the Pauli basis may fail.

\n", + "\r\n", + "
Single-qubit error rate0.001\r\n", + "

Error rate for single-qubit Clifford gate (p)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.

\n", + "\r\n", + "
Two-qubit error rate0.001\r\n", + "

Error rate for two-qubit Clifford gate

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.

\n", + "\r\n", + "
T gate error rate0.001\r\n", + "

Error rate to prepare single-qubit T state or apply a T gate (p_T)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which executing a single T gate may fail.

\n", + "\r\n", + "
\n", + "
\r\n", + " Assumptions\r\n", + "
    \n", + "

  • More details on the following lists of assumptions can be found in the paper Accessing requirements for scaling quantum computers and their applications.

    \n", + "
    • \n", + "

  • Uniform independent physical noise. We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.

    \n", + "
    • \n", + "

  • Efficient classical computation. We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.

    \n", + "
    • \n", + "

  • Extraction circuits for planar quantum ISA. We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).

    \n", + "
    • \n", + "

  • Uniform independent logical noise. We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.

    \n", + "
    • \n", + "

  • Negligible Clifford costs for synthesis. We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.

    \n", + "
    • \n", + "

  • Smooth magic state consumption rate. We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.

    \n", + "
    • \n", + "
\n" + ], + "text/plain": [ + "{'errorBudget': {'logical': 0.0005, 'rotations': 0.0, 'tstates': 0.0005},\n", + " 'jobParams': {'errorBudget': 0.001,\n", + " 'qecScheme': {'crossingPrefactor': 0.03,\n", + " 'errorCorrectionThreshold': 0.01,\n", + " 'logicalCycleTime': '(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance',\n", + " 'name': 'surface_code',\n", + " 'physicalQubitsPerLogicalQubit': '2 * codeDistance * codeDistance'},\n", + " 'qubitParams': {'instructionSet': 'GateBased',\n", + " 'name': 'qubit_gate_ns_e3',\n", + " 'oneQubitGateErrorRate': 0.001,\n", + " 'oneQubitGateTime': '50 ns',\n", + " 'oneQubitMeasurementErrorRate': 0.001,\n", + " 'oneQubitMeasurementTime': '100 ns',\n", + " 'tGateErrorRate': 0.001,\n", + " 'tGateTime': '50 ns',\n", + " 'twoQubitGateErrorRate': 0.001,\n", + " 'twoQubitGateTime': '50 ns'}},\n", + " 'logicalCounts': {'ccixCount': 0,\n", + " 'cczCount': 1,\n", + " 'measurementCount': 0,\n", + " 'numQubits': 4,\n", + " 'rotationCount': 0,\n", + " 'rotationDepth': 0,\n", + " 'tCount': 0},\n", + " 'logicalQubit': {'codeDistance': 9,\n", + " 'logicalCycleTime': 3600.0,\n", + " 'logicalErrorRate': 3.0000000000000015e-07,\n", + " 'physicalQubits': 162},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 3,\n", + " 'algorithmicLogicalQubits': 15,\n", + " 'cliffordErrorRate': 0.001,\n", + " 'logicalDepth': 13,\n", + " 'numTfactories': 4,\n", + " 'numTfactoryRuns': 1,\n", + " 'numTsPerRotation': None,\n", + " 'numTstates': 4,\n", + " 'physicalQubitsForAlgorithm': 2430,\n", + " 'physicalQubitsForTfactories': 15680,\n", + " 'requiredLogicalQubitErrorRate': 2.564102564102564e-06,\n", + " 'requiredLogicalTstateErrorRate': 0.000125},\n", + " 'physicalQubits': 18110,\n", + " 'runtime': 46800},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '7',\n", + " 'errorBudget': '1.00e-3',\n", + " 'errorBudgetLogical': '5.00e-4',\n", + " 'errorBudgetRotations': '0.00e0',\n", + " 'errorBudgetTstates': '5.00e-4',\n", + " 'logicalCycleTime': '3us 600ns',\n", + " 'logicalErrorRate': '3.00e-7',\n", + " 'numTsPerRotation': 'No rotations in algorithm',\n", + " 'numUnitsPerRound': '2',\n", + " 'physicalQubitsForTfactoriesPercentage': '86.58 %',\n", + " 'physicalQubitsPerRound': '3920',\n", + " 'requiredLogicalQubitErrorRate': '2.56e-6',\n", + " 'requiredLogicalTstateErrorRate': '1.25e-4',\n", + " 'runtime': '46us 800ns',\n", + " 'tfactoryRuntime': '36us 400ns',\n", + " 'tfactoryRuntimePerRound': '36us 400ns',\n", + " 'tstateLogicalErrorRate': '2.13e-5',\n", + " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", + " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", + " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", + " '**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.',\n", + " '**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).',\n", + " '**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.',\n", + " '**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.',\n", + " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", + " 'groups': [{'alwaysVisible': True,\n", + " 'entries': [{'description': 'Number of physical qubits',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 2430 physical qubits to implement the algorithm logic, and 15680 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'physicalCounts/physicalQubits'},\n", + " {'description': 'Total runtime',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 3 logical cycles to run the algorithm. If however the duration of a single T factory (here: 36us 400ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/runtime'}],\n", + " 'title': 'Physical resource estimates'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 4$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 15$ logical qubits.',\n", + " 'label': 'Logical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", + " {'description': 'Number of logical cycles for the algorithm',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 0 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 1 CCZ and 0 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'label': 'Algorithmic depth',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", + " {'description': 'Number of logical cycles performed',\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 3. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'label': 'Logical depth',\n", + " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", + " {'description': 'Number of T states consumed by the algorithm',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 1 CCZ and 0 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'label': 'Number of T states',\n", + " 'path': 'physicalCounts/breakdown/numTstates'},\n", + " {'description': \"Number of T factories capable of producing the demanded 4 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 4 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{4\\\\;\\\\text{T states} \\\\cdot 36us 400ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 46us 800ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " 'label': 'Number of T factories',\n", + " 'path': 'physicalCounts/breakdown/numTfactories'},\n", + " {'description': 'Number of times all T factories are invoked',\n", + " 'explanation': 'In order to prepare the 4 T states, the 4 copies of the T factory are repeatedly invoked 1 times.',\n", + " 'label': 'Number of T factory invocations',\n", + " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", + " {'description': 'Number of physical qubits for the algorithm after layout',\n", + " 'explanation': 'The 2430 are the product of the 15 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.',\n", + " 'label': 'Physical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", + " {'description': 'Number of physical qubits for the T factories',\n", + " 'explanation': 'Each T factory requires 3920 physical qubits and we run 4 in parallel, therefore we need $15680 = 3920 \\\\cdot 4$ qubits.',\n", + " 'label': 'Physical T factory qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", + " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 15 logical qubits and the total cycle count 13.',\n", + " 'label': 'Required logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", + " {'description': 'The minimum T state error rate required for distilled T states',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 4.',\n", + " 'label': 'Required logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", + " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", + " 'explanation': 'The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.',\n", + " 'label': 'Number of T states per rotation',\n", + " 'path': 'physicalCountsFormatted/numTsPerRotation'}],\n", + " 'title': 'Resource estimates breakdown'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Name of QEC scheme',\n", + " 'explanation': 'You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.',\n", + " 'label': 'QEC scheme',\n", + " 'path': 'jobParams/qecScheme/name'},\n", + " {'description': 'Required code distance for error correction',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.000002564102564102564)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'label': 'Code distance',\n", + " 'path': 'logicalQubit/codeDistance'},\n", + " {'description': 'Number of physical qubits per logical qubit',\n", + " 'explanation': 'The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'logicalQubit/physicalQubits'},\n", + " {'description': 'Duration of a logical cycle in nanoseconds',\n", + " 'explanation': 'The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.',\n", + " 'label': 'Logical cycle time',\n", + " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", + " {'description': 'Logical qubit error rate',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{9 + 1}{2}$',\n", + " 'label': 'Logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", + " {'description': 'Crossing prefactor used in QEC scheme',\n", + " 'explanation': 'The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.',\n", + " 'label': 'Crossing prefactor',\n", + " 'path': 'jobParams/qecScheme/crossingPrefactor'},\n", + " {'description': 'Error correction threshold used in QEC scheme',\n", + " 'explanation': 'The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.',\n", + " 'label': 'Error correction threshold',\n", + " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", + " {'description': 'QEC scheme formula used to compute logical cycle time',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 3us 600ns.',\n", + " 'label': 'Logical cycle time formula',\n", + " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", + " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 162.',\n", + " 'label': 'Physical qubits formula',\n", + " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", + " 'title': 'Logical qubit parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of physical qubits for a single T factory',\n", + " 'explanation': 'This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'tfactory/physicalQubits'},\n", + " {'description': 'Runtime of a single T factory',\n", + " 'explanation': 'The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", + " {'description': 'Number of output T states produced in a single run of T factory',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.13e-5.',\n", + " 'label': 'Number of output T states per run',\n", + " 'path': 'tfactory/numTstates'},\n", + " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", + " 'explanation': 'This value includes the physical input T states of all copies of the distillation unit in the first round.',\n", + " 'label': 'Number of input T states per run',\n", + " 'path': 'tfactory/numInputTstates'},\n", + " {'description': 'The number of distillation rounds',\n", + " 'explanation': 'This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.',\n", + " 'label': 'Distillation rounds',\n", + " 'path': 'tfactory/numRounds'},\n", + " {'description': 'The number of units in each round of distillation',\n", + " 'explanation': 'This is the number of copies for the distillation units per round.',\n", + " 'label': 'Distillation units per round',\n", + " 'path': 'physicalCountsFormatted/numUnitsPerRound'},\n", + " {'description': 'The types of distillation units',\n", + " 'explanation': 'These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.',\n", + " 'label': 'Distillation units',\n", + " 'path': 'physicalCountsFormatted/unitNamePerRound'},\n", + " {'description': 'The code distance in each round of distillation',\n", + " 'explanation': 'This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.',\n", + " 'label': 'Distillation code distances',\n", + " 'path': 'physicalCountsFormatted/codeDistancePerRound'},\n", + " {'description': 'The number of physical qubits used in each round of distillation',\n", + " 'explanation': 'The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.',\n", + " 'label': 'Number of physical qubits per round',\n", + " 'path': 'physicalCountsFormatted/physicalQubitsPerRound'},\n", + " {'description': 'The runtime of each distillation round',\n", + " 'explanation': 'The runtime of the T factory is the sum of the runtimes in all rounds.',\n", + " 'label': 'Runtime per round',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", + " {'description': 'Logical T state error rate',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-4.',\n", + " 'label': 'Logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", + " 'title': 'T factory parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", + " 'explanation': 'We determine 15 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'label': 'Logical qubits (pre-layout)',\n", + " 'path': 'logicalCounts/numQubits'},\n", + " {'description': 'Number of T gates in the input quantum program',\n", + " 'explanation': 'This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.',\n", + " 'label': 'T gates',\n", + " 'path': 'logicalCounts/tCount'},\n", + " {'description': 'Number of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.',\n", + " 'label': 'Rotation gates',\n", + " 'path': 'logicalCounts/rotationCount'},\n", + " {'description': 'Depth of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.',\n", + " 'label': 'Rotation depth',\n", + " 'path': 'logicalCounts/rotationDepth'},\n", + " {'description': 'Number of CCZ-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCZ gates.',\n", + " 'label': 'CCZ gates',\n", + " 'path': 'logicalCounts/cczCount'},\n", + " {'description': 'Number of CCiX-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].',\n", + " 'label': 'CCiX gates',\n", + " 'path': 'logicalCounts/ccixCount'},\n", + " {'description': 'Number of single qubit measurements in the input quantum program',\n", + " 'explanation': 'This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.',\n", + " 'label': 'Measurement operations',\n", + " 'path': 'logicalCounts/measurementCount'}],\n", + " 'title': 'Pre-layout logical resources'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Total error budget for the algorithm',\n", + " 'explanation': \"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\n", + " 'label': 'Total error budget',\n", + " 'path': 'physicalCountsFormatted/errorBudget'},\n", + " {'description': 'Probability of at least one logical error',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'Logical error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetLogical'},\n", + " {'description': 'Probability of at least one faulty T distillation',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'T distillation error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetTstates'},\n", + " {'description': 'Probability of at least one failed rotation synthesis',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3.',\n", + " 'label': 'Rotation synthesis error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetRotations'}],\n", + " 'title': 'Assumed error budget'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Some descriptive name for the qubit model',\n", + " 'explanation': 'You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).',\n", + " 'label': 'Qubit name',\n", + " 'path': 'jobParams/qubitParams/name'},\n", + " {'description': 'Underlying qubit technology (gate-based or Majorana)',\n", + " 'explanation': 'When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.',\n", + " 'label': 'Instruction set',\n", + " 'path': 'jobParams/qubitParams/instructionSet'},\n", + " {'description': 'Operation time for single-qubit measurement (t_meas) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.',\n", + " 'label': 'Single-qubit measurement time',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementTime'},\n", + " {'description': 'Operation time for single-qubit gate (t_gate) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.',\n", + " 'label': 'Single-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateTime'},\n", + " {'description': 'Operation time for two-qubit gate in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.',\n", + " 'label': 'Two-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateTime'},\n", + " {'description': 'Operation time for a T gate',\n", + " 'explanation': 'This is the operation time in nanoseconds to execute a T gate.',\n", + " 'label': 'T gate time',\n", + " 'path': 'jobParams/qubitParams/tGateTime'},\n", + " {'description': 'Error rate for single-qubit measurement',\n", + " 'explanation': 'This is the probability in which a single-qubit measurement in the Pauli basis may fail.',\n", + " 'label': 'Single-qubit measurement error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementErrorRate'},\n", + " {'description': 'Error rate for single-qubit Clifford gate (p)',\n", + " 'explanation': 'This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.',\n", + " 'label': 'Single-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateErrorRate'},\n", + " {'description': 'Error rate for two-qubit Clifford gate',\n", + " 'explanation': 'This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.',\n", + " 'label': 'Two-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateErrorRate'},\n", + " {'description': 'Error rate to prepare single-qubit T state or apply a T gate (p_T)',\n", + " 'explanation': 'This is the probability in which executing a single T gate may fail.',\n", + " 'label': 'T gate error rate',\n", + " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", + " 'title': 'Physical qubit parameters'}]},\n", + " 'status': 'success',\n", + " 'tfactory': {'codeDistancePerRound': [7],\n", + " 'logicalErrorRate': 2.133500000000001e-05,\n", + " 'numInputTstates': 30,\n", + " 'numRounds': 1,\n", + " 'numTstates': 1,\n", + " 'numUnitsPerRound': [2],\n", + " 'physicalQubits': 3920,\n", + " 'physicalQubitsPerRound': [3920],\n", + " 'runtime': 36400.0,\n", + " 'runtimePerRound': [36400.0],\n", + " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", "# result = qsharp.azure.output(\"...\")\n", @@ -371,7 +1811,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 27, "metadata": { "collapsed": false, "jupyter": { @@ -398,7 +1838,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 28, "metadata": { "collapsed": false, "jupyter": { @@ -411,10 +1851,44 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Logical algorithmic qubits = 15\n", + "Algorithmic depth = 3\n", + "Score = 45\n" + ] + }, + { + "data": { + "text/plain": [ + "45" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "evaluate_results(result)" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -422,9 +1896,9 @@ "name": "python3" }, "kernelspec": { - "display_name": "Python 3 [Default]", + "display_name": "Python 3 [Q#]", "language": "python", - "name": "python3" + "name": "python3_qsharp_b54crn" }, "language_info": { "codemirror_mode": { diff --git a/iQuHack-challenge-2023-task2.ipynb b/iQuHack-challenge-2023-task2.ipynb index 44cc5cd..01cf0da 100644 --- a/iQuHack-challenge-2023-task2.ipynb +++ b/iQuHack-challenge-2023-task2.ipynb @@ -34,7 +34,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "collapsed": false, "jupyter": { @@ -47,7 +47,41 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\u001b[93mTo sign in, use a web browser to open the page https://microsoft.com/devicelogin and enter the code F88GK2SR2 to authenticate.\u001b[0m\n", + "[\n", + " {\n", + " \"cloudName\": \"AzureCloud\",\n", + " \"homeTenantId\": \"b4e518fe-3bdc-4371-a4be-7f3d83d7acbd\",\n", + " \"id\": \"7fc54e95-14cf-4a6f-b50e-d6155c241309\",\n", + " \"isDefault\": true,\n", + " \"managedByTenants\": [\n", + " {\n", + " \"tenantId\": \"d0ecd01b-d782-448e-bae0-c3cad0e0543a\"\n", + " },\n", + " {\n", + " \"tenantId\": \"94c4857e-1130-4ab8-8eac-069b40c9db20\"\n", + " },\n", + " {\n", + " \"tenantId\": \"f702a9dc-ae48-4dc7-8f0a-8155a6dfa4e5\"\n", + " }\n", + " ],\n", + " \"name\": \"Azure subscription 1\",\n", + " \"state\": \"Enabled\",\n", + " \"tenantId\": \"b4e518fe-3bdc-4371-a4be-7f3d83d7acbd\",\n", + " \"user\": {\n", + " \"name\": \"hachall@hotmail.com\",\n", + " \"type\": \"user\"\n", + " }\n", + " }\n", + "]\n" + ] + } + ], "source": [ "!az login" ] @@ -67,7 +101,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "collapsed": false, "jupyter": { @@ -80,7 +114,16 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Preparing Q# environment...\n", + "...." + ] + } + ], "source": [ "# Run this code cell to import the modules required to work with Q# and Azure\n", "import qsharp\n", @@ -89,7 +132,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": { "collapsed": false, "jupyter": { @@ -104,14 +147,14 @@ }, "outputs": [], "source": [ - "teamname=\"msft_is_the_best\" # Update this field with your team name\n", + "teamname=\"schrodingers-duck\" # Update this field with your team name\n", "task=[\"task2\"]\n", - "slack_id=\"myslackid\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + "slack_id=\"U04L3SFUCQ2\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": { "collapsed": false, "jupyter": { @@ -148,7 +191,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, "metadata": { "collapsed": false, "jupyter": { @@ -164,15 +207,25 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "/snippet_.qs(18,9): warning QS3306: Deprecated syntax. Parentheses here are no longer required and will not be supported in the future.\n" + ] + } + ], "source": [ "%%qsharp\n", "open Microsoft.Quantum.Canon;\n", + "open Microsoft.Quantum.Bitwise;\n", "open Microsoft.Quantum.Diagnostics;\n", "\n", "// Task 2. Celebrate MIT iQuHack!\n", "// (input will contain 5 qubits)\n", - "operation Task2(input : Qubit[], target : Qubit) : Unit is Adj {\n", + "\n", + "operation old(input : Qubit[], target : Qubit) : Unit is Adj {\n", " ControlledOnInt(13, X)(input, target); // M\n", " ControlledOnInt( 9, X)(input, target); // I\n", " ControlledOnInt(20, X)(input, target); // T\n", @@ -184,12 +237,44 @@ " ControlledOnInt( 1, X)(input, target); // A\n", " ControlledOnInt( 3, X)(input, target); // C\n", " ControlledOnInt(11, X)(input, target); // K\n", - "}" + "}\n", + "\n", + "operation Task2(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " ControlledOnInt(13, X)(input, target); // M\n", + "\n", + " ControlledOnInt(17, X)(input, target); // Q\n", + " ControlledOnInt(21, X)(input, target); // U\n", + " ControlledOnInt( 8, X)(input, target); // H\n", + " ControlledOnInt( 1, X)(input, target); // A\n", + " ControlledOnInt( 3, X)(input, target); // C\n", + " ControlledOnInt(11, X)(input, target); // K\n", + "\n", + " for (index in 0 .. Length(input) - 1) {\n", + " X(input[index]);\n", + " }\n", + " ControlledOnInt(11, X)(input, target); // T (flipped)\n", + "}\n", + "\n" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "UsageError: Cell magic `%%qsharp` not found.\n" + ] + } + ], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 11, "metadata": { "collapsed": false, "jupyter": { @@ -246,7 +331,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "metadata": { "collapsed": false, "jupyter": { @@ -259,7 +344,1710 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": 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$\\left|110010\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110100\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110101\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110110\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111000\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111010\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111011\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111100\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111110\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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"execution_count": null, + "execution_count": 13, "metadata": { "collapsed": false, "jupyter": { @@ -297,19 +2085,68 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "\"Connecting to Azure Quantum...\"", + "text/plain": [ + "Connecting to Azure Quantum..." + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Connected to Azure Quantum workspace azure-q in location uksouth.\n" + ] + }, + { + "data": { + "text/plain": [ + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 278400},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 408469},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 2},\n", + " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 257411},\n", + " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 4298},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 139},\n", + " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 257411},\n", + " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 4298},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 139},\n", + " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.qpu.aspen-m-2', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", "# If you're using this notebook in qBraid, keep it\n", "qsharp.azure.connect(\n", - " resourceId=\"...\",\n", - " location=\"...\",\n", + " resourceId=\"/subscriptions/7fc54e95-14cf-4a6f-b50e-d6155c241309/resourceGroups/AzureQuantum/providers/Microsoft.Quantum/Workspaces/azure-q\",\n", + " location=\"UK South\",\n", " credential=\"CLI\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 14, "metadata": { "collapsed": false, "jupyter": { @@ -322,14 +2159,33 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loading package Microsoft.Quantum.Providers.Core and dependencies...\n", + "Active target is now microsoft.estimator\n" + ] + }, + { + "data": { + "text/plain": [ + "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "qsharp.azure.target(\"microsoft.estimator\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 15, "metadata": { "collapsed": false, "jupyter": { @@ -342,7 +2198,21 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Submitting Task2_ResourceEstimationWrapper to target microsoft.estimator...\n", + "Job successfully submitted.\n", + " Job name: RE for the task 2\n", + " Job ID: 5d90fa2d-f0ad-4caf-a994-eccabd42cb19\n", + "Waiting up to 30 seconds for Azure Quantum job to complete...\n", + "[10:17:52 PM] Current job status: Waiting\n", + "[10:17:57 PM] Current job status: Succeeded\n" + ] + } + ], "source": [ "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", "result = qsharp.azure.execute(Task2_ResourceEstimationWrapper, jobName=\"RE for the task 2\")" @@ -350,7 +2220,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 16, "metadata": { "collapsed": false, "jupyter": { @@ -363,7 +2233,1051 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":24,\"cczCount\":8,\"measurementCount\":24,\"numQubits\":9,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":120,\"algorithmicLogicalQubits\":28,\"cliffordErrorRate\":0.001,\"logicalDepth\":120,\"numTfactories\":12,\"numTfactoryRuns\":11,\"numTsPerRotation\":null,\"numTstates\":128,\"physicalQubitsForAlgorithm\":6776,\"physicalQubitsForTfactories\":77760,\"requiredLogicalQubitErrorRate\":1.4880952380952382E-07,\"requiredLogicalTstateErrorRate\":3.90625E-06},\"physicalQubits\":84536,\"runtime\":528000},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"91.98 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"1.49e-7\",\"requiredLogicalTstateErrorRate\":\"3.91e-6\",\"runtime\":\"528us\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 6776 physical qubits to implement the algorithm logic, and 77760 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 120 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 9$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 28$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 24 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 8 CCZ and 24 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 120. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 8 CCZ and 24 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 128 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{128\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 528us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 128 T states, the 12 copies of the T factory are repeatedly invoked 11 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 6776 are the product of the 28 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 12 in parallel, therefore we need $77760 = 6480 \\\\cdot 12$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 28 logical qubits and the total cycle count 120.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 128.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000014880952380952382)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 3.91e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 28 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or ¬µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "text/html": [ + "\r\n", + "
\r\n", + " \r\n", + " Physical resource estimates\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits84536\r\n", + "

Number of physical qubits

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This value represents the total number of physical qubits, which is the sum of 6776 physical qubits to implement the algorithm logic, and 77760 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

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Runtime528us\r\n", + "

Total runtime

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This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 120 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

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Logical algorithmic qubits28\r\n", + "

Number of logical qubits for the algorithm after layout

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Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 9\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 28$ logical qubits.

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Algorithmic depth120\r\n", + "

Number of logical cycles for the algorithm

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To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 24 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 8 CCZ and 24 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

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Logical depth120\r\n", + "

Number of logical cycles performed

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This number is usually equal to the logical depth of the algorithm, which is 120. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

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Number of T states128\r\n", + "

Number of T states consumed by the algorithm

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To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 8 CCZ and 24 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

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Number of T factories12\r\n", + "

Number of T factories capable of producing the demanded 128 T states during the algorithm's runtime

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The total number of T factories 12 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{128\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 528us\\;\\text{algorithm runtime}}\\right\\rceil\\)

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Number of T factory invocations11\r\n", + "

Number of times all T factories are invoked

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In order to prepare the 128 T states, the 12 copies of the T factory are repeatedly invoked 11 times.

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Physical algorithmic qubits6776\r\n", + "

Number of physical qubits for the algorithm after layout

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The 6776 are the product of the 28 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.

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Physical T factory qubits77760\r\n", + "

Number of physical qubits for the T factories

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Each T factory requires 6480 physical qubits and we run 12 in parallel, therefore we need $77760 = 6480 \\cdot 12$ qubits.

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Required logical qubit error rate1.49e-7\r\n", + "

The minimum logical qubit error rate required to run the algorithm within the error budget

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The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 28 logical qubits and the total cycle count 120.

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Required logical T state error rate3.91e-6\r\n", + "

The minimum T state error rate required for distilled T states

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The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 128.

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Number of T states per rotationNo rotations in algorithm\r\n", + "

Number of T states to implement a rotation with an arbitrary angle

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The number of T states to implement a rotation with an arbitrary angle is \\(\\lceil 0.53 \\log_2(0 / 0) + 5.3\\rceil\\) [arXiv:2203.10064]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.

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QEC schemesurface_code\r\n", + "

Name of QEC scheme

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You can load pre-defined QEC schemes by using the name surface_code or floquet_code. The latter only works with Majorana qubits.

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Code distance11\r\n", + "

Required code distance for error correction

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The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000014880952380952382)}{\\log(0.01/0.001)} - 1\\)

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Physical qubits242\r\n", + "

Number of physical qubits per logical qubit

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The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.

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Logical cycle time4us 400ns\r\n", + "

Duration of a logical cycle in nanoseconds

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The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.

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Logical qubit error rate3.00e-8\r\n", + "

Logical qubit error rate

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The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{11 + 1}{2}$

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Crossing prefactor0.03\r\n", + "

Crossing prefactor used in QEC scheme

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The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.

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Error correction threshold0.01\r\n", + "

Error correction threshold used in QEC scheme

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The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.

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Logical cycle time formula(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\r\n", + "

QEC scheme formula used to compute logical cycle time

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This is the formula that is used to compute the logical cycle time 4us 400ns.

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Physical qubits formula2 * codeDistance * codeDistance\r\n", + "

QEC scheme formula used to compute number of physical qubits per logical qubit

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This is the formula that is used to compute the number of physical qubits per logical qubits 242.

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Physical qubits6480\r\n", + "

Number of physical qubits for a single T factory

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This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.

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Runtime46us 800ns\r\n", + "

Runtime of a single T factory

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The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.

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Number of output T states per run1\r\n", + "

Number of output T states produced in a single run of T factory

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The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.

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Number of input T states per run30\r\n", + "

Number of physical input T states consumed in a single run of a T factory

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This value includes the physical input T states of all copies of the distillation unit in the first round.

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Distillation rounds1\r\n", + "

The number of distillation rounds

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This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.

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Distillation units per round2\r\n", + "

The number of units in each round of distillation

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This is the number of copies for the distillation units per round.

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Distillation units15-to-1 space efficient logical\r\n", + "

The types of distillation units

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These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.

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Distillation code distances9\r\n", + "

The code distance in each round of distillation

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This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.

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Number of physical qubits per round6480\r\n", + "

The number of physical qubits used in each round of distillation

\n", + "\r\n", + "
\r\n", + "

The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.

\n", + "\r\n", + "
Runtime per round46us 800ns\r\n", + "

The runtime of each distillation round

\n", + "\r\n", + "
\r\n", + "

The runtime of the T factory is the sum of the runtimes in all rounds.

\n", + "\r\n", + "
Logical T state error rate2.17e-6\r\n", + "

Logical T state error rate

\n", + "\r\n", + "
\r\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 3.91e-6.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Pre-layout logical resources\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Logical qubits (pre-layout)9\r\n", + "

Number of logical qubits in the input quantum program

\n", + "\r\n", + "
\r\n", + "

We determine 28 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", + "\r\n", + "
T gates0\r\n", + "

Number of T gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.

\n", + "\r\n", + "
Rotation gates0\r\n", + "

Number of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.

\n", + "\r\n", + "
Rotation depth0\r\n", + "

Depth of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.

\n", + "\r\n", + "
CCZ gates8\r\n", + "

Number of CCZ-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCZ gates.

\n", + "\r\n", + "
CCiX gates24\r\n", + "

Number of CCiX-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCiX gates, which applies \\(-iX\\) controlled on two control qubits [1212.5069].

\n", + "\r\n", + "
Measurement operations24\r\n", + "

Number of single qubit measurements in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Assumed error budget\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Total error budget1.00e-3\r\n", + "

Total error budget for the algorithm

\n", + "\r\n", + "
\r\n", + "

The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget \\(\\epsilon = \\epsilon_{\\log} + \\epsilon_{\\rm dis} + \\epsilon_{\\rm syn}\\) is uniformly distributed and applies to errors \\(\\epsilon_{\\log}\\) to implement logical qubits, an error budget \\(\\epsilon_{\\rm dis}\\) to produce T states through distillation, and an error budget \\(\\epsilon_{\\rm syn}\\) to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets \\(\\epsilon_{\\rm dis}\\) and \\(\\epsilon_{\\rm syn}\\) are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.

\n", + "\r\n", + "
Logical error probability5.00e-4\r\n", + "

Probability of at least one logical error

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
T distillation error probability5.00e-4\r\n", + "

Probability of at least one faulty T distillation

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
Rotation synthesis error probability0.00e0\r\n", + "

Probability of at least one failed rotation synthesis

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Physical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Qubit namequbit_gate_ns_e3\r\n", + "

Some descriptive name for the qubit model

\n", + "\r\n", + "
\r\n", + "

You can load pre-defined qubit parameters by using the names qubit_gate_ns_e3, qubit_gate_ns_e4, qubit_gate_us_e3, qubit_gate_us_e4, qubit_maj_ns_e4, or qubit_maj_ns_e6. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).

\n", + "\r\n", + "
Instruction setGateBased\r\n", + "

Underlying qubit technology (gate-based or Majorana)

\n", + "\r\n", + "
\r\n", + "

When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either gate-based or Majorana. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.

\n", + "\r\n", + "
Single-qubit measurement time100 ns\r\n", + "

Operation time for single-qubit measurement (t_meas) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.

\n", + "\r\n", + "
Single-qubit gate time50 ns\r\n", + "

Operation time for single-qubit gate (t_gate) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.

\n", + "\r\n", + "
Two-qubit gate time50 ns\r\n", + "

Operation time for two-qubit gate in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.

\n", + "\r\n", + "
T gate time50 ns\r\n", + "

Operation time for a T gate

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to execute a T gate.

\n", + "\r\n", + "
Single-qubit measurement error rate0.001\r\n", + "

Error rate for single-qubit measurement

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit measurement in the Pauli basis may fail.

\n", + "\r\n", + "
Single-qubit error rate0.001\r\n", + "

Error rate for single-qubit Clifford gate (p)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.

\n", + "\r\n", + "
Two-qubit error rate0.001\r\n", + "

Error rate for two-qubit Clifford gate

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.

\n", + "\r\n", + "
T gate error rate0.001\r\n", + "

Error rate to prepare single-qubit T state or apply a T gate (p_T)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which executing a single T gate may fail.

\n", + "\r\n", + "
\n", + "
\r\n", + " Assumptions\r\n", + "
    \n", + "

  • More details on the following lists of assumptions can be found in the paper Accessing requirements for scaling quantum computers and their applications.

    \n", + "
    • \n", + "

  • Uniform independent physical noise. We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.

    \n", + "
    • \n", + "

  • Efficient classical computation. We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.

    \n", + "
    • \n", + "

  • Extraction circuits for planar quantum ISA. We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).

    \n", + "
    • \n", + "

  • Uniform independent logical noise. We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.

    \n", + "
    • \n", + "

  • Negligible Clifford costs for synthesis. We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.

    \n", + "
    • \n", + "

  • Smooth magic state consumption rate. We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.

    \n", + "
    • \n", + "
\n" + ], + "text/plain": [ + "{'errorBudget': {'logical': 0.0005, 'rotations': 0.0, 'tstates': 0.0005},\n", + " 'jobParams': {'errorBudget': 0.001,\n", + " 'qecScheme': {'crossingPrefactor': 0.03,\n", + " 'errorCorrectionThreshold': 0.01,\n", + " 'logicalCycleTime': '(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance',\n", + " 'name': 'surface_code',\n", + " 'physicalQubitsPerLogicalQubit': '2 * codeDistance * codeDistance'},\n", + " 'qubitParams': {'instructionSet': 'GateBased',\n", + " 'name': 'qubit_gate_ns_e3',\n", + " 'oneQubitGateErrorRate': 0.001,\n", + " 'oneQubitGateTime': '50 ns',\n", + " 'oneQubitMeasurementErrorRate': 0.001,\n", + " 'oneQubitMeasurementTime': '100 ns',\n", + " 'tGateErrorRate': 0.001,\n", + " 'tGateTime': '50 ns',\n", + " 'twoQubitGateErrorRate': 0.001,\n", + " 'twoQubitGateTime': '50 ns'}},\n", + " 'logicalCounts': {'ccixCount': 24,\n", + " 'cczCount': 8,\n", + " 'measurementCount': 24,\n", + " 'numQubits': 9,\n", + " 'rotationCount': 0,\n", + " 'rotationDepth': 0,\n", + " 'tCount': 0},\n", + " 'logicalQubit': {'codeDistance': 11,\n", + " 'logicalCycleTime': 4400.0,\n", + " 'logicalErrorRate': 3.000000000000002e-08,\n", + " 'physicalQubits': 242},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 120,\n", + " 'algorithmicLogicalQubits': 28,\n", + " 'cliffordErrorRate': 0.001,\n", + " 'logicalDepth': 120,\n", + " 'numTfactories': 12,\n", + " 'numTfactoryRuns': 11,\n", + " 'numTsPerRotation': None,\n", + " 'numTstates': 128,\n", + " 'physicalQubitsForAlgorithm': 6776,\n", + " 'physicalQubitsForTfactories': 77760,\n", + " 'requiredLogicalQubitErrorRate': 1.4880952380952382e-07,\n", + " 'requiredLogicalTstateErrorRate': 3.90625e-06},\n", + " 'physicalQubits': 84536,\n", + " 'runtime': 528000},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", + " 'errorBudget': '1.00e-3',\n", + " 'errorBudgetLogical': '5.00e-4',\n", + " 'errorBudgetRotations': '0.00e0',\n", + " 'errorBudgetTstates': '5.00e-4',\n", + " 'logicalCycleTime': '4us 400ns',\n", + " 'logicalErrorRate': '3.00e-8',\n", + " 'numTsPerRotation': 'No rotations in algorithm',\n", + " 'numUnitsPerRound': '2',\n", + " 'physicalQubitsForTfactoriesPercentage': '91.98 %',\n", + " 'physicalQubitsPerRound': '6480',\n", + " 'requiredLogicalQubitErrorRate': '1.49e-7',\n", + " 'requiredLogicalTstateErrorRate': '3.91e-6',\n", + " 'runtime': '528us',\n", + " 'tfactoryRuntime': '46us 800ns',\n", + " 'tfactoryRuntimePerRound': '46us 800ns',\n", + " 'tstateLogicalErrorRate': '2.17e-6',\n", + " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", + " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", + " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", + " '**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.',\n", + " '**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).',\n", + " '**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.',\n", + " '**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.',\n", + " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", + " 'groups': [{'alwaysVisible': True,\n", + " 'entries': [{'description': 'Number of physical qubits',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 6776 physical qubits to implement the algorithm logic, and 77760 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'physicalCounts/physicalQubits'},\n", + " {'description': 'Total runtime',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 120 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/runtime'}],\n", + " 'title': 'Physical resource estimates'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 9$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 28$ logical qubits.',\n", + " 'label': 'Logical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", + " {'description': 'Number of logical cycles for the algorithm',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 24 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 8 CCZ and 24 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'label': 'Algorithmic depth',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", + " {'description': 'Number of logical cycles performed',\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 120. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'label': 'Logical depth',\n", + " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", + " {'description': 'Number of T states consumed by the algorithm',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 8 CCZ and 24 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'label': 'Number of T states',\n", + " 'path': 'physicalCounts/breakdown/numTstates'},\n", + " {'description': \"Number of T factories capable of producing the demanded 128 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{128\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 528us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " 'label': 'Number of T factories',\n", + " 'path': 'physicalCounts/breakdown/numTfactories'},\n", + " {'description': 'Number of times all T factories are invoked',\n", + " 'explanation': 'In order to prepare the 128 T states, the 12 copies of the T factory are repeatedly invoked 11 times.',\n", + " 'label': 'Number of T factory invocations',\n", + " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", + " {'description': 'Number of physical qubits for the algorithm after layout',\n", + " 'explanation': 'The 6776 are the product of the 28 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.',\n", + " 'label': 'Physical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", + " {'description': 'Number of physical qubits for the T factories',\n", + " 'explanation': 'Each T factory requires 6480 physical qubits and we run 12 in parallel, therefore we need $77760 = 6480 \\\\cdot 12$ qubits.',\n", + " 'label': 'Physical T factory qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", + " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 28 logical qubits and the total cycle count 120.',\n", + " 'label': 'Required logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", + " {'description': 'The minimum T state error rate required for distilled T states',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 128.',\n", + " 'label': 'Required logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", + " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", + " 'explanation': 'The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.',\n", + " 'label': 'Number of T states per rotation',\n", + " 'path': 'physicalCountsFormatted/numTsPerRotation'}],\n", + " 'title': 'Resource estimates breakdown'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Name of QEC scheme',\n", + " 'explanation': 'You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.',\n", + " 'label': 'QEC scheme',\n", + " 'path': 'jobParams/qecScheme/name'},\n", + " {'description': 'Required code distance for error correction',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000014880952380952382)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'label': 'Code distance',\n", + " 'path': 'logicalQubit/codeDistance'},\n", + " {'description': 'Number of physical qubits per logical qubit',\n", + " 'explanation': 'The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'logicalQubit/physicalQubits'},\n", + " {'description': 'Duration of a logical cycle in nanoseconds',\n", + " 'explanation': 'The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.',\n", + " 'label': 'Logical cycle time',\n", + " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", + " {'description': 'Logical qubit error rate',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$',\n", + " 'label': 'Logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", + " {'description': 'Crossing prefactor used in QEC scheme',\n", + " 'explanation': 'The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.',\n", + " 'label': 'Crossing prefactor',\n", + " 'path': 'jobParams/qecScheme/crossingPrefactor'},\n", + " {'description': 'Error correction threshold used in QEC scheme',\n", + " 'explanation': 'The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.',\n", + " 'label': 'Error correction threshold',\n", + " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", + " {'description': 'QEC scheme formula used to compute logical cycle time',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 4us 400ns.',\n", + " 'label': 'Logical cycle time formula',\n", + " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", + " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 242.',\n", + " 'label': 'Physical qubits formula',\n", + " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", + " 'title': 'Logical qubit parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of physical qubits for a single T factory',\n", + " 'explanation': 'This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'tfactory/physicalQubits'},\n", + " {'description': 'Runtime of a single T factory',\n", + " 'explanation': 'The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", + " {'description': 'Number of output T states produced in a single run of T factory',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.',\n", + " 'label': 'Number of output T states per run',\n", + " 'path': 'tfactory/numTstates'},\n", + " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", + " 'explanation': 'This value includes the physical input T states of all copies of the distillation unit in the first round.',\n", + " 'label': 'Number of input T states per run',\n", + " 'path': 'tfactory/numInputTstates'},\n", + " {'description': 'The number of distillation rounds',\n", + " 'explanation': 'This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.',\n", + " 'label': 'Distillation rounds',\n", + " 'path': 'tfactory/numRounds'},\n", + " {'description': 'The number of units in each round of distillation',\n", + " 'explanation': 'This is the number of copies for the distillation units per round.',\n", + " 'label': 'Distillation units per round',\n", + " 'path': 'physicalCountsFormatted/numUnitsPerRound'},\n", + " {'description': 'The types of distillation units',\n", + " 'explanation': 'These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.',\n", + " 'label': 'Distillation units',\n", + " 'path': 'physicalCountsFormatted/unitNamePerRound'},\n", + " {'description': 'The code distance in each round of distillation',\n", + " 'explanation': 'This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.',\n", + " 'label': 'Distillation code distances',\n", + " 'path': 'physicalCountsFormatted/codeDistancePerRound'},\n", + " {'description': 'The number of physical qubits used in each round of distillation',\n", + " 'explanation': 'The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.',\n", + " 'label': 'Number of physical qubits per round',\n", + " 'path': 'physicalCountsFormatted/physicalQubitsPerRound'},\n", + " {'description': 'The runtime of each distillation round',\n", + " 'explanation': 'The runtime of the T factory is the sum of the runtimes in all rounds.',\n", + " 'label': 'Runtime per round',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", + " {'description': 'Logical T state error rate',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 3.91e-6.',\n", + " 'label': 'Logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", + " 'title': 'T factory parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", + " 'explanation': 'We determine 28 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'label': 'Logical qubits (pre-layout)',\n", + " 'path': 'logicalCounts/numQubits'},\n", + " {'description': 'Number of T gates in the input quantum program',\n", + " 'explanation': 'This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.',\n", + " 'label': 'T gates',\n", + " 'path': 'logicalCounts/tCount'},\n", + " {'description': 'Number of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.',\n", + " 'label': 'Rotation gates',\n", + " 'path': 'logicalCounts/rotationCount'},\n", + " {'description': 'Depth of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.',\n", + " 'label': 'Rotation depth',\n", + " 'path': 'logicalCounts/rotationDepth'},\n", + " {'description': 'Number of CCZ-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCZ gates.',\n", + " 'label': 'CCZ gates',\n", + " 'path': 'logicalCounts/cczCount'},\n", + " {'description': 'Number of CCiX-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].',\n", + " 'label': 'CCiX gates',\n", + " 'path': 'logicalCounts/ccixCount'},\n", + " {'description': 'Number of single qubit measurements in the input quantum program',\n", + " 'explanation': 'This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.',\n", + " 'label': 'Measurement operations',\n", + " 'path': 'logicalCounts/measurementCount'}],\n", + " 'title': 'Pre-layout logical resources'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Total error budget for the algorithm',\n", + " 'explanation': \"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\n", + " 'label': 'Total error budget',\n", + " 'path': 'physicalCountsFormatted/errorBudget'},\n", + " {'description': 'Probability of at least one logical error',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'Logical error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetLogical'},\n", + " {'description': 'Probability of at least one faulty T distillation',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'T distillation error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetTstates'},\n", + " {'description': 'Probability of at least one failed rotation synthesis',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3.',\n", + " 'label': 'Rotation synthesis error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetRotations'}],\n", + " 'title': 'Assumed error budget'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Some descriptive name for the qubit model',\n", + " 'explanation': 'You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).',\n", + " 'label': 'Qubit name',\n", + " 'path': 'jobParams/qubitParams/name'},\n", + " {'description': 'Underlying qubit technology (gate-based or Majorana)',\n", + " 'explanation': 'When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.',\n", + " 'label': 'Instruction set',\n", + " 'path': 'jobParams/qubitParams/instructionSet'},\n", + " {'description': 'Operation time for single-qubit measurement (t_meas) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.',\n", + " 'label': 'Single-qubit measurement time',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementTime'},\n", + " {'description': 'Operation time for single-qubit gate (t_gate) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.',\n", + " 'label': 'Single-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateTime'},\n", + " {'description': 'Operation time for two-qubit gate in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.',\n", + " 'label': 'Two-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateTime'},\n", + " {'description': 'Operation time for a T gate',\n", + " 'explanation': 'This is the operation time in nanoseconds to execute a T gate.',\n", + " 'label': 'T gate time',\n", + " 'path': 'jobParams/qubitParams/tGateTime'},\n", + " {'description': 'Error rate for single-qubit measurement',\n", + " 'explanation': 'This is the probability in which a single-qubit measurement in the Pauli basis may fail.',\n", + " 'label': 'Single-qubit measurement error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementErrorRate'},\n", + " {'description': 'Error rate for single-qubit Clifford gate (p)',\n", + " 'explanation': 'This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.',\n", + " 'label': 'Single-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateErrorRate'},\n", + " {'description': 'Error rate for two-qubit Clifford gate',\n", + " 'explanation': 'This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.',\n", + " 'label': 'Two-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateErrorRate'},\n", + " {'description': 'Error rate to prepare single-qubit T state or apply a T gate (p_T)',\n", + " 'explanation': 'This is the probability in which executing a single T gate may fail.',\n", + " 'label': 'T gate error rate',\n", + " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", + " 'title': 'Physical qubit parameters'}]},\n", + " 'status': 'success',\n", + " 'tfactory': {'codeDistancePerRound': [9],\n", + " 'logicalErrorRate': 2.165000000000001e-06,\n", + " 'numInputTstates': 30,\n", + " 'numRounds': 1,\n", + " 'numTstates': 1,\n", + " 'numUnitsPerRound': [2],\n", + " 'physicalQubits': 6480,\n", + " 'physicalQubitsPerRound': [6480],\n", + " 'runtime': 46800.0,\n", + " 'runtimePerRound': [46800.0],\n", + " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", "# result = qsharp.azure.output(\"...\")\n", @@ -372,7 +3286,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 17, "metadata": { "collapsed": false, "jupyter": { @@ -399,7 +3313,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 18, "metadata": { "collapsed": false, "jupyter": { @@ -412,10 +3326,37 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Logical algorithmic qubits = 28\n", + "Algorithmic depth = 120\n", + "Score = 3360\n" + ] + }, + { + "data": { + "text/plain": [ + "3360" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "evaluate_results(result)" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -423,9 +3364,9 @@ "name": "python3" }, "kernelspec": { - "display_name": "Python 3 [Default]", + "display_name": "Python 3 [Q#]", "language": "python", - "name": "python3" + "name": "python3_qsharp_b54crn" }, "language_info": { "codemirror_mode": { diff --git a/iQuHack-challenge-2023-task3.ipynb b/iQuHack-challenge-2023-task3.ipynb index 77ca776..77007c4 100644 --- a/iQuHack-challenge-2023-task3.ipynb +++ b/iQuHack-challenge-2023-task3.ipynb @@ -67,7 +67,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "collapsed": false, "jupyter": { @@ -80,7 +80,15 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Preparing Q# environment...\n" + ] + } + ], "source": [ "# Run this code cell to import the modules required to work with Q# and Azure\n", "import qsharp\n", @@ -89,7 +97,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": { "collapsed": false, "jupyter": { @@ -111,7 +119,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": { "collapsed": false, "jupyter": { @@ -148,7 +156,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": { "collapsed": false, "jupyter": { @@ -172,16 +180,38 @@ "\n", "// Task 3. \n", "// (input will contain 6 qubits)\n", - "operation Task3(input : Qubit[], target : Qubit) : Unit is Adj {\n", + "operation original(input : Qubit[], target : Qubit) : Unit is Adj {\n", " for i in [7, 11, 13, 14, 19, 21, 22, 25, 26, 28, 35, 37, 38, 41, 42, 44, 49, 50, 52, 56] {\n", " ControlledOnInt(i, X)(input, target);\n", " }\n", - "}" + "}\n", + "\n", + "operation CarryN(carryIn: Qubit, summand1: Qubit, summand2: Qubit, carryOut: Qubit) : Unit is Adj + Ctl {\n", + " CCNOT (summand1, summand2, carryOut);\n", + " CNOT (summand1, summand2);\n", + " CCNOT (carryIn, summand2, carryOut);\n", + " CNOT(carryIn, summand2);\n", + "}\n", + "\n", + "operation Task3(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " use output = Qubit[Length(input)+1] {\n", + " within {\n", + " output[0] = input[0]\n", + " for i in 1 .. Length(input) - 1 { \n", + " \n", + " }\n", + " } apply {\n", + " ControlledOnInt(3, X)(output, target);\n", + " }\n", + "\n", + " }\n", + "}\n", + "\n" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": { "collapsed": false, "jupyter": { @@ -238,7 +268,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": { "collapsed": false, "jupyter": { @@ -251,7 +281,3374 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": 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\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + "
Qubit IDs0, 1, 2, 3, 4, 5, 6
Basis state (bitstring)AmplitudeMeas. Pr.
$\\left|0000000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0000001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0000010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0000011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0000100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0000101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0000110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0000111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0001000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0001001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0001010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0001011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0001100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0001101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0001110\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0001111\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0010000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0010001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0010010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0010011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0010100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0010101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0010110\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0010111\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0011000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0011001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0011010\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0011011\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0011100\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0011101\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0011110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0011111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0100000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0100001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0100010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0100011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0100100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0100101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0100110\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0100111\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0101000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0101001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0101010\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0101011\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0101100\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0101101\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0101110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0101111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0110000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0110001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0110010\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0110011\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0110100\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0110101\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0110110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0110111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0111000\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0111001\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0111010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0111011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0111100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0111101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0111110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0111111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1000000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1000001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1000010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1000011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1000100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1000101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1000110\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1000111\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1001000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1001001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1001010\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1001011\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1001100\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1001101\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1001110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1001111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1010000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1010001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1010010\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1010011\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1010100\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1010101\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1010110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1010111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1011000\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1011001\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1011010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1011011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1011100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1011101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1011110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1011111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1100000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1100001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1100010\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1100011\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1100100\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1100101\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1100110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1100111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1101000\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1101001\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1101010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1101011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1101100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1101101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

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$\\left|1110010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1110011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1110100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1110101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1110110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1110111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1111000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1111001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1111010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1111011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1111100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1111101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1111110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1111111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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"execution_count": null, + "execution_count": 8, "metadata": { "collapsed": false, "jupyter": { @@ -289,19 +3686,68 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "\"Connecting to Azure Quantum...\"", + "text/plain": [ + "Connecting to Azure Quantum..." + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Connected to Azure Quantum workspace azure-q in location uksouth.\n" + ] + }, + { + "data": { + "text/plain": [ + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 305641},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 361199},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 2},\n", + " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 184},\n", + " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 184},\n", + " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.qpu.aspen-m-2', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", "# If you're using this notebook in qBraid, keep it\n", "qsharp.azure.connect(\n", - " resourceId=\"...\",\n", - " location=\"...\",\n", + " resourceId=\"/subscriptions/7fc54e95-14cf-4a6f-b50e-d6155c241309/resourceGroups/AzureQuantum/providers/Microsoft.Quantum/Workspaces/azure-q\",\n", + " location=\"UK South\",\n", " credential=\"CLI\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "metadata": { "collapsed": false, "jupyter": { @@ -314,14 +3760,33 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loading package Microsoft.Quantum.Providers.Core and dependencies...\n", + "Active target is now microsoft.estimator\n" + ] + }, + { + "data": { + "text/plain": [ + "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "qsharp.azure.target(\"microsoft.estimator\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "metadata": { "collapsed": false, "jupyter": { @@ -334,7 +3799,21 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Submitting Task3_ResourceEstimationWrapper to target microsoft.estimator...\n", + "Job successfully submitted.\n", + " Job name: RE for the task 3\n", + " Job ID: 4ac53537-57cd-424e-9937-c6019dacbc0a\n", + "Waiting up to 30 seconds for Azure Quantum job to complete...\n", + "[6:25:13 AM] Current job status: Executing\n", + "[6:25:18 AM] Current job status: Succeeded\n" + ] + } + ], "source": [ "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", "result = qsharp.azure.execute(Task3_ResourceEstimationWrapper, jobName=\"RE for the task 3\")" @@ -342,7 +3821,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, "metadata": { "collapsed": false, "jupyter": { @@ -355,7 +3834,1051 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":80,\"cczCount\":20,\"measurementCount\":80,\"numQubits\":11,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":380,\"algorithmicLogicalQubits\":33,\"cliffordErrorRate\":0.001,\"logicalDepth\":380,\"numTfactories\":14,\"numTfactoryRuns\":29,\"numTsPerRotation\":null,\"numTstates\":400,\"physicalQubitsForAlgorithm\":7986,\"physicalQubitsForTfactories\":135520,\"requiredLogicalQubitErrorRate\":3.987240829346092E-08,\"requiredLogicalTstateErrorRate\":1.25E-06},\"physicalQubits\":143506,\"runtime\":1672000},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"11\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"94.44 %\",\"physicalQubitsPerRound\":\"9680\",\"requiredLogicalQubitErrorRate\":\"3.99e-8\",\"requiredLogicalTstateErrorRate\":\"1.25e-6\",\"runtime\":\"1ms 672us\",\"tfactoryRuntime\":\"57us 200ns\",\"tfactoryRuntimePerRound\":\"57us 200ns\",\"tstateLogicalErrorRate\":\"2.48e-7\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 7986 physical qubits to implement the algorithm logic, and 135520 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 380 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 11$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 33$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 80 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 20 CCZ and 80 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 380. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 20 CCZ and 80 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 400 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{400\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 1ms 672us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 400 T states, the 14 copies of the T factory are repeatedly invoked 29 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 7986 are the product of the 33 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 9680 physical qubits and we run 14 in parallel, therefore we need $135520 = 9680 \\\\cdot 14$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 380.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 400.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000003987240829346092)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or ¬µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[11],\"logicalErrorRate\":2.480000000000001E-07,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":9680,\"physicalQubitsPerRound\":[9680],\"runtime\":57200.0,\"runtimePerRound\":[57200.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "text/html": [ + "\r\n", + "
\r\n", + " \r\n", + " Physical resource estimates\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits143506\r\n", + "

Number of physical qubits

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This value represents the total number of physical qubits, which is the sum of 7986 physical qubits to implement the algorithm logic, and 135520 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

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Runtime1ms 672us\r\n", + "

Total runtime

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This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 380 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

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Logical algorithmic qubits33\r\n", + "

Number of logical qubits for the algorithm after layout

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Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 11\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 33$ logical qubits.

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Algorithmic depth380\r\n", + "

Number of logical cycles for the algorithm

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To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 80 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 20 CCZ and 80 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

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Logical depth380\r\n", + "

Number of logical cycles performed

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This number is usually equal to the logical depth of the algorithm, which is 380. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

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Number of T states400\r\n", + "

Number of T states consumed by the algorithm

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To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 20 CCZ and 80 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

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Number of T factories14\r\n", + "

Number of T factories capable of producing the demanded 400 T states during the algorithm's runtime

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The total number of T factories 14 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{400\\;\\text{T states} \\cdot 57us 200ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 1ms 672us\\;\\text{algorithm runtime}}\\right\\rceil\\)

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Number of T factory invocations29\r\n", + "

Number of times all T factories are invoked

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In order to prepare the 400 T states, the 14 copies of the T factory are repeatedly invoked 29 times.

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Physical algorithmic qubits7986\r\n", + "

Number of physical qubits for the algorithm after layout

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The 7986 are the product of the 33 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.

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Physical T factory qubits135520\r\n", + "

Number of physical qubits for the T factories

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Each T factory requires 9680 physical qubits and we run 14 in parallel, therefore we need $135520 = 9680 \\cdot 14$ qubits.

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Required logical qubit error rate3.99e-8\r\n", + "

The minimum logical qubit error rate required to run the algorithm within the error budget

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The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 380.

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Required logical T state error rate1.25e-6\r\n", + "

The minimum T state error rate required for distilled T states

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The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 400.

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Number of T states per rotationNo rotations in algorithm\r\n", + "

Number of T states to implement a rotation with an arbitrary angle

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The number of T states to implement a rotation with an arbitrary angle is \\(\\lceil 0.53 \\log_2(0 / 0) + 5.3\\rceil\\) [arXiv:2203.10064]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.

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QEC schemesurface_code\r\n", + "

Name of QEC scheme

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You can load pre-defined QEC schemes by using the name surface_code or floquet_code. The latter only works with Majorana qubits.

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Code distance11\r\n", + "

Required code distance for error correction

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The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000003987240829346092)}{\\log(0.01/0.001)} - 1\\)

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Physical qubits242\r\n", + "

Number of physical qubits per logical qubit

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The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.

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Logical cycle time4us 400ns\r\n", + "

Duration of a logical cycle in nanoseconds

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The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.

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Logical qubit error rate3.00e-8\r\n", + "

Logical qubit error rate

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\r\n", + "

The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{11 + 1}{2}$

\n", + "\r\n", + "
Crossing prefactor0.03\r\n", + "

Crossing prefactor used in QEC scheme

\n", + "\r\n", + "
\r\n", + "

The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.

\n", + "\r\n", + "
Error correction threshold0.01\r\n", + "

Error correction threshold used in QEC scheme

\n", + "\r\n", + "
\r\n", + "

The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.

\n", + "\r\n", + "
Logical cycle time formula(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\r\n", + "

QEC scheme formula used to compute logical cycle time

\n", + "\r\n", + "
\r\n", + "

This is the formula that is used to compute the logical cycle time 4us 400ns.

\n", + "\r\n", + "
Physical qubits formula2 * codeDistance * codeDistance\r\n", + "

QEC scheme formula used to compute number of physical qubits per logical qubit

\n", + "\r\n", + "
\r\n", + "

This is the formula that is used to compute the number of physical qubits per logical qubits 242.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " T factory parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits9680\r\n", + "

Number of physical qubits for a single T factory

\n", + "\r\n", + "
\r\n", + "

This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.

\n", + "\r\n", + "
Runtime57us 200ns\r\n", + "

Runtime of a single T factory

\n", + "\r\n", + "
\r\n", + "

The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.

\n", + "\r\n", + "
Number of output T states per run1\r\n", + "

Number of output T states produced in a single run of T factory

\n", + "\r\n", + "
\r\n", + "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.

\n", + "\r\n", + "
Number of input T states per run30\r\n", + "

Number of physical input T states consumed in a single run of a T factory

\n", + "\r\n", + "
\r\n", + "

This value includes the physical input T states of all copies of the distillation unit in the first round.

\n", + "\r\n", + "
Distillation rounds1\r\n", + "

The number of distillation rounds

\n", + "\r\n", + "
\r\n", + "

This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.

\n", + "\r\n", + "
Distillation units per round2\r\n", + "

The number of units in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the number of copies for the distillation units per round.

\n", + "\r\n", + "
Distillation units15-to-1 space efficient logical\r\n", + "

The types of distillation units

\n", + "\r\n", + "
\r\n", + "

These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.

\n", + "\r\n", + "
Distillation code distances11\r\n", + "

The code distance in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.

\n", + "\r\n", + "
Number of physical qubits per round9680\r\n", + "

The number of physical qubits used in each round of distillation

\n", + "\r\n", + "
\r\n", + "

The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.

\n", + "\r\n", + "
Runtime per round57us 200ns\r\n", + "

The runtime of each distillation round

\n", + "\r\n", + "
\r\n", + "

The runtime of the T factory is the sum of the runtimes in all rounds.

\n", + "\r\n", + "
Logical T state error rate2.48e-7\r\n", + "

Logical T state error rate

\n", + "\r\n", + "
\r\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-6.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Pre-layout logical resources\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Logical qubits (pre-layout)11\r\n", + "

Number of logical qubits in the input quantum program

\n", + "\r\n", + "
\r\n", + "

We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", + "\r\n", + "
T gates0\r\n", + "

Number of T gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.

\n", + "\r\n", + "
Rotation gates0\r\n", + "

Number of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.

\n", + "\r\n", + "
Rotation depth0\r\n", + "

Depth of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.

\n", + "\r\n", + "
CCZ gates20\r\n", + "

Number of CCZ-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCZ gates.

\n", + "\r\n", + "
CCiX gates80\r\n", + "

Number of CCiX-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCiX gates, which applies \\(-iX\\) controlled on two control qubits [1212.5069].

\n", + "\r\n", + "
Measurement operations80\r\n", + "

Number of single qubit measurements in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Assumed error budget\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Total error budget1.00e-3\r\n", + "

Total error budget for the algorithm

\n", + "\r\n", + "
\r\n", + "

The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget \\(\\epsilon = \\epsilon_{\\log} + \\epsilon_{\\rm dis} + \\epsilon_{\\rm syn}\\) is uniformly distributed and applies to errors \\(\\epsilon_{\\log}\\) to implement logical qubits, an error budget \\(\\epsilon_{\\rm dis}\\) to produce T states through distillation, and an error budget \\(\\epsilon_{\\rm syn}\\) to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets \\(\\epsilon_{\\rm dis}\\) and \\(\\epsilon_{\\rm syn}\\) are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.

\n", + "\r\n", + "
Logical error probability5.00e-4\r\n", + "

Probability of at least one logical error

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
T distillation error probability5.00e-4\r\n", + "

Probability of at least one faulty T distillation

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
Rotation synthesis error probability0.00e0\r\n", + "

Probability of at least one failed rotation synthesis

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Physical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Qubit namequbit_gate_ns_e3\r\n", + "

Some descriptive name for the qubit model

\n", + "\r\n", + "
\r\n", + "

You can load pre-defined qubit parameters by using the names qubit_gate_ns_e3, qubit_gate_ns_e4, qubit_gate_us_e3, qubit_gate_us_e4, qubit_maj_ns_e4, or qubit_maj_ns_e6. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).

\n", + "\r\n", + "
Instruction setGateBased\r\n", + "

Underlying qubit technology (gate-based or Majorana)

\n", + "\r\n", + "
\r\n", + "

When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either gate-based or Majorana. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.

\n", + "\r\n", + "
Single-qubit measurement time100 ns\r\n", + "

Operation time for single-qubit measurement (t_meas) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.

\n", + "\r\n", + "
Single-qubit gate time50 ns\r\n", + "

Operation time for single-qubit gate (t_gate) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.

\n", + "\r\n", + "
Two-qubit gate time50 ns\r\n", + "

Operation time for two-qubit gate in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.

\n", + "\r\n", + "
T gate time50 ns\r\n", + "

Operation time for a T gate

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to execute a T gate.

\n", + "\r\n", + "
Single-qubit measurement error rate0.001\r\n", + "

Error rate for single-qubit measurement

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit measurement in the Pauli basis may fail.

\n", + "\r\n", + "
Single-qubit error rate0.001\r\n", + "

Error rate for single-qubit Clifford gate (p)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.

\n", + "\r\n", + "
Two-qubit error rate0.001\r\n", + "

Error rate for two-qubit Clifford gate

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.

\n", + "\r\n", + "
T gate error rate0.001\r\n", + "

Error rate to prepare single-qubit T state or apply a T gate (p_T)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which executing a single T gate may fail.

\n", + "\r\n", + "
\n", + "
\r\n", + " Assumptions\r\n", + "
    \n", + "

  • More details on the following lists of assumptions can be found in the paper Accessing requirements for scaling quantum computers and their applications.

    \n", + "
    • \n", + "

  • Uniform independent physical noise. We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.

    \n", + "
    • \n", + "

  • Efficient classical computation. We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.

    \n", + "
    • \n", + "

  • Extraction circuits for planar quantum ISA. We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).

    \n", + "
    • \n", + "

  • Uniform independent logical noise. We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.

    \n", + "
    • \n", + "

  • Negligible Clifford costs for synthesis. We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.

    \n", + "
    • \n", + "

  • Smooth magic state consumption rate. We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.

    \n", + "
    • \n", + "
\n" + ], + "text/plain": [ + "{'errorBudget': {'logical': 0.0005, 'rotations': 0.0, 'tstates': 0.0005},\n", + " 'jobParams': {'errorBudget': 0.001,\n", + " 'qecScheme': {'crossingPrefactor': 0.03,\n", + " 'errorCorrectionThreshold': 0.01,\n", + " 'logicalCycleTime': '(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance',\n", + " 'name': 'surface_code',\n", + " 'physicalQubitsPerLogicalQubit': '2 * codeDistance * codeDistance'},\n", + " 'qubitParams': {'instructionSet': 'GateBased',\n", + " 'name': 'qubit_gate_ns_e3',\n", + " 'oneQubitGateErrorRate': 0.001,\n", + " 'oneQubitGateTime': '50 ns',\n", + " 'oneQubitMeasurementErrorRate': 0.001,\n", + " 'oneQubitMeasurementTime': '100 ns',\n", + " 'tGateErrorRate': 0.001,\n", + " 'tGateTime': '50 ns',\n", + " 'twoQubitGateErrorRate': 0.001,\n", + " 'twoQubitGateTime': '50 ns'}},\n", + " 'logicalCounts': {'ccixCount': 80,\n", + " 'cczCount': 20,\n", + " 'measurementCount': 80,\n", + " 'numQubits': 11,\n", + " 'rotationCount': 0,\n", + " 'rotationDepth': 0,\n", + " 'tCount': 0},\n", + " 'logicalQubit': {'codeDistance': 11,\n", + " 'logicalCycleTime': 4400.0,\n", + " 'logicalErrorRate': 3.000000000000002e-08,\n", + " 'physicalQubits': 242},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 380,\n", + " 'algorithmicLogicalQubits': 33,\n", + " 'cliffordErrorRate': 0.001,\n", + " 'logicalDepth': 380,\n", + " 'numTfactories': 14,\n", + " 'numTfactoryRuns': 29,\n", + " 'numTsPerRotation': None,\n", + " 'numTstates': 400,\n", + " 'physicalQubitsForAlgorithm': 7986,\n", + " 'physicalQubitsForTfactories': 135520,\n", + " 'requiredLogicalQubitErrorRate': 3.987240829346092e-08,\n", + " 'requiredLogicalTstateErrorRate': 1.25e-06},\n", + " 'physicalQubits': 143506,\n", + " 'runtime': 1672000},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '11',\n", + " 'errorBudget': '1.00e-3',\n", + " 'errorBudgetLogical': '5.00e-4',\n", + " 'errorBudgetRotations': '0.00e0',\n", + " 'errorBudgetTstates': '5.00e-4',\n", + " 'logicalCycleTime': '4us 400ns',\n", + " 'logicalErrorRate': '3.00e-8',\n", + " 'numTsPerRotation': 'No rotations in algorithm',\n", + " 'numUnitsPerRound': '2',\n", + " 'physicalQubitsForTfactoriesPercentage': '94.44 %',\n", + " 'physicalQubitsPerRound': '9680',\n", + " 'requiredLogicalQubitErrorRate': '3.99e-8',\n", + " 'requiredLogicalTstateErrorRate': '1.25e-6',\n", + " 'runtime': '1ms 672us',\n", + " 'tfactoryRuntime': '57us 200ns',\n", + " 'tfactoryRuntimePerRound': '57us 200ns',\n", + " 'tstateLogicalErrorRate': '2.48e-7',\n", + " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", + " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", + " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", + " '**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.',\n", + " '**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).',\n", + " '**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.',\n", + " '**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.',\n", + " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", + " 'groups': [{'alwaysVisible': True,\n", + " 'entries': [{'description': 'Number of physical qubits',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 7986 physical qubits to implement the algorithm logic, and 135520 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'physicalCounts/physicalQubits'},\n", + " {'description': 'Total runtime',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 380 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/runtime'}],\n", + " 'title': 'Physical resource estimates'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 11$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 33$ logical qubits.',\n", + " 'label': 'Logical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", + " {'description': 'Number of logical cycles for the algorithm',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 80 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 20 CCZ and 80 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'label': 'Algorithmic depth',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", + " {'description': 'Number of logical cycles performed',\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 380. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'label': 'Logical depth',\n", + " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", + " {'description': 'Number of T states consumed by the algorithm',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 20 CCZ and 80 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'label': 'Number of T states',\n", + " 'path': 'physicalCounts/breakdown/numTstates'},\n", + " {'description': \"Number of T factories capable of producing the demanded 400 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{400\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 1ms 672us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " 'label': 'Number of T factories',\n", + " 'path': 'physicalCounts/breakdown/numTfactories'},\n", + " {'description': 'Number of times all T factories are invoked',\n", + " 'explanation': 'In order to prepare the 400 T states, the 14 copies of the T factory are repeatedly invoked 29 times.',\n", + " 'label': 'Number of T factory invocations',\n", + " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", + " {'description': 'Number of physical qubits for the algorithm after layout',\n", + " 'explanation': 'The 7986 are the product of the 33 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.',\n", + " 'label': 'Physical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", + " {'description': 'Number of physical qubits for the T factories',\n", + " 'explanation': 'Each T factory requires 9680 physical qubits and we run 14 in parallel, therefore we need $135520 = 9680 \\\\cdot 14$ qubits.',\n", + " 'label': 'Physical T factory qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", + " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 380.',\n", + " 'label': 'Required logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", + " {'description': 'The minimum T state error rate required for distilled T states',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 400.',\n", + " 'label': 'Required logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", + " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", + " 'explanation': 'The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.',\n", + " 'label': 'Number of T states per rotation',\n", + " 'path': 'physicalCountsFormatted/numTsPerRotation'}],\n", + " 'title': 'Resource estimates breakdown'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Name of QEC scheme',\n", + " 'explanation': 'You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.',\n", + " 'label': 'QEC scheme',\n", + " 'path': 'jobParams/qecScheme/name'},\n", + " {'description': 'Required code distance for error correction',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000003987240829346092)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'label': 'Code distance',\n", + " 'path': 'logicalQubit/codeDistance'},\n", + " {'description': 'Number of physical qubits per logical qubit',\n", + " 'explanation': 'The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'logicalQubit/physicalQubits'},\n", + " {'description': 'Duration of a logical cycle in nanoseconds',\n", + " 'explanation': 'The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.',\n", + " 'label': 'Logical cycle time',\n", + " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", + " {'description': 'Logical qubit error rate',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$',\n", + " 'label': 'Logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", + " {'description': 'Crossing prefactor used in QEC scheme',\n", + " 'explanation': 'The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.',\n", + " 'label': 'Crossing prefactor',\n", + " 'path': 'jobParams/qecScheme/crossingPrefactor'},\n", + " {'description': 'Error correction threshold used in QEC scheme',\n", + " 'explanation': 'The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.',\n", + " 'label': 'Error correction threshold',\n", + " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", + " {'description': 'QEC scheme formula used to compute logical cycle time',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 4us 400ns.',\n", + " 'label': 'Logical cycle time formula',\n", + " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", + " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 242.',\n", + " 'label': 'Physical qubits formula',\n", + " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", + " 'title': 'Logical qubit parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of physical qubits for a single T factory',\n", + " 'explanation': 'This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'tfactory/physicalQubits'},\n", + " {'description': 'Runtime of a single T factory',\n", + " 'explanation': 'The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", + " {'description': 'Number of output T states produced in a single run of T factory',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.',\n", + " 'label': 'Number of output T states per run',\n", + " 'path': 'tfactory/numTstates'},\n", + " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", + " 'explanation': 'This value includes the physical input T states of all copies of the distillation unit in the first round.',\n", + " 'label': 'Number of input T states per run',\n", + " 'path': 'tfactory/numInputTstates'},\n", + " {'description': 'The number of distillation rounds',\n", + " 'explanation': 'This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.',\n", + " 'label': 'Distillation rounds',\n", + " 'path': 'tfactory/numRounds'},\n", + " {'description': 'The number of units in each round of distillation',\n", + " 'explanation': 'This is the number of copies for the distillation units per round.',\n", + " 'label': 'Distillation units per round',\n", + " 'path': 'physicalCountsFormatted/numUnitsPerRound'},\n", + " {'description': 'The types of distillation units',\n", + " 'explanation': 'These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.',\n", + " 'label': 'Distillation units',\n", + " 'path': 'physicalCountsFormatted/unitNamePerRound'},\n", + " {'description': 'The code distance in each round of distillation',\n", + " 'explanation': 'This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.',\n", + " 'label': 'Distillation code distances',\n", + " 'path': 'physicalCountsFormatted/codeDistancePerRound'},\n", + " {'description': 'The number of physical qubits used in each round of distillation',\n", + " 'explanation': 'The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.',\n", + " 'label': 'Number of physical qubits per round',\n", + " 'path': 'physicalCountsFormatted/physicalQubitsPerRound'},\n", + " {'description': 'The runtime of each distillation round',\n", + " 'explanation': 'The runtime of the T factory is the sum of the runtimes in all rounds.',\n", + " 'label': 'Runtime per round',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", + " {'description': 'Logical T state error rate',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-6.',\n", + " 'label': 'Logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", + " 'title': 'T factory parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", + " 'explanation': 'We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'label': 'Logical qubits (pre-layout)',\n", + " 'path': 'logicalCounts/numQubits'},\n", + " {'description': 'Number of T gates in the input quantum program',\n", + " 'explanation': 'This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.',\n", + " 'label': 'T gates',\n", + " 'path': 'logicalCounts/tCount'},\n", + " {'description': 'Number of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.',\n", + " 'label': 'Rotation gates',\n", + " 'path': 'logicalCounts/rotationCount'},\n", + " {'description': 'Depth of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.',\n", + " 'label': 'Rotation depth',\n", + " 'path': 'logicalCounts/rotationDepth'},\n", + " {'description': 'Number of CCZ-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCZ gates.',\n", + " 'label': 'CCZ gates',\n", + " 'path': 'logicalCounts/cczCount'},\n", + " {'description': 'Number of CCiX-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].',\n", + " 'label': 'CCiX gates',\n", + " 'path': 'logicalCounts/ccixCount'},\n", + " {'description': 'Number of single qubit measurements in the input quantum program',\n", + " 'explanation': 'This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.',\n", + " 'label': 'Measurement operations',\n", + " 'path': 'logicalCounts/measurementCount'}],\n", + " 'title': 'Pre-layout logical resources'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Total error budget for the algorithm',\n", + " 'explanation': \"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\n", + " 'label': 'Total error budget',\n", + " 'path': 'physicalCountsFormatted/errorBudget'},\n", + " {'description': 'Probability of at least one logical error',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'Logical error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetLogical'},\n", + " {'description': 'Probability of at least one faulty T distillation',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'T distillation error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetTstates'},\n", + " {'description': 'Probability of at least one failed rotation synthesis',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3.',\n", + " 'label': 'Rotation synthesis error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetRotations'}],\n", + " 'title': 'Assumed error budget'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Some descriptive name for the qubit model',\n", + " 'explanation': 'You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).',\n", + " 'label': 'Qubit name',\n", + " 'path': 'jobParams/qubitParams/name'},\n", + " {'description': 'Underlying qubit technology (gate-based or Majorana)',\n", + " 'explanation': 'When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.',\n", + " 'label': 'Instruction set',\n", + " 'path': 'jobParams/qubitParams/instructionSet'},\n", + " {'description': 'Operation time for single-qubit measurement (t_meas) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.',\n", + " 'label': 'Single-qubit measurement time',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementTime'},\n", + " {'description': 'Operation time for single-qubit gate (t_gate) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.',\n", + " 'label': 'Single-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateTime'},\n", + " {'description': 'Operation time for two-qubit gate in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.',\n", + " 'label': 'Two-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateTime'},\n", + " {'description': 'Operation time for a T gate',\n", + " 'explanation': 'This is the operation time in nanoseconds to execute a T gate.',\n", + " 'label': 'T gate time',\n", + " 'path': 'jobParams/qubitParams/tGateTime'},\n", + " {'description': 'Error rate for single-qubit measurement',\n", + " 'explanation': 'This is the probability in which a single-qubit measurement in the Pauli basis may fail.',\n", + " 'label': 'Single-qubit measurement error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementErrorRate'},\n", + " {'description': 'Error rate for single-qubit Clifford gate (p)',\n", + " 'explanation': 'This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.',\n", + " 'label': 'Single-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateErrorRate'},\n", + " {'description': 'Error rate for two-qubit Clifford gate',\n", + " 'explanation': 'This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.',\n", + " 'label': 'Two-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateErrorRate'},\n", + " {'description': 'Error rate to prepare single-qubit T state or apply a T gate (p_T)',\n", + " 'explanation': 'This is the probability in which executing a single T gate may fail.',\n", + " 'label': 'T gate error rate',\n", + " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", + " 'title': 'Physical qubit parameters'}]},\n", + " 'status': 'success',\n", + " 'tfactory': {'codeDistancePerRound': [11],\n", + " 'logicalErrorRate': 2.480000000000001e-07,\n", + " 'numInputTstates': 30,\n", + " 'numRounds': 1,\n", + " 'numTstates': 1,\n", + " 'numUnitsPerRound': [2],\n", + " 'physicalQubits': 9680,\n", + " 'physicalQubitsPerRound': [9680],\n", + " 'runtime': 57200.0,\n", + " 'runtimePerRound': [57200.0],\n", + " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", "# result = qsharp.azure.output(\"...\")\n", @@ -364,7 +4887,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "metadata": { "collapsed": false, "jupyter": { @@ -391,7 +4914,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, "metadata": { "collapsed": false, "jupyter": { @@ -404,10 +4927,44 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Logical algorithmic qubits = 33\n", + "Algorithmic depth = 380\n", + "Score = 12540\n" + ] + }, + { + "data": { + "text/plain": [ + "12540" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "evaluate_results(result)" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -415,9 +4972,9 @@ "name": "python3" }, "kernelspec": { - "display_name": "Python 3 [Default]", + "display_name": "Python 3 [Q#]", "language": "python", - "name": "python3" + "name": "python3_qsharp_b54crn" }, "language_info": { "codemirror_mode": { diff --git a/iQuHack-challenge-2023-task4.ipynb b/iQuHack-challenge-2023-task4.ipynb index 2dd1a7b..be835ea 100644 --- a/iQuHack-challenge-2023-task4.ipynb +++ b/iQuHack-challenge-2023-task4.ipynb @@ -34,7 +34,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "collapsed": false, "jupyter": { @@ -47,7 +47,41 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\u001b[93mTo sign in, use a web browser to open the page https://microsoft.com/devicelogin and enter the code AXM2895LG to authenticate.\u001b[0m\n", + "[\n", + " {\n", + " \"cloudName\": \"AzureCloud\",\n", + " \"homeTenantId\": \"b4e518fe-3bdc-4371-a4be-7f3d83d7acbd\",\n", + " \"id\": \"7fc54e95-14cf-4a6f-b50e-d6155c241309\",\n", + " \"isDefault\": true,\n", + " \"managedByTenants\": [\n", + " {\n", + " \"tenantId\": \"d0ecd01b-d782-448e-bae0-c3cad0e0543a\"\n", + " },\n", + " {\n", + " \"tenantId\": \"94c4857e-1130-4ab8-8eac-069b40c9db20\"\n", + " },\n", + " {\n", + " \"tenantId\": \"f702a9dc-ae48-4dc7-8f0a-8155a6dfa4e5\"\n", + " }\n", + " ],\n", + " \"name\": \"Azure subscription 1\",\n", + " \"state\": \"Enabled\",\n", + " \"tenantId\": \"b4e518fe-3bdc-4371-a4be-7f3d83d7acbd\",\n", + " \"user\": {\n", + " \"name\": \"hachall@hotmail.com\",\n", + " \"type\": \"user\"\n", + " }\n", + " }\n", + "]\n" + ] + } + ], "source": [ "!az login" ] @@ -67,7 +101,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, "metadata": { "collapsed": false, "jupyter": { @@ -89,7 +123,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "metadata": { "collapsed": false, "jupyter": { @@ -104,14 +138,14 @@ }, "outputs": [], "source": [ - "teamname=\"msft_is_the_best\" # Update this field with your team name\n", + "teamname=\"schrodingers-duck\" # Update this field with your team name\n", "task=[\"task4\"]\n", - "slack_id=\"myslackid\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + "slack_id=\"U04L3SFUCQ2\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, "metadata": { "collapsed": false, "jupyter": { @@ -148,7 +182,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 14, "metadata": { "collapsed": false, "jupyter": { @@ -169,20 +203,62 @@ "%%qsharp\n", "open Microsoft.Quantum.Canon;\n", "open Microsoft.Quantum.Diagnostics;\n", + "open Microsoft.Quantum.Arrays;\n", "\n", "// Task 4. \n", "// (input will contain 7 qubits)\n", - "operation Task4(input : Qubit[], target : Qubit) : Unit is Adj {\n", + "operation original(input : Qubit[], target : Qubit) : Unit is Adj {\n", " let N = Length(input);\n", " for i in 0 .. 3 .. 2^N - 1 {\n", " ControlledOnInt(i, X)(input, target);\n", " }\n", + "}\n", + "\n", + "operation mod3adder (reg : Qubit[]) : Unit is Adj+Ctl {\n", + " let sum = reg[0];\n", + " let carry = reg[1];\n", + " ControlledOnInt(0, X)([carry], sum);\n", + " ControlledOnInt(0, X)([sum], carry);\n", + "}\n", + "\n", + "operation Task4(input : Qubit[], target : Qubit) : Unit is Adj+Ctl {\n", + " use output = Qubit[2] {\n", + " within {\n", + " for i in 0 .. Length(input) - 1 {\n", + " if (i % 2 == 0) {\n", + " Controlled mod3adder([input[i]], output);\n", + " } else {\n", + " Controlled Adjoint mod3adder([input[i]], output);\n", + " }\n", + " }\n", + " } apply {\n", + " ControlledOnInt(0, X)(output, target);\n", + " }\n", + "\n", + " }\n", + "}\n", + "\n", + "operation QubitArrayWrapperOperation (op : ((Qubit[], Qubit) => Unit is Adj), qs : Qubit[]) : Unit is Adj { \n", + " op(Most(qs), Tail(qs));\n", + "}\n", + "\n", + "operation TestCompoundGate () : Unit {\n", + " AssertOperationsEqualReferenced(7+1, QubitArrayWrapperOperation(Task4, _), QubitArrayWrapperOperation (original, _));\n", "}" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "TestCompoundGate();" + ] + }, + { + "cell_type": "code", + "execution_count": 16, "metadata": { "collapsed": false, "jupyter": { @@ -239,7 +315,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 17, "metadata": { "collapsed": false, "jupyter": { @@ -252,7 +328,3374 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": 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Qubit IDs0, 1, 2, 3, 4, 5, 6, 7
Basis state (bitstring)AmplitudeMeas. Pr.
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$\\left|1010001100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1010111100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10110000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10110010\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1011010100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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"text/plain": [ + "()" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# Note that in the output of this cell the target qubit corresponds to the rightmost bit\n", "qsharp.config[\"dump.basisStateLabelingConvention\"]=\"Bitstring\"\n", @@ -277,7 +3720,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 18, "metadata": { "collapsed": false, "jupyter": { @@ -290,19 +3733,68 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "\"Connecting to Azure Quantum...\"", + "text/plain": [ + "Connecting to Azure Quantum..." + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Connected to Azure Quantum workspace azure-q in location uksouth.\n" + ] + }, + { + "data": { + "text/plain": [ + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 300492},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 366858},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 3},\n", + " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 184},\n", + " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 184},\n", + " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.qpu.aspen-m-2', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", "# If you're using this notebook in qBraid, keep it\n", "qsharp.azure.connect(\n", - " resourceId=\"...\",\n", - " location=\"...\",\n", + " resourceId=\"/subscriptions/7fc54e95-14cf-4a6f-b50e-d6155c241309/resourceGroups/AzureQuantum/providers/Microsoft.Quantum/Workspaces/azure-q\",\n", + " location=\"UK South\",\n", " credential=\"CLI\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 19, "metadata": { "collapsed": false, "jupyter": { @@ -315,14 +3807,33 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loading package Microsoft.Quantum.Providers.Core and dependencies...\n", + "Active target is now microsoft.estimator\n" + ] + }, + { + "data": { + "text/plain": [ + "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "qsharp.azure.target(\"microsoft.estimator\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 20, "metadata": { "collapsed": false, "jupyter": { @@ -335,7 +3846,21 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Submitting Task4_ResourceEstimationWrapper to target microsoft.estimator...\n", + "Job successfully submitted.\n", + " Job name: RE for the task 4\n", + " Job ID: 2a3bcaee-0b5a-4691-94a1-6518f829abac\n", + "Waiting up to 30 seconds for Azure Quantum job to complete...\n", + "[8:02:31 AM] Current job status: Executing\n", + "[8:02:36 AM] Current job status: Succeeded\n" + ] + } + ], "source": [ "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", "result = qsharp.azure.execute(Task4_ResourceEstimationWrapper, jobName=\"RE for the task 4\")" @@ -343,7 +3868,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 21, "metadata": { "collapsed": false, "jupyter": { @@ -356,7 +3881,1051 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":0,\"cczCount\":29,\"measurementCount\":0,\"numQubits\":10,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":87,\"algorithmicLogicalQubits\":30,\"cliffordErrorRate\":0.001,\"logicalDepth\":87,\"numTfactories\":15,\"numTfactoryRuns\":8,\"numTsPerRotation\":null,\"numTstates\":116,\"physicalQubitsForAlgorithm\":7260,\"physicalQubitsForTfactories\":97200,\"requiredLogicalQubitErrorRate\":1.9157088122605365E-07,\"requiredLogicalTstateErrorRate\":4.310344827586207E-06},\"physicalQubits\":104460,\"runtime\":382800},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"93.05 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"1.92e-7\",\"requiredLogicalTstateErrorRate\":\"4.31e-6\",\"runtime\":\"382us 800ns\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 7260 physical qubits to implement the algorithm logic, and 97200 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 87 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 10$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 30$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 0 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 29 CCZ and 0 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 87. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 29 CCZ and 0 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 116 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 15 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{116\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 382us 800ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 116 T states, the 15 copies of the T factory are repeatedly invoked 8 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 7260 are the product of the 30 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 15 in parallel, therefore we need $97200 = 6480 \\\\cdot 15$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 30 logical qubits and the total cycle count 87.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 116.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000019157088122605365)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 4.31e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 30 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or ¬µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "text/html": [ + "\r\n", + "
\r\n", + " \r\n", + " Physical resource estimates\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits104460\r\n", + "

Number of physical qubits

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This value represents the total number of physical qubits, which is the sum of 7260 physical qubits to implement the algorithm logic, and 97200 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

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Runtime382us 800ns\r\n", + "

Total runtime

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This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 87 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

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Logical algorithmic qubits30\r\n", + "

Number of logical qubits for the algorithm after layout

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Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 10\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 30$ logical qubits.

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Algorithmic depth87\r\n", + "

Number of logical cycles for the algorithm

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To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 0 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 29 CCZ and 0 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

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Logical depth87\r\n", + "

Number of logical cycles performed

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This number is usually equal to the logical depth of the algorithm, which is 87. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

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Number of T states116\r\n", + "

Number of T states consumed by the algorithm

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To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 29 CCZ and 0 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

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Number of T factories15\r\n", + "

Number of T factories capable of producing the demanded 116 T states during the algorithm's runtime

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The total number of T factories 15 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{116\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 382us 800ns\\;\\text{algorithm runtime}}\\right\\rceil\\)

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Number of T factory invocations8\r\n", + "

Number of times all T factories are invoked

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In order to prepare the 116 T states, the 15 copies of the T factory are repeatedly invoked 8 times.

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Physical algorithmic qubits7260\r\n", + "

Number of physical qubits for the algorithm after layout

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The 7260 are the product of the 30 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.

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Physical T factory qubits97200\r\n", + "

Number of physical qubits for the T factories

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Each T factory requires 6480 physical qubits and we run 15 in parallel, therefore we need $97200 = 6480 \\cdot 15$ qubits.

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Required logical qubit error rate1.92e-7\r\n", + "

The minimum logical qubit error rate required to run the algorithm within the error budget

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The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 30 logical qubits and the total cycle count 87.

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Required logical T state error rate4.31e-6\r\n", + "

The minimum T state error rate required for distilled T states

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The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 116.

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Number of T states per rotationNo rotations in algorithm\r\n", + "

Number of T states to implement a rotation with an arbitrary angle

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The number of T states to implement a rotation with an arbitrary angle is \\(\\lceil 0.53 \\log_2(0 / 0) + 5.3\\rceil\\) [arXiv:2203.10064]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.

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\r\n", + " \r\n", + " Logical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
QEC schemesurface_code\r\n", + "

Name of QEC scheme

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You can load pre-defined QEC schemes by using the name surface_code or floquet_code. The latter only works with Majorana qubits.

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Code distance11\r\n", + "

Required code distance for error correction

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The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000019157088122605365)}{\\log(0.01/0.001)} - 1\\)

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Physical qubits242\r\n", + "

Number of physical qubits per logical qubit

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The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.

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Logical cycle time4us 400ns\r\n", + "

Duration of a logical cycle in nanoseconds

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The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.

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Logical qubit error rate3.00e-8\r\n", + "

Logical qubit error rate

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The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{11 + 1}{2}$

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Crossing prefactor0.03\r\n", + "

Crossing prefactor used in QEC scheme

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The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.

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Error correction threshold0.01\r\n", + "

Error correction threshold used in QEC scheme

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The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.

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Logical cycle time formula(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\r\n", + "

QEC scheme formula used to compute logical cycle time

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This is the formula that is used to compute the logical cycle time 4us 400ns.

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Physical qubits formula2 * codeDistance * codeDistance\r\n", + "

QEC scheme formula used to compute number of physical qubits per logical qubit

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This is the formula that is used to compute the number of physical qubits per logical qubits 242.

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Physical qubits6480\r\n", + "

Number of physical qubits for a single T factory

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This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.

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Runtime46us 800ns\r\n", + "

Runtime of a single T factory

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The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.

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Number of output T states per run1\r\n", + "

Number of output T states produced in a single run of T factory

\n", + "\r\n", + "
\r\n", + "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.

\n", + "\r\n", + "
Number of input T states per run30\r\n", + "

Number of physical input T states consumed in a single run of a T factory

\n", + "\r\n", + "
\r\n", + "

This value includes the physical input T states of all copies of the distillation unit in the first round.

\n", + "\r\n", + "
Distillation rounds1\r\n", + "

The number of distillation rounds

\n", + "\r\n", + "
\r\n", + "

This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.

\n", + "\r\n", + "
Distillation units per round2\r\n", + "

The number of units in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the number of copies for the distillation units per round.

\n", + "\r\n", + "
Distillation units15-to-1 space efficient logical\r\n", + "

The types of distillation units

\n", + "\r\n", + "
\r\n", + "

These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.

\n", + "\r\n", + "
Distillation code distances9\r\n", + "

The code distance in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.

\n", + "\r\n", + "
Number of physical qubits per round6480\r\n", + "

The number of physical qubits used in each round of distillation

\n", + "\r\n", + "
\r\n", + "

The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.

\n", + "\r\n", + "
Runtime per round46us 800ns\r\n", + "

The runtime of each distillation round

\n", + "\r\n", + "
\r\n", + "

The runtime of the T factory is the sum of the runtimes in all rounds.

\n", + "\r\n", + "
Logical T state error rate2.17e-6\r\n", + "

Logical T state error rate

\n", + "\r\n", + "
\r\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 4.31e-6.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Pre-layout logical resources\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Logical qubits (pre-layout)10\r\n", + "

Number of logical qubits in the input quantum program

\n", + "\r\n", + "
\r\n", + "

We determine 30 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", + "\r\n", + "
T gates0\r\n", + "

Number of T gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.

\n", + "\r\n", + "
Rotation gates0\r\n", + "

Number of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.

\n", + "\r\n", + "
Rotation depth0\r\n", + "

Depth of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.

\n", + "\r\n", + "
CCZ gates29\r\n", + "

Number of CCZ-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCZ gates.

\n", + "\r\n", + "
CCiX gates0\r\n", + "

Number of CCiX-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCiX gates, which applies \\(-iX\\) controlled on two control qubits [1212.5069].

\n", + "\r\n", + "
Measurement operations0\r\n", + "

Number of single qubit measurements in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Assumed error budget\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Total error budget1.00e-3\r\n", + "

Total error budget for the algorithm

\n", + "\r\n", + "
\r\n", + "

The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget \\(\\epsilon = \\epsilon_{\\log} + \\epsilon_{\\rm dis} + \\epsilon_{\\rm syn}\\) is uniformly distributed and applies to errors \\(\\epsilon_{\\log}\\) to implement logical qubits, an error budget \\(\\epsilon_{\\rm dis}\\) to produce T states through distillation, and an error budget \\(\\epsilon_{\\rm syn}\\) to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets \\(\\epsilon_{\\rm dis}\\) and \\(\\epsilon_{\\rm syn}\\) are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.

\n", + "\r\n", + "
Logical error probability5.00e-4\r\n", + "

Probability of at least one logical error

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
T distillation error probability5.00e-4\r\n", + "

Probability of at least one faulty T distillation

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
Rotation synthesis error probability0.00e0\r\n", + "

Probability of at least one failed rotation synthesis

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Physical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Qubit namequbit_gate_ns_e3\r\n", + "

Some descriptive name for the qubit model

\n", + "\r\n", + "
\r\n", + "

You can load pre-defined qubit parameters by using the names qubit_gate_ns_e3, qubit_gate_ns_e4, qubit_gate_us_e3, qubit_gate_us_e4, qubit_maj_ns_e4, or qubit_maj_ns_e6. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).

\n", + "\r\n", + "
Instruction setGateBased\r\n", + "

Underlying qubit technology (gate-based or Majorana)

\n", + "\r\n", + "
\r\n", + "

When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either gate-based or Majorana. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.

\n", + "\r\n", + "
Single-qubit measurement time100 ns\r\n", + "

Operation time for single-qubit measurement (t_meas) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.

\n", + "\r\n", + "
Single-qubit gate time50 ns\r\n", + "

Operation time for single-qubit gate (t_gate) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.

\n", + "\r\n", + "
Two-qubit gate time50 ns\r\n", + "

Operation time for two-qubit gate in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.

\n", + "\r\n", + "
T gate time50 ns\r\n", + "

Operation time for a T gate

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to execute a T gate.

\n", + "\r\n", + "
Single-qubit measurement error rate0.001\r\n", + "

Error rate for single-qubit measurement

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit measurement in the Pauli basis may fail.

\n", + "\r\n", + "
Single-qubit error rate0.001\r\n", + "

Error rate for single-qubit Clifford gate (p)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.

\n", + "\r\n", + "
Two-qubit error rate0.001\r\n", + "

Error rate for two-qubit Clifford gate

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.

\n", + "\r\n", + "
T gate error rate0.001\r\n", + "

Error rate to prepare single-qubit T state or apply a T gate (p_T)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which executing a single T gate may fail.

\n", + "\r\n", + "
\n", + "
\r\n", + " Assumptions\r\n", + "
    \n", + "

  • More details on the following lists of assumptions can be found in the paper Accessing requirements for scaling quantum computers and their applications.

    \n", + "
    • \n", + "

  • Uniform independent physical noise. We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.

    \n", + "
    • \n", + "

  • Efficient classical computation. We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.

    \n", + "
    • \n", + "

  • Extraction circuits for planar quantum ISA. We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).

    \n", + "
    • \n", + "

  • Uniform independent logical noise. We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.

    \n", + "
    • \n", + "

  • Negligible Clifford costs for synthesis. We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.

    \n", + "
    • \n", + "

  • Smooth magic state consumption rate. We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.

    \n", + "
    • \n", + "
\n" + ], + "text/plain": [ + "{'errorBudget': {'logical': 0.0005, 'rotations': 0.0, 'tstates': 0.0005},\n", + " 'jobParams': {'errorBudget': 0.001,\n", + " 'qecScheme': {'crossingPrefactor': 0.03,\n", + " 'errorCorrectionThreshold': 0.01,\n", + " 'logicalCycleTime': '(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance',\n", + " 'name': 'surface_code',\n", + " 'physicalQubitsPerLogicalQubit': '2 * codeDistance * codeDistance'},\n", + " 'qubitParams': {'instructionSet': 'GateBased',\n", + " 'name': 'qubit_gate_ns_e3',\n", + " 'oneQubitGateErrorRate': 0.001,\n", + " 'oneQubitGateTime': '50 ns',\n", + " 'oneQubitMeasurementErrorRate': 0.001,\n", + " 'oneQubitMeasurementTime': '100 ns',\n", + " 'tGateErrorRate': 0.001,\n", + " 'tGateTime': '50 ns',\n", + " 'twoQubitGateErrorRate': 0.001,\n", + " 'twoQubitGateTime': '50 ns'}},\n", + " 'logicalCounts': {'ccixCount': 0,\n", + " 'cczCount': 29,\n", + " 'measurementCount': 0,\n", + " 'numQubits': 10,\n", + " 'rotationCount': 0,\n", + " 'rotationDepth': 0,\n", + " 'tCount': 0},\n", + " 'logicalQubit': {'codeDistance': 11,\n", + " 'logicalCycleTime': 4400.0,\n", + " 'logicalErrorRate': 3.000000000000002e-08,\n", + " 'physicalQubits': 242},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 87,\n", + " 'algorithmicLogicalQubits': 30,\n", + " 'cliffordErrorRate': 0.001,\n", + " 'logicalDepth': 87,\n", + " 'numTfactories': 15,\n", + " 'numTfactoryRuns': 8,\n", + " 'numTsPerRotation': None,\n", + " 'numTstates': 116,\n", + " 'physicalQubitsForAlgorithm': 7260,\n", + " 'physicalQubitsForTfactories': 97200,\n", + " 'requiredLogicalQubitErrorRate': 1.9157088122605365e-07,\n", + " 'requiredLogicalTstateErrorRate': 4.310344827586207e-06},\n", + " 'physicalQubits': 104460,\n", + " 'runtime': 382800},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", + " 'errorBudget': '1.00e-3',\n", + " 'errorBudgetLogical': '5.00e-4',\n", + " 'errorBudgetRotations': '0.00e0',\n", + " 'errorBudgetTstates': '5.00e-4',\n", + " 'logicalCycleTime': '4us 400ns',\n", + " 'logicalErrorRate': '3.00e-8',\n", + " 'numTsPerRotation': 'No rotations in algorithm',\n", + " 'numUnitsPerRound': '2',\n", + " 'physicalQubitsForTfactoriesPercentage': '93.05 %',\n", + " 'physicalQubitsPerRound': '6480',\n", + " 'requiredLogicalQubitErrorRate': '1.92e-7',\n", + " 'requiredLogicalTstateErrorRate': '4.31e-6',\n", + " 'runtime': '382us 800ns',\n", + " 'tfactoryRuntime': '46us 800ns',\n", + " 'tfactoryRuntimePerRound': '46us 800ns',\n", + " 'tstateLogicalErrorRate': '2.17e-6',\n", + " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", + " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", + " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", + " '**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.',\n", + " '**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).',\n", + " '**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.',\n", + " '**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.',\n", + " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", + " 'groups': [{'alwaysVisible': True,\n", + " 'entries': [{'description': 'Number of physical qubits',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 7260 physical qubits to implement the algorithm logic, and 97200 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'physicalCounts/physicalQubits'},\n", + " {'description': 'Total runtime',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 87 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/runtime'}],\n", + " 'title': 'Physical resource estimates'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 10$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 30$ logical qubits.',\n", + " 'label': 'Logical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", + " {'description': 'Number of logical cycles for the algorithm',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 0 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 29 CCZ and 0 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'label': 'Algorithmic depth',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", + " {'description': 'Number of logical cycles performed',\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 87. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'label': 'Logical depth',\n", + " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", + " {'description': 'Number of T states consumed by the algorithm',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 29 CCZ and 0 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'label': 'Number of T states',\n", + " 'path': 'physicalCounts/breakdown/numTstates'},\n", + " {'description': \"Number of T factories capable of producing the demanded 116 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 15 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{116\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 382us 800ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " 'label': 'Number of T factories',\n", + " 'path': 'physicalCounts/breakdown/numTfactories'},\n", + " {'description': 'Number of times all T factories are invoked',\n", + " 'explanation': 'In order to prepare the 116 T states, the 15 copies of the T factory are repeatedly invoked 8 times.',\n", + " 'label': 'Number of T factory invocations',\n", + " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", + " {'description': 'Number of physical qubits for the algorithm after layout',\n", + " 'explanation': 'The 7260 are the product of the 30 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.',\n", + " 'label': 'Physical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", + " {'description': 'Number of physical qubits for the T factories',\n", + " 'explanation': 'Each T factory requires 6480 physical qubits and we run 15 in parallel, therefore we need $97200 = 6480 \\\\cdot 15$ qubits.',\n", + " 'label': 'Physical T factory qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", + " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 30 logical qubits and the total cycle count 87.',\n", + " 'label': 'Required logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", + " {'description': 'The minimum T state error rate required for distilled T states',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 116.',\n", + " 'label': 'Required logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", + " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", + " 'explanation': 'The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.',\n", + " 'label': 'Number of T states per rotation',\n", + " 'path': 'physicalCountsFormatted/numTsPerRotation'}],\n", + " 'title': 'Resource estimates breakdown'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Name of QEC scheme',\n", + " 'explanation': 'You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.',\n", + " 'label': 'QEC scheme',\n", + " 'path': 'jobParams/qecScheme/name'},\n", + " {'description': 'Required code distance for error correction',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000019157088122605365)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'label': 'Code distance',\n", + " 'path': 'logicalQubit/codeDistance'},\n", + " {'description': 'Number of physical qubits per logical qubit',\n", + " 'explanation': 'The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'logicalQubit/physicalQubits'},\n", + " {'description': 'Duration of a logical cycle in nanoseconds',\n", + " 'explanation': 'The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.',\n", + " 'label': 'Logical cycle time',\n", + " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", + " {'description': 'Logical qubit error rate',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$',\n", + " 'label': 'Logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", + " {'description': 'Crossing prefactor used in QEC scheme',\n", + " 'explanation': 'The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.',\n", + " 'label': 'Crossing prefactor',\n", + " 'path': 'jobParams/qecScheme/crossingPrefactor'},\n", + " {'description': 'Error correction threshold used in QEC scheme',\n", + " 'explanation': 'The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.',\n", + " 'label': 'Error correction threshold',\n", + " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", + " {'description': 'QEC scheme formula used to compute logical cycle time',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 4us 400ns.',\n", + " 'label': 'Logical cycle time formula',\n", + " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", + " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 242.',\n", + " 'label': 'Physical qubits formula',\n", + " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", + " 'title': 'Logical qubit parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of physical qubits for a single T factory',\n", + " 'explanation': 'This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'tfactory/physicalQubits'},\n", + " {'description': 'Runtime of a single T factory',\n", + " 'explanation': 'The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", + " {'description': 'Number of output T states produced in a single run of T factory',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.',\n", + " 'label': 'Number of output T states per run',\n", + " 'path': 'tfactory/numTstates'},\n", + " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", + " 'explanation': 'This value includes the physical input T states of all copies of the distillation unit in the first round.',\n", + " 'label': 'Number of input T states per run',\n", + " 'path': 'tfactory/numInputTstates'},\n", + " {'description': 'The number of distillation rounds',\n", + " 'explanation': 'This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.',\n", + " 'label': 'Distillation rounds',\n", + " 'path': 'tfactory/numRounds'},\n", + " {'description': 'The number of units in each round of distillation',\n", + " 'explanation': 'This is the number of copies for the distillation units per round.',\n", + " 'label': 'Distillation units per round',\n", + " 'path': 'physicalCountsFormatted/numUnitsPerRound'},\n", + " {'description': 'The types of distillation units',\n", + " 'explanation': 'These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.',\n", + " 'label': 'Distillation units',\n", + " 'path': 'physicalCountsFormatted/unitNamePerRound'},\n", + " {'description': 'The code distance in each round of distillation',\n", + " 'explanation': 'This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.',\n", + " 'label': 'Distillation code distances',\n", + " 'path': 'physicalCountsFormatted/codeDistancePerRound'},\n", + " {'description': 'The number of physical qubits used in each round of distillation',\n", + " 'explanation': 'The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.',\n", + " 'label': 'Number of physical qubits per round',\n", + " 'path': 'physicalCountsFormatted/physicalQubitsPerRound'},\n", + " {'description': 'The runtime of each distillation round',\n", + " 'explanation': 'The runtime of the T factory is the sum of the runtimes in all rounds.',\n", + " 'label': 'Runtime per round',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", + " {'description': 'Logical T state error rate',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 4.31e-6.',\n", + " 'label': 'Logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", + " 'title': 'T factory parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", + " 'explanation': 'We determine 30 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'label': 'Logical qubits (pre-layout)',\n", + " 'path': 'logicalCounts/numQubits'},\n", + " {'description': 'Number of T gates in the input quantum program',\n", + " 'explanation': 'This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.',\n", + " 'label': 'T gates',\n", + " 'path': 'logicalCounts/tCount'},\n", + " {'description': 'Number of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.',\n", + " 'label': 'Rotation gates',\n", + " 'path': 'logicalCounts/rotationCount'},\n", + " {'description': 'Depth of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.',\n", + " 'label': 'Rotation depth',\n", + " 'path': 'logicalCounts/rotationDepth'},\n", + " {'description': 'Number of CCZ-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCZ gates.',\n", + " 'label': 'CCZ gates',\n", + " 'path': 'logicalCounts/cczCount'},\n", + " {'description': 'Number of CCiX-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].',\n", + " 'label': 'CCiX gates',\n", + " 'path': 'logicalCounts/ccixCount'},\n", + " {'description': 'Number of single qubit measurements in the input quantum program',\n", + " 'explanation': 'This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.',\n", + " 'label': 'Measurement operations',\n", + " 'path': 'logicalCounts/measurementCount'}],\n", + " 'title': 'Pre-layout logical resources'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Total error budget for the algorithm',\n", + " 'explanation': \"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\n", + " 'label': 'Total error budget',\n", + " 'path': 'physicalCountsFormatted/errorBudget'},\n", + " {'description': 'Probability of at least one logical error',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'Logical error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetLogical'},\n", + " {'description': 'Probability of at least one faulty T distillation',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'T distillation error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetTstates'},\n", + " {'description': 'Probability of at least one failed rotation synthesis',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3.',\n", + " 'label': 'Rotation synthesis error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetRotations'}],\n", + " 'title': 'Assumed error budget'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Some descriptive name for the qubit model',\n", + " 'explanation': 'You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).',\n", + " 'label': 'Qubit name',\n", + " 'path': 'jobParams/qubitParams/name'},\n", + " {'description': 'Underlying qubit technology (gate-based or Majorana)',\n", + " 'explanation': 'When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.',\n", + " 'label': 'Instruction set',\n", + " 'path': 'jobParams/qubitParams/instructionSet'},\n", + " {'description': 'Operation time for single-qubit measurement (t_meas) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.',\n", + " 'label': 'Single-qubit measurement time',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementTime'},\n", + " {'description': 'Operation time for single-qubit gate (t_gate) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.',\n", + " 'label': 'Single-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateTime'},\n", + " {'description': 'Operation time for two-qubit gate in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.',\n", + " 'label': 'Two-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateTime'},\n", + " {'description': 'Operation time for a T gate',\n", + " 'explanation': 'This is the operation time in nanoseconds to execute a T gate.',\n", + " 'label': 'T gate time',\n", + " 'path': 'jobParams/qubitParams/tGateTime'},\n", + " {'description': 'Error rate for single-qubit measurement',\n", + " 'explanation': 'This is the probability in which a single-qubit measurement in the Pauli basis may fail.',\n", + " 'label': 'Single-qubit measurement error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementErrorRate'},\n", + " {'description': 'Error rate for single-qubit Clifford gate (p)',\n", + " 'explanation': 'This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.',\n", + " 'label': 'Single-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateErrorRate'},\n", + " {'description': 'Error rate for two-qubit Clifford gate',\n", + " 'explanation': 'This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.',\n", + " 'label': 'Two-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateErrorRate'},\n", + " {'description': 'Error rate to prepare single-qubit T state or apply a T gate (p_T)',\n", + " 'explanation': 'This is the probability in which executing a single T gate may fail.',\n", + " 'label': 'T gate error rate',\n", + " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", + " 'title': 'Physical qubit parameters'}]},\n", + " 'status': 'success',\n", + " 'tfactory': {'codeDistancePerRound': [9],\n", + " 'logicalErrorRate': 2.165000000000001e-06,\n", + " 'numInputTstates': 30,\n", + " 'numRounds': 1,\n", + " 'numTstates': 1,\n", + " 'numUnitsPerRound': [2],\n", + " 'physicalQubits': 6480,\n", + " 'physicalQubitsPerRound': [6480],\n", + " 'runtime': 46800.0,\n", + " 'runtimePerRound': [46800.0],\n", + " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", "# result = qsharp.azure.output(\"...\")\n", @@ -365,7 +4934,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 22, "metadata": { "collapsed": false, "jupyter": { @@ -392,7 +4961,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 23, "metadata": { "collapsed": false, "jupyter": { @@ -405,10 +4974,37 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Logical algorithmic qubits = 30\n", + "Algorithmic depth = 87\n", + "Score = 2610\n" + ] + }, + { + "data": { + "text/plain": [ + "2610" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "evaluate_results(result)" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -416,9 +5012,9 @@ "name": "python3" }, "kernelspec": { - "display_name": "Python 3 [Default]", + "display_name": "Python 3 [Q#]", "language": "python", - "name": "python3" + "name": "python3_qsharp_b54crn" }, "language_info": { "codemirror_mode": { diff --git a/iQuHack-challenge-2023-task5.ipynb b/iQuHack-challenge-2023-task5.ipynb index 85e5038..9d4c433 100644 --- a/iQuHack-challenge-2023-task5.ipynb +++ b/iQuHack-challenge-2023-task5.ipynb @@ -104,9 +104,9 @@ }, "outputs": [], "source": [ - "teamname=\"msft_is_the_best\" # Update this field with your team name\n", + "teamname=\"schrodingers-duck\" # Update this field with your team name\n", "task=[\"task5\"]\n", - "slack_id=\"myslackid\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + "slack_id=\"U04L3SFUCQ2\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" ] }, { @@ -169,19 +169,125 @@ "%%qsharp\n", "open Microsoft.Quantum.Canon;\n", "open Microsoft.Quantum.Diagnostics;\n", + "open Microsoft.Quantum.Arrays;\n", + "\n", "\n", "// Task 5. \n", "// (input will contain 6 qubits)\n", "operation Task5(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " for i in [21,42] {\n", + " ControlledOnInt(i, X)(input, target);\n", + " }\n", + " use equality = Qubit[3];\n", + " use storageWire = Qubit[1];\n", + " within {\n", + " CNOT(input[0], equality[0]);\n", + " CNOT(input[3], equality[0]);\n", + " CNOT(input[1], equality[1]);\n", + " CNOT(input[4], equality[1]);\n", + " CNOT(input[2], equality[2]);\n", + " CNOT(input[5], equality[2]);\n", + " X(equality[0]); X(equality[1]); X(equality[2]);\n", + " CCNOT(equality[0], equality[1], storageWire[0]);\n", + " } apply {\n", + " CCNOT(equality[2], storageWire[0], target);\n", + " }\n", + "}\n", + "\n", + "operation original(input : Qubit[], target : Qubit) : Unit is Adj {\n", " for i in [0, 9, 18, 21, 27, 36, 42, 45, 54, 63] {\n", " ControlledOnInt(i, X)(input, target);\n", " }\n", + "}\n", + "\n", + "operation QubitArrayWrapperOperation (op : ((Qubit[], Qubit) => Unit is Adj), qs : Qubit[]) : Unit is Adj { \n", + " op(Most(qs), Tail(qs));\n", + "}\n", + "\n", + "operation TestCompoundGate () : Unit {\n", + " AssertOperationsEqualReferenced(6+1, QubitArrayWrapperOperation(Task5, _), QubitArrayWrapperOperation (original, _));\n", "}" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "\r\n", + "
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SourceCallable
(notebook)Task5
(notebook)QubitArrayWrapperOperation
/home/jovyan/2023_microsoft/D:\\a\\1\\s\\submodules\\qsharp-runtime\\src\\Simulation\\TargetDefinitions\\Decompositions\\AssertOperationsEqualReferenced.qs:0Microsoft.Quantum.Diagnostics.AssertOperationsEqualReferenced
(notebook)TestCompoundGate
\r\n", + "
\r\n", + " " + ], + "text/plain": [ + "Unhandled exception. System.ArgumentOutOfRangeException: Specified argument was out of the range of valid values.\n", + " ---> SNIPPET.Task5 on /snippet_.qs:line 0\n", + " at SNIPPET.QubitArrayWrapperOperation on /snippet_.qs:line 0\n", + " at Microsoft.Quantum.Diagnostics.AssertOperationsEqualReferenced on /home/jovyan/2023_microsoft/D:\\a\\1\\s\\submodules\\qsharp-runtime\\src\\Simulation\\TargetDefinitions\\Decompositions\\AssertOperationsEqualReferenced.qs:line 0\n", + " at SNIPPET.TestCompoundGate on /snippet_.qs:line 0\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Specified argument was out of the range of valid values.\n" + ] + } + ], + "source": [ + "TestCompoundGate();" + ] + }, + { + "cell_type": "code", + "execution_count": 5, "metadata": { "collapsed": false, "jupyter": { @@ -238,7 +344,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": { "collapsed": false, "jupyter": { @@ -251,7 +357,1710 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": 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Qubit IDs0, 1, 2, 3, 4, 5, 6
Basis state (bitstring)AmplitudeMeas. Pr.
$\\left|0000001\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

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$\\left|0000010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0000100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0000110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0001000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0001010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0001100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0001110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0010000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0010011\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0010100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0010110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0011000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0011010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0011100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0011110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0100000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0100010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0100101\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0100110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0101000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0101011\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0101100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0101110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0110000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0110010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0110100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0110111\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0111000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0111010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0111100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0111110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1000000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1000010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1000100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1000110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1001001\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1001010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1001100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1001110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1010000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1010010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|1010101\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1010110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1011000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1011011\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1011100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1011110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1100000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1100010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1100100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1100110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1101000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1101010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1101101\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1101110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1110000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1110010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1110100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1110110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1111000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1111010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1111100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1111111\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
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"execution_count": null, + "execution_count": 8, "metadata": { "collapsed": false, "jupyter": { @@ -289,19 +2098,68 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "\"Connecting to Azure Quantum...\"", + "text/plain": [ + "Connecting to Azure Quantum..." + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Connected to Azure Quantum workspace azure-q in location uksouth.\n" + ] + }, + { + "data": { + "text/plain": [ + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 284985},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 412930},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 2},\n", + " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 257411},\n", + " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 4298},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 137},\n", + " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 257411},\n", + " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 4298},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 137},\n", + " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.qpu.aspen-m-2', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", "# If you're using this notebook in qBraid, keep it\n", "qsharp.azure.connect(\n", - " resourceId=\"...\",\n", - " location=\"...\",\n", + " resourceId=\"/subscriptions/7fc54e95-14cf-4a6f-b50e-d6155c241309/resourceGroups/AzureQuantum/providers/Microsoft.Quantum/Workspaces/azure-q\",\n", + " location=\"UK South\",\n", " credential=\"CLI\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "metadata": { "collapsed": false, "jupyter": { @@ -314,14 +2172,33 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loading package Microsoft.Quantum.Providers.Core and dependencies...\n", + "Active target is now microsoft.estimator\n" + ] + }, + { + "data": { + "text/plain": [ + "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "qsharp.azure.target(\"microsoft.estimator\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "metadata": { "collapsed": false, "jupyter": { @@ -334,7 +2211,21 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Submitting Task5_ResourceEstimationWrapper to target microsoft.estimator...\n", + "Job successfully submitted.\n", + " Job name: RE for the task 5\n", + " Job ID: ce9dd9e8-528c-46ec-94d2-289b8fed02a7\n", + "Waiting up to 30 seconds for Azure Quantum job to complete...\n", + "[11:30:22 PM] Current job status: Executing\n", + "[11:30:27 PM] Current job status: Succeeded\n" + ] + } + ], "source": [ "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", "result = qsharp.azure.execute(Task5_ResourceEstimationWrapper, jobName=\"RE for the task 5\")" @@ -342,7 +2233,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, "metadata": { "collapsed": false, "jupyter": { @@ -355,7 +2246,1051 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":8,\"cczCount\":5,\"measurementCount\":8,\"numQubits\":11,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":9,\"logicalCycleTime\":3600.0,\"logicalErrorRate\":3.0000000000000015E-07,\"physicalQubits\":162},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":47,\"algorithmicLogicalQubits\":33,\"cliffordErrorRate\":0.001,\"logicalDepth\":47,\"numTfactories\":15,\"numTfactoryRuns\":4,\"numTsPerRotation\":null,\"numTstates\":52,\"physicalQubitsForAlgorithm\":5346,\"physicalQubitsForTfactories\":97200,\"requiredLogicalQubitErrorRate\":3.2237266279819474E-07,\"requiredLogicalTstateErrorRate\":9.615384615384616E-06},\"physicalQubits\":102546,\"runtime\":169200},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"3us 600ns\",\"logicalErrorRate\":\"3.00e-7\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"94.79 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"3.22e-7\",\"requiredLogicalTstateErrorRate\":\"9.62e-6\",\"runtime\":\"169us 200ns\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 5346 physical qubits to implement the algorithm logic, and 97200 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 47 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 11$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 33$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 8 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 5 CCZ and 8 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 47. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 5 CCZ and 8 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 52 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 15 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{52\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 169us 200ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 52 T states, the 15 copies of the T factory are repeatedly invoked 4 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 5346 are the product of the 33 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 15 in parallel, therefore we need $97200 = 6480 \\\\cdot 15$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 47.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 52.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000032237266279819474)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{9 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 3us 600ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 162.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 9.62e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or ¬µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "text/html": [ + "\r\n", + "
\r\n", + " \r\n", + " Physical resource estimates\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits102546\r\n", + "

Number of physical qubits

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This value represents the total number of physical qubits, which is the sum of 5346 physical qubits to implement the algorithm logic, and 97200 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

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Runtime169us 200ns\r\n", + "

Total runtime

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This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 47 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

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\r\n", + " \r\n", + " Resource estimates breakdown\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Logical algorithmic qubits33\r\n", + "

Number of logical qubits for the algorithm after layout

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Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 11\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 33$ logical qubits.

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Algorithmic depth47\r\n", + "

Number of logical cycles for the algorithm

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To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 8 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 5 CCZ and 8 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

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Logical depth47\r\n", + "

Number of logical cycles performed

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This number is usually equal to the logical depth of the algorithm, which is 47. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

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Number of T states52\r\n", + "

Number of T states consumed by the algorithm

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To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 5 CCZ and 8 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

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Number of T factories15\r\n", + "

Number of T factories capable of producing the demanded 52 T states during the algorithm's runtime

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The total number of T factories 15 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{52\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 169us 200ns\\;\\text{algorithm runtime}}\\right\\rceil\\)

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Number of T factory invocations4\r\n", + "

Number of times all T factories are invoked

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In order to prepare the 52 T states, the 15 copies of the T factory are repeatedly invoked 4 times.

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Physical algorithmic qubits5346\r\n", + "

Number of physical qubits for the algorithm after layout

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The 5346 are the product of the 33 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.

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Physical T factory qubits97200\r\n", + "

Number of physical qubits for the T factories

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Each T factory requires 6480 physical qubits and we run 15 in parallel, therefore we need $97200 = 6480 \\cdot 15$ qubits.

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Required logical qubit error rate3.22e-7\r\n", + "

The minimum logical qubit error rate required to run the algorithm within the error budget

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The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 47.

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Required logical T state error rate9.62e-6\r\n", + "

The minimum T state error rate required for distilled T states

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The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 52.

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Number of T states per rotationNo rotations in algorithm\r\n", + "

Number of T states to implement a rotation with an arbitrary angle

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The number of T states to implement a rotation with an arbitrary angle is \\(\\lceil 0.53 \\log_2(0 / 0) + 5.3\\rceil\\) [arXiv:2203.10064]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.

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\r\n", + " \r\n", + " Logical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
QEC schemesurface_code\r\n", + "

Name of QEC scheme

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You can load pre-defined QEC schemes by using the name surface_code or floquet_code. The latter only works with Majorana qubits.

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Code distance9\r\n", + "

Required code distance for error correction

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The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000032237266279819474)}{\\log(0.01/0.001)} - 1\\)

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Physical qubits162\r\n", + "

Number of physical qubits per logical qubit

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The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.

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Logical cycle time3us 600ns\r\n", + "

Duration of a logical cycle in nanoseconds

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The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.

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Logical qubit error rate3.00e-7\r\n", + "

Logical qubit error rate

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The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{9 + 1}{2}$

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Crossing prefactor0.03\r\n", + "

Crossing prefactor used in QEC scheme

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The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.

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Error correction threshold0.01\r\n", + "

Error correction threshold used in QEC scheme

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The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.

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Logical cycle time formula(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\r\n", + "

QEC scheme formula used to compute logical cycle time

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This is the formula that is used to compute the logical cycle time 3us 600ns.

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Physical qubits formula2 * codeDistance * codeDistance\r\n", + "

QEC scheme formula used to compute number of physical qubits per logical qubit

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This is the formula that is used to compute the number of physical qubits per logical qubits 162.

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Physical qubits6480\r\n", + "

Number of physical qubits for a single T factory

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This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.

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Runtime46us 800ns\r\n", + "

Runtime of a single T factory

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The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.

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Number of output T states per run1\r\n", + "

Number of output T states produced in a single run of T factory

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The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.

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Number of input T states per run30\r\n", + "

Number of physical input T states consumed in a single run of a T factory

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This value includes the physical input T states of all copies of the distillation unit in the first round.

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Distillation rounds1\r\n", + "

The number of distillation rounds

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This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.

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Distillation units per round2\r\n", + "

The number of units in each round of distillation

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This is the number of copies for the distillation units per round.

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Distillation units15-to-1 space efficient logical\r\n", + "

The types of distillation units

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These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.

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Distillation code distances9\r\n", + "

The code distance in each round of distillation

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This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.

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Number of physical qubits per round6480\r\n", + "

The number of physical qubits used in each round of distillation

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The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.

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Runtime per round46us 800ns\r\n", + "

The runtime of each distillation round

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The runtime of the T factory is the sum of the runtimes in all rounds.

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Logical T state error rate2.17e-6\r\n", + "

Logical T state error rate

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This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 9.62e-6.

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Logical qubits (pre-layout)11\r\n", + "

Number of logical qubits in the input quantum program

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We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

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T gates0\r\n", + "

Number of T gates in the input quantum program

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This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.

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Rotation gates0\r\n", + "

Number of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.

\n", + "\r\n", + "
Rotation depth0\r\n", + "

Depth of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.

\n", + "\r\n", + "
CCZ gates5\r\n", + "

Number of CCZ-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCZ gates.

\n", + "\r\n", + "
CCiX gates8\r\n", + "

Number of CCiX-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCiX gates, which applies \\(-iX\\) controlled on two control qubits [1212.5069].

\n", + "\r\n", + "
Measurement operations8\r\n", + "

Number of single qubit measurements in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Assumed error budget\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Total error budget1.00e-3\r\n", + "

Total error budget for the algorithm

\n", + "\r\n", + "
\r\n", + "

The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget \\(\\epsilon = \\epsilon_{\\log} + \\epsilon_{\\rm dis} + \\epsilon_{\\rm syn}\\) is uniformly distributed and applies to errors \\(\\epsilon_{\\log}\\) to implement logical qubits, an error budget \\(\\epsilon_{\\rm dis}\\) to produce T states through distillation, and an error budget \\(\\epsilon_{\\rm syn}\\) to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets \\(\\epsilon_{\\rm dis}\\) and \\(\\epsilon_{\\rm syn}\\) are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.

\n", + "\r\n", + "
Logical error probability5.00e-4\r\n", + "

Probability of at least one logical error

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
T distillation error probability5.00e-4\r\n", + "

Probability of at least one faulty T distillation

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
Rotation synthesis error probability0.00e0\r\n", + "

Probability of at least one failed rotation synthesis

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Physical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Qubit namequbit_gate_ns_e3\r\n", + "

Some descriptive name for the qubit model

\n", + "\r\n", + "
\r\n", + "

You can load pre-defined qubit parameters by using the names qubit_gate_ns_e3, qubit_gate_ns_e4, qubit_gate_us_e3, qubit_gate_us_e4, qubit_maj_ns_e4, or qubit_maj_ns_e6. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).

\n", + "\r\n", + "
Instruction setGateBased\r\n", + "

Underlying qubit technology (gate-based or Majorana)

\n", + "\r\n", + "
\r\n", + "

When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either gate-based or Majorana. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.

\n", + "\r\n", + "
Single-qubit measurement time100 ns\r\n", + "

Operation time for single-qubit measurement (t_meas) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.

\n", + "\r\n", + "
Single-qubit gate time50 ns\r\n", + "

Operation time for single-qubit gate (t_gate) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.

\n", + "\r\n", + "
Two-qubit gate time50 ns\r\n", + "

Operation time for two-qubit gate in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.

\n", + "\r\n", + "
T gate time50 ns\r\n", + "

Operation time for a T gate

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to execute a T gate.

\n", + "\r\n", + "
Single-qubit measurement error rate0.001\r\n", + "

Error rate for single-qubit measurement

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit measurement in the Pauli basis may fail.

\n", + "\r\n", + "
Single-qubit error rate0.001\r\n", + "

Error rate for single-qubit Clifford gate (p)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.

\n", + "\r\n", + "
Two-qubit error rate0.001\r\n", + "

Error rate for two-qubit Clifford gate

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.

\n", + "\r\n", + "
T gate error rate0.001\r\n", + "

Error rate to prepare single-qubit T state or apply a T gate (p_T)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which executing a single T gate may fail.

\n", + "\r\n", + "
\n", + "
\r\n", + " Assumptions\r\n", + "
    \n", + "

  • More details on the following lists of assumptions can be found in the paper Accessing requirements for scaling quantum computers and their applications.

    \n", + "
    • \n", + "

  • Uniform independent physical noise. We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.

    \n", + "
    • \n", + "

  • Efficient classical computation. We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.

    \n", + "
    • \n", + "

  • Extraction circuits for planar quantum ISA. We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).

    \n", + "
    • \n", + "

  • Uniform independent logical noise. We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.

    \n", + "
    • \n", + "

  • Negligible Clifford costs for synthesis. We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.

    \n", + "
    • \n", + "

  • Smooth magic state consumption rate. We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.

    \n", + "
    • \n", + "
\n" + ], + "text/plain": [ + "{'errorBudget': {'logical': 0.0005, 'rotations': 0.0, 'tstates': 0.0005},\n", + " 'jobParams': {'errorBudget': 0.001,\n", + " 'qecScheme': {'crossingPrefactor': 0.03,\n", + " 'errorCorrectionThreshold': 0.01,\n", + " 'logicalCycleTime': '(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance',\n", + " 'name': 'surface_code',\n", + " 'physicalQubitsPerLogicalQubit': '2 * codeDistance * codeDistance'},\n", + " 'qubitParams': {'instructionSet': 'GateBased',\n", + " 'name': 'qubit_gate_ns_e3',\n", + " 'oneQubitGateErrorRate': 0.001,\n", + " 'oneQubitGateTime': '50 ns',\n", + " 'oneQubitMeasurementErrorRate': 0.001,\n", + " 'oneQubitMeasurementTime': '100 ns',\n", + " 'tGateErrorRate': 0.001,\n", + " 'tGateTime': '50 ns',\n", + " 'twoQubitGateErrorRate': 0.001,\n", + " 'twoQubitGateTime': '50 ns'}},\n", + " 'logicalCounts': {'ccixCount': 8,\n", + " 'cczCount': 5,\n", + " 'measurementCount': 8,\n", + " 'numQubits': 11,\n", + " 'rotationCount': 0,\n", + " 'rotationDepth': 0,\n", + " 'tCount': 0},\n", + " 'logicalQubit': {'codeDistance': 9,\n", + " 'logicalCycleTime': 3600.0,\n", + " 'logicalErrorRate': 3.0000000000000015e-07,\n", + " 'physicalQubits': 162},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 47,\n", + " 'algorithmicLogicalQubits': 33,\n", + " 'cliffordErrorRate': 0.001,\n", + " 'logicalDepth': 47,\n", + " 'numTfactories': 15,\n", + " 'numTfactoryRuns': 4,\n", + " 'numTsPerRotation': None,\n", + " 'numTstates': 52,\n", + " 'physicalQubitsForAlgorithm': 5346,\n", + " 'physicalQubitsForTfactories': 97200,\n", + " 'requiredLogicalQubitErrorRate': 3.2237266279819474e-07,\n", + " 'requiredLogicalTstateErrorRate': 9.615384615384616e-06},\n", + " 'physicalQubits': 102546,\n", + " 'runtime': 169200},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", + " 'errorBudget': '1.00e-3',\n", + " 'errorBudgetLogical': '5.00e-4',\n", + " 'errorBudgetRotations': '0.00e0',\n", + " 'errorBudgetTstates': '5.00e-4',\n", + " 'logicalCycleTime': '3us 600ns',\n", + " 'logicalErrorRate': '3.00e-7',\n", + " 'numTsPerRotation': 'No rotations in algorithm',\n", + " 'numUnitsPerRound': '2',\n", + " 'physicalQubitsForTfactoriesPercentage': '94.79 %',\n", + " 'physicalQubitsPerRound': '6480',\n", + " 'requiredLogicalQubitErrorRate': '3.22e-7',\n", + " 'requiredLogicalTstateErrorRate': '9.62e-6',\n", + " 'runtime': '169us 200ns',\n", + " 'tfactoryRuntime': '46us 800ns',\n", + " 'tfactoryRuntimePerRound': '46us 800ns',\n", + " 'tstateLogicalErrorRate': '2.17e-6',\n", + " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", + " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", + " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", + " '**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.',\n", + " '**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).',\n", + " '**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.',\n", + " '**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.',\n", + " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", + " 'groups': [{'alwaysVisible': True,\n", + " 'entries': [{'description': 'Number of physical qubits',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 5346 physical qubits to implement the algorithm logic, and 97200 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'physicalCounts/physicalQubits'},\n", + " {'description': 'Total runtime',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 47 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/runtime'}],\n", + " 'title': 'Physical resource estimates'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 11$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 33$ logical qubits.',\n", + " 'label': 'Logical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", + " {'description': 'Number of logical cycles for the algorithm',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 8 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 5 CCZ and 8 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'label': 'Algorithmic depth',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", + " {'description': 'Number of logical cycles performed',\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 47. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'label': 'Logical depth',\n", + " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", + " {'description': 'Number of T states consumed by the algorithm',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 5 CCZ and 8 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'label': 'Number of T states',\n", + " 'path': 'physicalCounts/breakdown/numTstates'},\n", + " {'description': \"Number of T factories capable of producing the demanded 52 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 15 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{52\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 169us 200ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " 'label': 'Number of T factories',\n", + " 'path': 'physicalCounts/breakdown/numTfactories'},\n", + " {'description': 'Number of times all T factories are invoked',\n", + " 'explanation': 'In order to prepare the 52 T states, the 15 copies of the T factory are repeatedly invoked 4 times.',\n", + " 'label': 'Number of T factory invocations',\n", + " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", + " {'description': 'Number of physical qubits for the algorithm after layout',\n", + " 'explanation': 'The 5346 are the product of the 33 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.',\n", + " 'label': 'Physical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", + " {'description': 'Number of physical qubits for the T factories',\n", + " 'explanation': 'Each T factory requires 6480 physical qubits and we run 15 in parallel, therefore we need $97200 = 6480 \\\\cdot 15$ qubits.',\n", + " 'label': 'Physical T factory qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", + " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 47.',\n", + " 'label': 'Required logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", + " {'description': 'The minimum T state error rate required for distilled T states',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 52.',\n", + " 'label': 'Required logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", + " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", + " 'explanation': 'The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.',\n", + " 'label': 'Number of T states per rotation',\n", + " 'path': 'physicalCountsFormatted/numTsPerRotation'}],\n", + " 'title': 'Resource estimates breakdown'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Name of QEC scheme',\n", + " 'explanation': 'You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.',\n", + " 'label': 'QEC scheme',\n", + " 'path': 'jobParams/qecScheme/name'},\n", + " {'description': 'Required code distance for error correction',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000032237266279819474)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'label': 'Code distance',\n", + " 'path': 'logicalQubit/codeDistance'},\n", + " {'description': 'Number of physical qubits per logical qubit',\n", + " 'explanation': 'The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'logicalQubit/physicalQubits'},\n", + " {'description': 'Duration of a logical cycle in nanoseconds',\n", + " 'explanation': 'The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.',\n", + " 'label': 'Logical cycle time',\n", + " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", + " {'description': 'Logical qubit error rate',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{9 + 1}{2}$',\n", + " 'label': 'Logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", + " {'description': 'Crossing prefactor used in QEC scheme',\n", + " 'explanation': 'The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.',\n", + " 'label': 'Crossing prefactor',\n", + " 'path': 'jobParams/qecScheme/crossingPrefactor'},\n", + " {'description': 'Error correction threshold used in QEC scheme',\n", + " 'explanation': 'The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.',\n", + " 'label': 'Error correction threshold',\n", + " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", + " {'description': 'QEC scheme formula used to compute logical cycle time',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 3us 600ns.',\n", + " 'label': 'Logical cycle time formula',\n", + " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", + " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 162.',\n", + " 'label': 'Physical qubits formula',\n", + " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", + " 'title': 'Logical qubit parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of physical qubits for a single T factory',\n", + " 'explanation': 'This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'tfactory/physicalQubits'},\n", + " {'description': 'Runtime of a single T factory',\n", + " 'explanation': 'The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", + " {'description': 'Number of output T states produced in a single run of T factory',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.',\n", + " 'label': 'Number of output T states per run',\n", + " 'path': 'tfactory/numTstates'},\n", + " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", + " 'explanation': 'This value includes the physical input T states of all copies of the distillation unit in the first round.',\n", + " 'label': 'Number of input T states per run',\n", + " 'path': 'tfactory/numInputTstates'},\n", + " {'description': 'The number of distillation rounds',\n", + " 'explanation': 'This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.',\n", + " 'label': 'Distillation rounds',\n", + " 'path': 'tfactory/numRounds'},\n", + " {'description': 'The number of units in each round of distillation',\n", + " 'explanation': 'This is the number of copies for the distillation units per round.',\n", + " 'label': 'Distillation units per round',\n", + " 'path': 'physicalCountsFormatted/numUnitsPerRound'},\n", + " {'description': 'The types of distillation units',\n", + " 'explanation': 'These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.',\n", + " 'label': 'Distillation units',\n", + " 'path': 'physicalCountsFormatted/unitNamePerRound'},\n", + " {'description': 'The code distance in each round of distillation',\n", + " 'explanation': 'This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.',\n", + " 'label': 'Distillation code distances',\n", + " 'path': 'physicalCountsFormatted/codeDistancePerRound'},\n", + " {'description': 'The number of physical qubits used in each round of distillation',\n", + " 'explanation': 'The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.',\n", + " 'label': 'Number of physical qubits per round',\n", + " 'path': 'physicalCountsFormatted/physicalQubitsPerRound'},\n", + " {'description': 'The runtime of each distillation round',\n", + " 'explanation': 'The runtime of the T factory is the sum of the runtimes in all rounds.',\n", + " 'label': 'Runtime per round',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", + " {'description': 'Logical T state error rate',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 9.62e-6.',\n", + " 'label': 'Logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", + " 'title': 'T factory parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", + " 'explanation': 'We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'label': 'Logical qubits (pre-layout)',\n", + " 'path': 'logicalCounts/numQubits'},\n", + " {'description': 'Number of T gates in the input quantum program',\n", + " 'explanation': 'This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.',\n", + " 'label': 'T gates',\n", + " 'path': 'logicalCounts/tCount'},\n", + " {'description': 'Number of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.',\n", + " 'label': 'Rotation gates',\n", + " 'path': 'logicalCounts/rotationCount'},\n", + " {'description': 'Depth of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.',\n", + " 'label': 'Rotation depth',\n", + " 'path': 'logicalCounts/rotationDepth'},\n", + " {'description': 'Number of CCZ-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCZ gates.',\n", + " 'label': 'CCZ gates',\n", + " 'path': 'logicalCounts/cczCount'},\n", + " {'description': 'Number of CCiX-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].',\n", + " 'label': 'CCiX gates',\n", + " 'path': 'logicalCounts/ccixCount'},\n", + " {'description': 'Number of single qubit measurements in the input quantum program',\n", + " 'explanation': 'This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.',\n", + " 'label': 'Measurement operations',\n", + " 'path': 'logicalCounts/measurementCount'}],\n", + " 'title': 'Pre-layout logical resources'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Total error budget for the algorithm',\n", + " 'explanation': \"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\n", + " 'label': 'Total error budget',\n", + " 'path': 'physicalCountsFormatted/errorBudget'},\n", + " {'description': 'Probability of at least one logical error',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'Logical error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetLogical'},\n", + " {'description': 'Probability of at least one faulty T distillation',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'T distillation error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetTstates'},\n", + " {'description': 'Probability of at least one failed rotation synthesis',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3.',\n", + " 'label': 'Rotation synthesis error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetRotations'}],\n", + " 'title': 'Assumed error budget'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Some descriptive name for the qubit model',\n", + " 'explanation': 'You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).',\n", + " 'label': 'Qubit name',\n", + " 'path': 'jobParams/qubitParams/name'},\n", + " {'description': 'Underlying qubit technology (gate-based or Majorana)',\n", + " 'explanation': 'When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.',\n", + " 'label': 'Instruction set',\n", + " 'path': 'jobParams/qubitParams/instructionSet'},\n", + " {'description': 'Operation time for single-qubit measurement (t_meas) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.',\n", + " 'label': 'Single-qubit measurement time',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementTime'},\n", + " {'description': 'Operation time for single-qubit gate (t_gate) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.',\n", + " 'label': 'Single-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateTime'},\n", + " {'description': 'Operation time for two-qubit gate in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.',\n", + " 'label': 'Two-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateTime'},\n", + " {'description': 'Operation time for a T gate',\n", + " 'explanation': 'This is the operation time in nanoseconds to execute a T gate.',\n", + " 'label': 'T gate time',\n", + " 'path': 'jobParams/qubitParams/tGateTime'},\n", + " {'description': 'Error rate for single-qubit measurement',\n", + " 'explanation': 'This is the probability in which a single-qubit measurement in the Pauli basis may fail.',\n", + " 'label': 'Single-qubit measurement error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementErrorRate'},\n", + " {'description': 'Error rate for single-qubit Clifford gate (p)',\n", + " 'explanation': 'This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.',\n", + " 'label': 'Single-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateErrorRate'},\n", + " {'description': 'Error rate for two-qubit Clifford gate',\n", + " 'explanation': 'This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.',\n", + " 'label': 'Two-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateErrorRate'},\n", + " {'description': 'Error rate to prepare single-qubit T state or apply a T gate (p_T)',\n", + " 'explanation': 'This is the probability in which executing a single T gate may fail.',\n", + " 'label': 'T gate error rate',\n", + " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", + " 'title': 'Physical qubit parameters'}]},\n", + " 'status': 'success',\n", + " 'tfactory': {'codeDistancePerRound': [9],\n", + " 'logicalErrorRate': 2.165000000000001e-06,\n", + " 'numInputTstates': 30,\n", + " 'numRounds': 1,\n", + " 'numTstates': 1,\n", + " 'numUnitsPerRound': [2],\n", + " 'physicalQubits': 6480,\n", + " 'physicalQubitsPerRound': [6480],\n", + " 'runtime': 46800.0,\n", + " 'runtimePerRound': [46800.0],\n", + " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", "# result = qsharp.azure.output(\"...\")\n", @@ -364,7 +3299,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "metadata": { "collapsed": false, "jupyter": { @@ -391,7 +3326,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, "metadata": { "collapsed": false, "jupyter": { @@ -404,10 +3339,37 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Logical algorithmic qubits = 33\n", + "Algorithmic depth = 47\n", + "Score = 1551\n" + ] + }, + { + "data": { + "text/plain": [ + "1551" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "evaluate_results(result)" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -415,9 +3377,9 @@ "name": "python3" }, "kernelspec": { - "display_name": "Python 3 [Default]", + "display_name": "Python 3 [Q#]", "language": "python", - "name": "python3" + "name": "python3_qsharp_b54crn" }, "language_info": { "codemirror_mode": { diff --git a/iQuHack-challenge-2023-task6.ipynb b/iQuHack-challenge-2023-task6.ipynb index 4d2f2c8..5205348 100644 --- a/iQuHack-challenge-2023-task6.ipynb +++ b/iQuHack-challenge-2023-task6.ipynb @@ -67,7 +67,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "collapsed": false, "jupyter": { @@ -89,7 +89,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": { "collapsed": false, "jupyter": { @@ -104,14 +104,14 @@ }, "outputs": [], "source": [ - "teamname=\"msft_is_the_best\" # Update this field with your team name\n", + "teamname=\"schrodingers-duck\" # Update this field with your team name\n", "task=[\"task6\"]\n", - "slack_id=\"myslackid\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + "slack_id=\"U04L3SFUCQ2\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": { "collapsed": false, "jupyter": { @@ -148,7 +148,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": { "collapsed": false, "jupyter": { @@ -169,19 +169,68 @@ "%%qsharp\n", "open Microsoft.Quantum.Canon;\n", "open Microsoft.Quantum.Diagnostics;\n", + "open Microsoft.Quantum.Arrays;\n", "\n", "// Task 6. \n", "// (input will contain 8 qubits)\n", - "operation Task6(input : Qubit[], target : Qubit) : Unit is Adj {\n", + "operation original(input : Qubit[], target : Qubit) : Unit is Adj {\n", " for i in [144, 145, 148, 149, 152, 153, 156, 157, 208, 209, 212, 213, 216, 217, 220, 221] {\n", " ControlledOnInt(i, X)(input, target);\n", " }\n", + "}\n", + "\n", + "operation Task6(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " for i in [20,22] {\n", + " ControlledOnInt(i, X)([input[1],input[2],input[4], input[5], input[7]], target);\n", + " }\n", + "}\n", + "\n", + "operation QubitArrayWrapperOperation (op : ((Qubit[], Qubit) => Unit is Adj), qs : Qubit[]) : Unit is Adj { \n", + " op(Most(qs), Tail(qs));\n", + "}\n", + "\n", + "operation TestCompoundGate () : Unit {\n", + " AssertOperationsEqualReferenced(8+1, QubitArrayWrapperOperation(Task6, _), QubitArrayWrapperOperation (original, _));\n", "}" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Traceback (most recent call last):\n", + " File \"/opt/conda/lib/python3.9/runpy.py\", line 197, in _run_module_as_main\n", + " return _run_code(code, main_globals, None,\n", + " File \"/opt/conda/lib/python3.9/runpy.py\", line 87, in _run_code\n", + " exec(code, run_globals)\n", + " File \"/opt/conda/lib/python3.9/site-packages/ipykernel_launcher.py\", line 17, in \n", + " app.launch_new_instance()\n", + " File \"/opt/conda/lib/python3.9/site-packages/traitlets/config/application.py\", line 1041, in launch_instance\n", + " app.start()\n", + " File \"/opt/conda/lib/python3.9/site-packages/ipykernel/kernelapp.py\", line 724, in start\n", + " self.io_loop.start()\n", + " File \"/opt/conda/lib/python3.9/site-packages/tornado/platform/asyncio.py\", line 199, in start\n", + " self.asyncio_loop.run_forever()\n", + " File \"/opt/conda/lib/python3.9/asyncio/base_events.py\", line 596, in run_forever\n", + " self._run_once()\n", + " File \"/opt/conda/lib/python3.9/asyncio/base_events.py\", line 1875, in _run_once\n", + " handle = self._ready.popleft()\n", + "IndexError: pop from an empty deque\n" + ] + } + ], + "source": [ + "TestCompoundGate();" + ] + }, + { + "cell_type": "code", + "execution_count": 32, "metadata": { "collapsed": false, "jupyter": { @@ -238,7 +287,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 33, "metadata": { "collapsed": false, "jupyter": { @@ -251,7 +300,6702 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": 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Qubit IDs0, 1, 2, 3, 4, 5, 6, 7, 8
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$\\left|001000110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001001000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001001010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001001100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001001110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001010000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001010010100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001010100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001010110100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001011000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001011010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001011100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001011110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001100000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001100010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001100100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001100110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001101000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001101010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001101100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001101110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001110000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001110010100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001110100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001110110100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001111000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001111010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001111100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001111110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010000010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010000100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010000110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010001000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010001010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010001100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010001110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010010000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|010010010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010010100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010010110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010011000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010011010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010011100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010011110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010100000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010100010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010100100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010100110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010101000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010101010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010101100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|010101110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|010110000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|010110010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010110100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010110110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010111000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|010111010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010111100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|010111110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011000010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011000100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011000110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011001000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|011001010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011001100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011001110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011010000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011010010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011010100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011010110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011011000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011011010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011011100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011011110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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$\\left|011101010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|011101110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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\r\n", + "
$\\left|011110010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011110110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
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\r\n", + "
$\\left|011111010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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\r\n", + "
$\\left|011111110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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\r\n", + "
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\r\n", + "

\r\n", + "
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\r\n", + "

\r\n", + "
$\\left|100000110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
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\r\n", + "

\r\n", + "
$\\left|100001010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|100001100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|100001110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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\r\n", + "
$\\left|100010010100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
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\r\n", + "
$\\left|100010110100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|100011000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100011010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100011100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100011110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100100000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100100010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100100100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100100110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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\r\n", + "
$\\left|100101010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100101100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100101110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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\r\n", + "
$\\left|100110010100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100110100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100110110100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100111000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100111010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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\r\n", + "
$\\left|100111110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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\r\n", + "
$\\left|101000010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|101000100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|101000110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|101001000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101011000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101011100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101011110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101100000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101111000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101111010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101111100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110000010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110000100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110010000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110010010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110010100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110010110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110011000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110011010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110011100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110011110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110100000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110100010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110100100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110100110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110101000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110101010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

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$\\left|110101100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110101110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110110000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110110010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110110100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110110110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110111000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110111010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110111100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110111110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111000010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111000100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111000110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111001000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111001010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111001100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111001110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111010010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111010110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111011000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111011010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111011100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111011110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111100010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111100110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111101000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111101010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111101110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111110000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111110010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111110100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111110110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111111000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111111010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111111100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111111110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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"output_type": "execute_result" + } + ], "source": [ "# Note that in the output of this cell the target qubit corresponds to the rightmost bit\n", "qsharp.config[\"dump.basisStateLabelingConvention\"]=\"Bitstring\"\n", @@ -276,7 +7020,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 34, "metadata": { "collapsed": false, "jupyter": { @@ -289,19 +7033,68 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "\"Connecting to Azure Quantum...\"", + "text/plain": [ + "Connecting to Azure Quantum..." + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Connected to Azure Quantum workspace azure-q in location uksouth.\n" + ] + }, + { + "data": { + "text/plain": [ + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 47232},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 383474},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 2},\n", + " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 180},\n", + " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 180},\n", + " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.qpu.aspen-m-2', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", "# If you're using this notebook in qBraid, keep it\n", "qsharp.azure.connect(\n", - " resourceId=\"...\",\n", - " location=\"...\",\n", + " resourceId=\"/subscriptions/7fc54e95-14cf-4a6f-b50e-d6155c241309/resourceGroups/AzureQuantum/providers/Microsoft.Quantum/Workspaces/azure-q\",\n", + " location=\"UK South\",\n", " credential=\"CLI\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 35, "metadata": { "collapsed": false, "jupyter": { @@ -314,14 +7107,33 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loading package Microsoft.Quantum.Providers.Core and dependencies...\n", + "Active target is now microsoft.estimator\n" + ] + }, + { + "data": { + "text/plain": [ + "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "qsharp.azure.target(\"microsoft.estimator\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 36, "metadata": { "collapsed": false, "jupyter": { @@ -334,7 +7146,20 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Submitting Task6_ResourceEstimationWrapper to target microsoft.estimator...\n", + "Job successfully submitted.\n", + " Job name: RE for the task 6\n", + " Job ID: c796f8ea-2157-429d-b6d6-9315680622eb\n", + "Waiting up to 30 seconds for Azure Quantum job to complete...\n", + "[9:02:21 AM] Current job status: Succeeded\n" + ] + } + ], "source": [ "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", "result = qsharp.azure.execute(Task6_ResourceEstimationWrapper, jobName=\"RE for the task 6\")" @@ -342,7 +7167,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 37, "metadata": { "collapsed": false, "jupyter": { @@ -355,7 +7180,1051 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":6,\"cczCount\":2,\"measurementCount\":6,\"numQubits\":12,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":9,\"logicalCycleTime\":3600.0,\"logicalErrorRate\":3.0000000000000015E-07,\"physicalQubits\":162},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":30,\"algorithmicLogicalQubits\":35,\"cliffordErrorRate\":0.001,\"logicalDepth\":30,\"numTfactories\":14,\"numTfactoryRuns\":3,\"numTsPerRotation\":null,\"numTstates\":32,\"physicalQubitsForAlgorithm\":5670,\"physicalQubitsForTfactories\":90720,\"requiredLogicalQubitErrorRate\":4.761904761904762E-07,\"requiredLogicalTstateErrorRate\":1.5625E-05},\"physicalQubits\":96390,\"runtime\":108000},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"3us 600ns\",\"logicalErrorRate\":\"3.00e-7\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"94.12 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"4.76e-7\",\"requiredLogicalTstateErrorRate\":\"1.56e-5\",\"runtime\":\"108us\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 5670 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 30 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 12$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 35$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 6 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 2 CCZ and 6 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 30. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 2 CCZ and 6 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 32 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{32\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 108us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 32 T states, the 14 copies of the T factory are repeatedly invoked 3 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 5670 are the product of the 35 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\\\cdot 14$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 35 logical qubits and the total cycle count 30.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 32.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.0000004761904761904762)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{9 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 3us 600ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 162.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.56e-5.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 35 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or ¬µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "text/html": [ + "\r\n", + "
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Physical qubits96390\r\n", + "

Number of physical qubits

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This value represents the total number of physical qubits, which is the sum of 5670 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

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Runtime108us\r\n", + "

Total runtime

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This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 30 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

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Logical algorithmic qubits35\r\n", + "

Number of logical qubits for the algorithm after layout

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Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 12\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 35$ logical qubits.

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Algorithmic depth30\r\n", + "

Number of logical cycles for the algorithm

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To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 6 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 2 CCZ and 6 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

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Logical depth30\r\n", + "

Number of logical cycles performed

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This number is usually equal to the logical depth of the algorithm, which is 30. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", + "\r\n", + "
Number of T states32\r\n", + "

Number of T states consumed by the algorithm

\n", + "\r\n", + "
\r\n", + "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 2 CCZ and 6 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", + "\r\n", + "
Number of T factories14\r\n", + "

Number of T factories capable of producing the demanded 32 T states during the algorithm's runtime

\n", + "\r\n", + "
\r\n", + "

The total number of T factories 14 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{32\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 108us\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", + "\r\n", + "
Number of T factory invocations3\r\n", + "

Number of times all T factories are invoked

\n", + "\r\n", + "
\r\n", + "

In order to prepare the 32 T states, the 14 copies of the T factory are repeatedly invoked 3 times.

\n", + "\r\n", + "
Physical algorithmic qubits5670\r\n", + "

Number of physical qubits for the algorithm after layout

\n", + "\r\n", + "
\r\n", + "

The 5670 are the product of the 35 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.

\n", + "\r\n", + "
Physical T factory qubits90720\r\n", + "

Number of physical qubits for the T factories

\n", + "\r\n", + "
\r\n", + "

Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\cdot 14$ qubits.

\n", + "\r\n", + "
Required logical qubit error rate4.76e-7\r\n", + "

The minimum logical qubit error rate required to run the algorithm within the error budget

\n", + "\r\n", + "
\r\n", + "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 35 logical qubits and the total cycle count 30.

\n", + "\r\n", + "
Required logical T state error rate1.56e-5\r\n", + "

The minimum T state error rate required for distilled T states

\n", + "\r\n", + "
\r\n", + "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 32.

\n", + "\r\n", + "
Number of T states per rotationNo rotations in algorithm\r\n", + "

Number of T states to implement a rotation with an arbitrary angle

\n", + "\r\n", + "
\r\n", + "

The number of T states to implement a rotation with an arbitrary angle is \\(\\lceil 0.53 \\log_2(0 / 0) + 5.3\\rceil\\) [arXiv:2203.10064]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Logical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
QEC schemesurface_code\r\n", + "

Name of QEC scheme

\n", + "\r\n", + "
\r\n", + "

You can load pre-defined QEC schemes by using the name surface_code or floquet_code. The latter only works with Majorana qubits.

\n", + "\r\n", + "
Code distance9\r\n", + "

Required code distance for error correction

\n", + "\r\n", + "
\r\n", + "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.0000004761904761904762)}{\\log(0.01/0.001)} - 1\\)

\n", + "\r\n", + "
Physical qubits162\r\n", + "

Number of physical qubits per logical qubit

\n", + "\r\n", + "
\r\n", + "

The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.

\n", + "\r\n", + "
Logical cycle time3us 600ns\r\n", + "

Duration of a logical cycle in nanoseconds

\n", + "\r\n", + "
\r\n", + "

The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.

\n", + "\r\n", + "
Logical qubit error rate3.00e-7\r\n", + "

Logical qubit error rate

\n", + "\r\n", + "
\r\n", + "

The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{9 + 1}{2}$

\n", + "\r\n", + "
Crossing prefactor0.03\r\n", + "

Crossing prefactor used in QEC scheme

\n", + "\r\n", + "
\r\n", + "

The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.

\n", + "\r\n", + "
Error correction threshold0.01\r\n", + "

Error correction threshold used in QEC scheme

\n", + "\r\n", + "
\r\n", + "

The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.

\n", + "\r\n", + "
Logical cycle time formula(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\r\n", + "

QEC scheme formula used to compute logical cycle time

\n", + "\r\n", + "
\r\n", + "

This is the formula that is used to compute the logical cycle time 3us 600ns.

\n", + "\r\n", + "
Physical qubits formula2 * codeDistance * codeDistance\r\n", + "

QEC scheme formula used to compute number of physical qubits per logical qubit

\n", + "\r\n", + "
\r\n", + "

This is the formula that is used to compute the number of physical qubits per logical qubits 162.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " T factory parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits6480\r\n", + "

Number of physical qubits for a single T factory

\n", + "\r\n", + "
\r\n", + "

This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.

\n", + "\r\n", + "
Runtime46us 800ns\r\n", + "

Runtime of a single T factory

\n", + "\r\n", + "
\r\n", + "

The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.

\n", + "\r\n", + "
Number of output T states per run1\r\n", + "

Number of output T states produced in a single run of T factory

\n", + "\r\n", + "
\r\n", + "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.

\n", + "\r\n", + "
Number of input T states per run30\r\n", + "

Number of physical input T states consumed in a single run of a T factory

\n", + "\r\n", + "
\r\n", + "

This value includes the physical input T states of all copies of the distillation unit in the first round.

\n", + "\r\n", + "
Distillation rounds1\r\n", + "

The number of distillation rounds

\n", + "\r\n", + "
\r\n", + "

This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.

\n", + "\r\n", + "
Distillation units per round2\r\n", + "

The number of units in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the number of copies for the distillation units per round.

\n", + "\r\n", + "
Distillation units15-to-1 space efficient logical\r\n", + "

The types of distillation units

\n", + "\r\n", + "
\r\n", + "

These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.

\n", + "\r\n", + "
Distillation code distances9\r\n", + "

The code distance in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.

\n", + "\r\n", + "
Number of physical qubits per round6480\r\n", + "

The number of physical qubits used in each round of distillation

\n", + "\r\n", + "
\r\n", + "

The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.

\n", + "\r\n", + "
Runtime per round46us 800ns\r\n", + "

The runtime of each distillation round

\n", + "\r\n", + "
\r\n", + "

The runtime of the T factory is the sum of the runtimes in all rounds.

\n", + "\r\n", + "
Logical T state error rate2.17e-6\r\n", + "

Logical T state error rate

\n", + "\r\n", + "
\r\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.56e-5.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Pre-layout logical resources\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Logical qubits (pre-layout)12\r\n", + "

Number of logical qubits in the input quantum program

\n", + "\r\n", + "
\r\n", + "

We determine 35 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", + "\r\n", + "
T gates0\r\n", + "

Number of T gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.

\n", + "\r\n", + "
Rotation gates0\r\n", + "

Number of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.

\n", + "\r\n", + "
Rotation depth0\r\n", + "

Depth of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.

\n", + "\r\n", + "
CCZ gates2\r\n", + "

Number of CCZ-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCZ gates.

\n", + "\r\n", + "
CCiX gates6\r\n", + "

Number of CCiX-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCiX gates, which applies \\(-iX\\) controlled on two control qubits [1212.5069].

\n", + "\r\n", + "
Measurement operations6\r\n", + "

Number of single qubit measurements in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Assumed error budget\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Total error budget1.00e-3\r\n", + "

Total error budget for the algorithm

\n", + "\r\n", + "
\r\n", + "

The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget \\(\\epsilon = \\epsilon_{\\log} + \\epsilon_{\\rm dis} + \\epsilon_{\\rm syn}\\) is uniformly distributed and applies to errors \\(\\epsilon_{\\log}\\) to implement logical qubits, an error budget \\(\\epsilon_{\\rm dis}\\) to produce T states through distillation, and an error budget \\(\\epsilon_{\\rm syn}\\) to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets \\(\\epsilon_{\\rm dis}\\) and \\(\\epsilon_{\\rm syn}\\) are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.

\n", + "\r\n", + "
Logical error probability5.00e-4\r\n", + "

Probability of at least one logical error

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
T distillation error probability5.00e-4\r\n", + "

Probability of at least one faulty T distillation

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
Rotation synthesis error probability0.00e0\r\n", + "

Probability of at least one failed rotation synthesis

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Physical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Qubit namequbit_gate_ns_e3\r\n", + "

Some descriptive name for the qubit model

\n", + "\r\n", + "
\r\n", + "

You can load pre-defined qubit parameters by using the names qubit_gate_ns_e3, qubit_gate_ns_e4, qubit_gate_us_e3, qubit_gate_us_e4, qubit_maj_ns_e4, or qubit_maj_ns_e6. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).

\n", + "\r\n", + "
Instruction setGateBased\r\n", + "

Underlying qubit technology (gate-based or Majorana)

\n", + "\r\n", + "
\r\n", + "

When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either gate-based or Majorana. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.

\n", + "\r\n", + "
Single-qubit measurement time100 ns\r\n", + "

Operation time for single-qubit measurement (t_meas) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.

\n", + "\r\n", + "
Single-qubit gate time50 ns\r\n", + "

Operation time for single-qubit gate (t_gate) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.

\n", + "\r\n", + "
Two-qubit gate time50 ns\r\n", + "

Operation time for two-qubit gate in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.

\n", + "\r\n", + "
T gate time50 ns\r\n", + "

Operation time for a T gate

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to execute a T gate.

\n", + "\r\n", + "
Single-qubit measurement error rate0.001\r\n", + "

Error rate for single-qubit measurement

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit measurement in the Pauli basis may fail.

\n", + "\r\n", + "
Single-qubit error rate0.001\r\n", + "

Error rate for single-qubit Clifford gate (p)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.

\n", + "\r\n", + "
Two-qubit error rate0.001\r\n", + "

Error rate for two-qubit Clifford gate

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.

\n", + "\r\n", + "
T gate error rate0.001\r\n", + "

Error rate to prepare single-qubit T state or apply a T gate (p_T)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which executing a single T gate may fail.

\n", + "\r\n", + "
\n", + "
\r\n", + " Assumptions\r\n", + "
    \n", + "

  • More details on the following lists of assumptions can be found in the paper Accessing requirements for scaling quantum computers and their applications.

    \n", + "
    • \n", + "

  • Uniform independent physical noise. We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.

    \n", + "
    • \n", + "

  • Efficient classical computation. We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.

    \n", + "
    • \n", + "

  • Extraction circuits for planar quantum ISA. We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).

    \n", + "
    • \n", + "

  • Uniform independent logical noise. We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.

    \n", + "
    • \n", + "

  • Negligible Clifford costs for synthesis. We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.

    \n", + "
    • \n", + "

  • Smooth magic state consumption rate. We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.

    \n", + "
    • \n", + "
\n" + ], + "text/plain": [ + "{'errorBudget': {'logical': 0.0005, 'rotations': 0.0, 'tstates': 0.0005},\n", + " 'jobParams': {'errorBudget': 0.001,\n", + " 'qecScheme': {'crossingPrefactor': 0.03,\n", + " 'errorCorrectionThreshold': 0.01,\n", + " 'logicalCycleTime': '(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance',\n", + " 'name': 'surface_code',\n", + " 'physicalQubitsPerLogicalQubit': '2 * codeDistance * codeDistance'},\n", + " 'qubitParams': {'instructionSet': 'GateBased',\n", + " 'name': 'qubit_gate_ns_e3',\n", + " 'oneQubitGateErrorRate': 0.001,\n", + " 'oneQubitGateTime': '50 ns',\n", + " 'oneQubitMeasurementErrorRate': 0.001,\n", + " 'oneQubitMeasurementTime': '100 ns',\n", + " 'tGateErrorRate': 0.001,\n", + " 'tGateTime': '50 ns',\n", + " 'twoQubitGateErrorRate': 0.001,\n", + " 'twoQubitGateTime': '50 ns'}},\n", + " 'logicalCounts': {'ccixCount': 6,\n", + " 'cczCount': 2,\n", + " 'measurementCount': 6,\n", + " 'numQubits': 12,\n", + " 'rotationCount': 0,\n", + " 'rotationDepth': 0,\n", + " 'tCount': 0},\n", + " 'logicalQubit': {'codeDistance': 9,\n", + " 'logicalCycleTime': 3600.0,\n", + " 'logicalErrorRate': 3.0000000000000015e-07,\n", + " 'physicalQubits': 162},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 30,\n", + " 'algorithmicLogicalQubits': 35,\n", + " 'cliffordErrorRate': 0.001,\n", + " 'logicalDepth': 30,\n", + " 'numTfactories': 14,\n", + " 'numTfactoryRuns': 3,\n", + " 'numTsPerRotation': None,\n", + " 'numTstates': 32,\n", + " 'physicalQubitsForAlgorithm': 5670,\n", + " 'physicalQubitsForTfactories': 90720,\n", + " 'requiredLogicalQubitErrorRate': 4.761904761904762e-07,\n", + " 'requiredLogicalTstateErrorRate': 1.5625e-05},\n", + " 'physicalQubits': 96390,\n", + " 'runtime': 108000},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", + " 'errorBudget': '1.00e-3',\n", + " 'errorBudgetLogical': '5.00e-4',\n", + " 'errorBudgetRotations': '0.00e0',\n", + " 'errorBudgetTstates': '5.00e-4',\n", + " 'logicalCycleTime': '3us 600ns',\n", + " 'logicalErrorRate': '3.00e-7',\n", + " 'numTsPerRotation': 'No rotations in algorithm',\n", + " 'numUnitsPerRound': '2',\n", + " 'physicalQubitsForTfactoriesPercentage': '94.12 %',\n", + " 'physicalQubitsPerRound': '6480',\n", + " 'requiredLogicalQubitErrorRate': '4.76e-7',\n", + " 'requiredLogicalTstateErrorRate': '1.56e-5',\n", + " 'runtime': '108us',\n", + " 'tfactoryRuntime': '46us 800ns',\n", + " 'tfactoryRuntimePerRound': '46us 800ns',\n", + " 'tstateLogicalErrorRate': '2.17e-6',\n", + " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", + " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", + " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", + " '**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.',\n", + " '**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).',\n", + " '**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.',\n", + " '**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.',\n", + " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", + " 'groups': [{'alwaysVisible': True,\n", + " 'entries': [{'description': 'Number of physical qubits',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 5670 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'physicalCounts/physicalQubits'},\n", + " {'description': 'Total runtime',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 30 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/runtime'}],\n", + " 'title': 'Physical resource estimates'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 12$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 35$ logical qubits.',\n", + " 'label': 'Logical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", + " {'description': 'Number of logical cycles for the algorithm',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 6 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 2 CCZ and 6 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'label': 'Algorithmic depth',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", + " {'description': 'Number of logical cycles performed',\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 30. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'label': 'Logical depth',\n", + " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", + " {'description': 'Number of T states consumed by the algorithm',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 2 CCZ and 6 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'label': 'Number of T states',\n", + " 'path': 'physicalCounts/breakdown/numTstates'},\n", + " {'description': \"Number of T factories capable of producing the demanded 32 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{32\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 108us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " 'label': 'Number of T factories',\n", + " 'path': 'physicalCounts/breakdown/numTfactories'},\n", + " {'description': 'Number of times all T factories are invoked',\n", + " 'explanation': 'In order to prepare the 32 T states, the 14 copies of the T factory are repeatedly invoked 3 times.',\n", + " 'label': 'Number of T factory invocations',\n", + " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", + " {'description': 'Number of physical qubits for the algorithm after layout',\n", + " 'explanation': 'The 5670 are the product of the 35 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.',\n", + " 'label': 'Physical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", + " {'description': 'Number of physical qubits for the T factories',\n", + " 'explanation': 'Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\\\cdot 14$ qubits.',\n", + " 'label': 'Physical T factory qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", + " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 35 logical qubits and the total cycle count 30.',\n", + " 'label': 'Required logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", + " {'description': 'The minimum T state error rate required for distilled T states',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 32.',\n", + " 'label': 'Required logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", + " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", + " 'explanation': 'The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.',\n", + " 'label': 'Number of T states per rotation',\n", + " 'path': 'physicalCountsFormatted/numTsPerRotation'}],\n", + " 'title': 'Resource estimates breakdown'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Name of QEC scheme',\n", + " 'explanation': 'You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.',\n", + " 'label': 'QEC scheme',\n", + " 'path': 'jobParams/qecScheme/name'},\n", + " {'description': 'Required code distance for error correction',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.0000004761904761904762)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'label': 'Code distance',\n", + " 'path': 'logicalQubit/codeDistance'},\n", + " {'description': 'Number of physical qubits per logical qubit',\n", + " 'explanation': 'The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'logicalQubit/physicalQubits'},\n", + " {'description': 'Duration of a logical cycle in nanoseconds',\n", + " 'explanation': 'The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.',\n", + " 'label': 'Logical cycle time',\n", + " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", + " {'description': 'Logical qubit error rate',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{9 + 1}{2}$',\n", + " 'label': 'Logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", + " {'description': 'Crossing prefactor used in QEC scheme',\n", + " 'explanation': 'The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.',\n", + " 'label': 'Crossing prefactor',\n", + " 'path': 'jobParams/qecScheme/crossingPrefactor'},\n", + " {'description': 'Error correction threshold used in QEC scheme',\n", + " 'explanation': 'The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.',\n", + " 'label': 'Error correction threshold',\n", + " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", + " {'description': 'QEC scheme formula used to compute logical cycle time',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 3us 600ns.',\n", + " 'label': 'Logical cycle time formula',\n", + " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", + " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 162.',\n", + " 'label': 'Physical qubits formula',\n", + " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", + " 'title': 'Logical qubit parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of physical qubits for a single T factory',\n", + " 'explanation': 'This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'tfactory/physicalQubits'},\n", + " {'description': 'Runtime of a single T factory',\n", + " 'explanation': 'The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", + " {'description': 'Number of output T states produced in a single run of T factory',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.',\n", + " 'label': 'Number of output T states per run',\n", + " 'path': 'tfactory/numTstates'},\n", + " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", + " 'explanation': 'This value includes the physical input T states of all copies of the distillation unit in the first round.',\n", + " 'label': 'Number of input T states per run',\n", + " 'path': 'tfactory/numInputTstates'},\n", + " {'description': 'The number of distillation rounds',\n", + " 'explanation': 'This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.',\n", + " 'label': 'Distillation rounds',\n", + " 'path': 'tfactory/numRounds'},\n", + " {'description': 'The number of units in each round of distillation',\n", + " 'explanation': 'This is the number of copies for the distillation units per round.',\n", + " 'label': 'Distillation units per round',\n", + " 'path': 'physicalCountsFormatted/numUnitsPerRound'},\n", + " {'description': 'The types of distillation units',\n", + " 'explanation': 'These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.',\n", + " 'label': 'Distillation units',\n", + " 'path': 'physicalCountsFormatted/unitNamePerRound'},\n", + " {'description': 'The code distance in each round of distillation',\n", + " 'explanation': 'This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.',\n", + " 'label': 'Distillation code distances',\n", + " 'path': 'physicalCountsFormatted/codeDistancePerRound'},\n", + " {'description': 'The number of physical qubits used in each round of distillation',\n", + " 'explanation': 'The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.',\n", + " 'label': 'Number of physical qubits per round',\n", + " 'path': 'physicalCountsFormatted/physicalQubitsPerRound'},\n", + " {'description': 'The runtime of each distillation round',\n", + " 'explanation': 'The runtime of the T factory is the sum of the runtimes in all rounds.',\n", + " 'label': 'Runtime per round',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", + " {'description': 'Logical T state error rate',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.56e-5.',\n", + " 'label': 'Logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", + " 'title': 'T factory parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", + " 'explanation': 'We determine 35 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'label': 'Logical qubits (pre-layout)',\n", + " 'path': 'logicalCounts/numQubits'},\n", + " {'description': 'Number of T gates in the input quantum program',\n", + " 'explanation': 'This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.',\n", + " 'label': 'T gates',\n", + " 'path': 'logicalCounts/tCount'},\n", + " {'description': 'Number of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.',\n", + " 'label': 'Rotation gates',\n", + " 'path': 'logicalCounts/rotationCount'},\n", + " {'description': 'Depth of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.',\n", + " 'label': 'Rotation depth',\n", + " 'path': 'logicalCounts/rotationDepth'},\n", + " {'description': 'Number of CCZ-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCZ gates.',\n", + " 'label': 'CCZ gates',\n", + " 'path': 'logicalCounts/cczCount'},\n", + " {'description': 'Number of CCiX-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].',\n", + " 'label': 'CCiX gates',\n", + " 'path': 'logicalCounts/ccixCount'},\n", + " {'description': 'Number of single qubit measurements in the input quantum program',\n", + " 'explanation': 'This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.',\n", + " 'label': 'Measurement operations',\n", + " 'path': 'logicalCounts/measurementCount'}],\n", + " 'title': 'Pre-layout logical resources'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Total error budget for the algorithm',\n", + " 'explanation': \"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\n", + " 'label': 'Total error budget',\n", + " 'path': 'physicalCountsFormatted/errorBudget'},\n", + " {'description': 'Probability of at least one logical error',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'Logical error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetLogical'},\n", + " {'description': 'Probability of at least one faulty T distillation',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'T distillation error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetTstates'},\n", + " {'description': 'Probability of at least one failed rotation synthesis',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3.',\n", + " 'label': 'Rotation synthesis error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetRotations'}],\n", + " 'title': 'Assumed error budget'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Some descriptive name for the qubit model',\n", + " 'explanation': 'You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).',\n", + " 'label': 'Qubit name',\n", + " 'path': 'jobParams/qubitParams/name'},\n", + " {'description': 'Underlying qubit technology (gate-based or Majorana)',\n", + " 'explanation': 'When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.',\n", + " 'label': 'Instruction set',\n", + " 'path': 'jobParams/qubitParams/instructionSet'},\n", + " {'description': 'Operation time for single-qubit measurement (t_meas) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.',\n", + " 'label': 'Single-qubit measurement time',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementTime'},\n", + " {'description': 'Operation time for single-qubit gate (t_gate) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.',\n", + " 'label': 'Single-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateTime'},\n", + " {'description': 'Operation time for two-qubit gate in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.',\n", + " 'label': 'Two-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateTime'},\n", + " {'description': 'Operation time for a T gate',\n", + " 'explanation': 'This is the operation time in nanoseconds to execute a T gate.',\n", + " 'label': 'T gate time',\n", + " 'path': 'jobParams/qubitParams/tGateTime'},\n", + " {'description': 'Error rate for single-qubit measurement',\n", + " 'explanation': 'This is the probability in which a single-qubit measurement in the Pauli basis may fail.',\n", + " 'label': 'Single-qubit measurement error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementErrorRate'},\n", + " {'description': 'Error rate for single-qubit Clifford gate (p)',\n", + " 'explanation': 'This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.',\n", + " 'label': 'Single-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateErrorRate'},\n", + " {'description': 'Error rate for two-qubit Clifford gate',\n", + " 'explanation': 'This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.',\n", + " 'label': 'Two-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateErrorRate'},\n", + " {'description': 'Error rate to prepare single-qubit T state or apply a T gate (p_T)',\n", + " 'explanation': 'This is the probability in which executing a single T gate may fail.',\n", + " 'label': 'T gate error rate',\n", + " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", + " 'title': 'Physical qubit parameters'}]},\n", + " 'status': 'success',\n", + " 'tfactory': {'codeDistancePerRound': [9],\n", + " 'logicalErrorRate': 2.165000000000001e-06,\n", + " 'numInputTstates': 30,\n", + " 'numRounds': 1,\n", + " 'numTstates': 1,\n", + " 'numUnitsPerRound': [2],\n", + " 'physicalQubits': 6480,\n", + " 'physicalQubitsPerRound': [6480],\n", + " 'runtime': 46800.0,\n", + " 'runtimePerRound': [46800.0],\n", + " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", "# result = qsharp.azure.output(\"...\")\n", @@ -364,7 +8233,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 38, "metadata": { "collapsed": false, "jupyter": { @@ -391,7 +8260,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 39, "metadata": { "collapsed": false, "jupyter": { @@ -404,10 +8273,44 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Logical algorithmic qubits = 35\n", + "Algorithmic depth = 30\n", + "Score = 1050\n" + ] + }, + { + "data": { + "text/plain": [ + "1050" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "evaluate_results(result)" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -415,9 +8318,9 @@ "name": "python3" }, "kernelspec": { - "display_name": "Python 3 [Default]", + "display_name": "Python 3 [Q#]", "language": "python", - "name": "python3" + "name": "python3_qsharp_b54crn" }, "language_info": { "codemirror_mode": { diff --git a/iQuHack-challenge-2023-task8.ipynb b/iQuHack-challenge-2023-task8.ipynb index a84b05a..ecf01d4 100644 --- a/iQuHack-challenge-2023-task8.ipynb +++ b/iQuHack-challenge-2023-task8.ipynb @@ -67,7 +67,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "collapsed": false, "jupyter": { @@ -80,7 +80,15 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Preparing Q# environment...\n" + ] + } + ], "source": [ "# Run this code cell to import the modules required to work with Q# and Azure\n", "import qsharp\n", @@ -89,7 +97,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": { "collapsed": false, "jupyter": { @@ -104,14 +112,14 @@ }, "outputs": [], "source": [ - "teamname=\"msft_is_the_best\" # Update this field with your team name\n", + "teamname=\"schrodingers-duck\" # Update this field with your team name\n", "task=[\"task8\"]\n", - "slack_id=\"myslackid\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + "slack_id=\"U04L3SFUCQ2\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": { "collapsed": false, "jupyter": { @@ -148,7 +156,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": { "collapsed": false, "jupyter": { @@ -169,22 +177,70 @@ "%%qsharp\n", "open Microsoft.Quantum.Canon;\n", "open Microsoft.Quantum.Diagnostics;\n", + "open Microsoft.Quantum.Arithmetic;\n", + "open Microsoft.Quantum.Math;\n", + "open Microsoft.Quantum.Synthesis;\n", + "open Microsoft.Quantum.Arrays;\n", "\n", "// Task 8. \n", "// (input will contain 7 qubits)\n", - "operation Task8(input : Qubit[], target : Qubit) : Unit is Adj {\n", + "operation original(input : Qubit[], target : Qubit) : Unit is Adj {\n", " for i in [15,23,27,29,30,31,39,43, 45,46,47,51,53,54,55,57, \n", " 58,59,60,61,62,63,71,75, 77,78,79,83,85,86,87,89,\n", " 90,91,92,93,94,95,99,101, 102,103,105,106,107,108,109,110,\n", " 111,113,114,115,116,117,118,119, 120,121,122,123,124,125,126,127] {\n", " ControlledOnInt(i, X)(input, target);\n", " }\n", - "}" + "}\n", + "\n", + "operation Task8(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " use sumWires = Qubit[7];\n", + " use zero = Qubit[1];\n", + " within{\n", + " //Ebene 1\n", + " CarryN(input[0], input[1], input[2], sumWires[0]);\n", + " CarryN(input[3], input[4], input[5], sumWires[1]);\n", + " //Ebene 2\n", + " CarryN(zero[0], input[2], input[5], sumWires[2]);\n", + " CarryN(sumWires[2], sumWires[0], sumWires[1], sumWires[3]);\n", + " //Ebene 3\n", + " CarryN(zero[0], input[6], input[5], sumWires[4]);\n", + " CarryN(sumWires[4], zero[0], sumWires[1], sumWires[5]);\n", + " CarryN(sumWires[5], zero[0], sumWires[3], sumWires[6]);\n", + " } apply{\n", + " //CNOT(sumWires[3], target);\n", + " CNOT(sumWires[3], target);\n", + " }\n", + "}\n", + "operation CarryN(carryIn: Qubit, summand1: Qubit, summand2: Qubit, carryOut: Qubit) : Unit is Adj + Ctl {\n", + " CCNOT (summand1, summand2, carryOut);\n", + " CNOT (summand1, summand2);\n", + " CCNOT (carryIn, summand2, carryOut);\n", + " CNOT(carryIn, summand2);\n", + "}\n", + "\n", + "operation QubitArrayWrapperOperation (op : ((Qubit[], Qubit) => Unit is Adj), qs : Qubit[]) : Unit is Adj { \n", + " op(Most(qs), Tail(qs));\n", + "}\n", + "\n", + "operation TestCompoundGate () : Unit {\n", + " AssertOperationsEqualReferenced(7+1, QubitArrayWrapperOperation(Task8, _), QubitArrayWrapperOperation (original, _));\n", + "}\n", + "\n" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "TestCompoundGate();" + ] + }, + { + "cell_type": "code", + "execution_count": 6, "metadata": { "collapsed": false, "jupyter": { @@ -241,7 +297,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "metadata": { "collapsed": false, "jupyter": { @@ -254,7 +310,3374 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": 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Qubit IDs0, 1, 2, 3, 4, 5, 6, 7
Basis state (bitstring)AmplitudeMeas. Pr.
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$\\left|0011011100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|00111000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0011101100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|01000110\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1010111100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10110000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1011001100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1011010100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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+ 0𝑖\n", + "|1111110100000000⟩\t0.0883883476483185 + 0𝑖\n", + "|1111111100000000⟩\t0.0883883476483185 + 0𝑖" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "()" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# Note that in the output of this cell the target qubit corresponds to the rightmost bit\n", "qsharp.config[\"dump.basisStateLabelingConvention\"]=\"Bitstring\"\n", @@ -279,7 +3702,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "metadata": { "collapsed": false, "jupyter": { @@ -292,19 +3715,68 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "\"Connecting to Azure Quantum...\"", + "text/plain": [ + "Connecting to Azure Quantum..." + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Connected to Azure Quantum workspace azure-q in location uksouth.\n" + ] + }, + { + "data": { + "text/plain": [ + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 296609},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 366858},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 3},\n", + " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 183},\n", + " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 183},\n", + " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.qpu.aspen-m-2', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", "# If you're using this notebook in qBraid, keep it\n", "qsharp.azure.connect(\n", - " resourceId=\"...\",\n", - " location=\"...\",\n", + " resourceId=\"/subscriptions/7fc54e95-14cf-4a6f-b50e-d6155c241309/resourceGroups/AzureQuantum/providers/Microsoft.Quantum/Workspaces/azure-q\",\n", + " location=\"UK South\",\n", " credential=\"CLI\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "metadata": { "collapsed": false, "jupyter": { @@ -317,14 +3789,33 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loading package Microsoft.Quantum.Providers.Core and dependencies...\n", + "Active target is now microsoft.estimator\n" + ] + }, + { + "data": { + "text/plain": [ + "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "qsharp.azure.target(\"microsoft.estimator\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, "metadata": { "collapsed": false, "jupyter": { @@ -337,7 +3828,20 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Submitting Task8_ResourceEstimationWrapper to target microsoft.estimator...\n", + "Job successfully submitted.\n", + " Job name: RE for the task 8\n", + " Job ID: e310d987-293a-4420-8db8-d09b15c2f5ac\n", + "Waiting up to 30 seconds for Azure Quantum job to complete...\n", + "[8:04:56 AM] Current job status: Succeeded\n" + ] + } + ], "source": [ "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", "result = qsharp.azure.execute(Task8_ResourceEstimationWrapper, jobName=\"RE for the task 8\")" @@ -345,7 +3849,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "metadata": { "collapsed": false, "jupyter": { @@ -358,7 +3862,1051 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":0,\"cczCount\":28,\"measurementCount\":0,\"numQubits\":16,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":84,\"algorithmicLogicalQubits\":45,\"cliffordErrorRate\":0.001,\"logicalDepth\":84,\"numTfactories\":15,\"numTfactoryRuns\":8,\"numTsPerRotation\":null,\"numTstates\":112,\"physicalQubitsForAlgorithm\":10890,\"physicalQubitsForTfactories\":97200,\"requiredLogicalQubitErrorRate\":1.3227513227513228E-07,\"requiredLogicalTstateErrorRate\":4.464285714285715E-06},\"physicalQubits\":108090,\"runtime\":369600},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"89.93 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"1.32e-7\",\"requiredLogicalTstateErrorRate\":\"4.46e-6\",\"runtime\":\"369us 600ns\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 10890 physical qubits to implement the algorithm logic, and 97200 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 84 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 16$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 45$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 0 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 28 CCZ and 0 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 84. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 28 CCZ and 0 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 112 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 15 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{112\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 369us 600ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 112 T states, the 15 copies of the T factory are repeatedly invoked 8 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 10890 are the product of the 45 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 15 in parallel, therefore we need $97200 = 6480 \\\\cdot 15$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 45 logical qubits and the total cycle count 84.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 112.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000013227513227513228)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 4.46e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 45 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or ¬µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "text/html": [ + "\r\n", + "
\r\n", + " \r\n", + " Physical resource estimates\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits108090\r\n", + "

Number of physical qubits

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This value represents the total number of physical qubits, which is the sum of 10890 physical qubits to implement the algorithm logic, and 97200 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

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Runtime369us 600ns\r\n", + "

Total runtime

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This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 84 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

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Logical algorithmic qubits45\r\n", + "

Number of logical qubits for the algorithm after layout

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Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 16\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 45$ logical qubits.

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Algorithmic depth84\r\n", + "

Number of logical cycles for the algorithm

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To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 0 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 28 CCZ and 0 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

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Logical depth84\r\n", + "

Number of logical cycles performed

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This number is usually equal to the logical depth of the algorithm, which is 84. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

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Number of T states112\r\n", + "

Number of T states consumed by the algorithm

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To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 28 CCZ and 0 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

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Number of T factories15\r\n", + "

Number of T factories capable of producing the demanded 112 T states during the algorithm's runtime

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The total number of T factories 15 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{112\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 369us 600ns\\;\\text{algorithm runtime}}\\right\\rceil\\)

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Number of T factory invocations8\r\n", + "

Number of times all T factories are invoked

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In order to prepare the 112 T states, the 15 copies of the T factory are repeatedly invoked 8 times.

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Physical algorithmic qubits10890\r\n", + "

Number of physical qubits for the algorithm after layout

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The 10890 are the product of the 45 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.

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Physical T factory qubits97200\r\n", + "

Number of physical qubits for the T factories

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Each T factory requires 6480 physical qubits and we run 15 in parallel, therefore we need $97200 = 6480 \\cdot 15$ qubits.

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Required logical qubit error rate1.32e-7\r\n", + "

The minimum logical qubit error rate required to run the algorithm within the error budget

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The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 45 logical qubits and the total cycle count 84.

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Required logical T state error rate4.46e-6\r\n", + "

The minimum T state error rate required for distilled T states

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The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 112.

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Number of T states per rotationNo rotations in algorithm\r\n", + "

Number of T states to implement a rotation with an arbitrary angle

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The number of T states to implement a rotation with an arbitrary angle is \\(\\lceil 0.53 \\log_2(0 / 0) + 5.3\\rceil\\) [arXiv:2203.10064]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.

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\r\n", + " \r\n", + " Logical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
QEC schemesurface_code\r\n", + "

Name of QEC scheme

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You can load pre-defined QEC schemes by using the name surface_code or floquet_code. The latter only works with Majorana qubits.

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Code distance11\r\n", + "

Required code distance for error correction

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The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000013227513227513228)}{\\log(0.01/0.001)} - 1\\)

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Physical qubits242\r\n", + "

Number of physical qubits per logical qubit

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The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.

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Logical cycle time4us 400ns\r\n", + "

Duration of a logical cycle in nanoseconds

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The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.

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Logical qubit error rate3.00e-8\r\n", + "

Logical qubit error rate

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The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{11 + 1}{2}$

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Crossing prefactor0.03\r\n", + "

Crossing prefactor used in QEC scheme

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The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.

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Error correction threshold0.01\r\n", + "

Error correction threshold used in QEC scheme

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The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.

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Logical cycle time formula(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\r\n", + "

QEC scheme formula used to compute logical cycle time

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This is the formula that is used to compute the logical cycle time 4us 400ns.

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Physical qubits formula2 * codeDistance * codeDistance\r\n", + "

QEC scheme formula used to compute number of physical qubits per logical qubit

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This is the formula that is used to compute the number of physical qubits per logical qubits 242.

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Physical qubits6480\r\n", + "

Number of physical qubits for a single T factory

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This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.

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Runtime46us 800ns\r\n", + "

Runtime of a single T factory

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The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.

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Number of output T states per run1\r\n", + "

Number of output T states produced in a single run of T factory

\n", + "\r\n", + "
\r\n", + "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.

\n", + "\r\n", + "
Number of input T states per run30\r\n", + "

Number of physical input T states consumed in a single run of a T factory

\n", + "\r\n", + "
\r\n", + "

This value includes the physical input T states of all copies of the distillation unit in the first round.

\n", + "\r\n", + "
Distillation rounds1\r\n", + "

The number of distillation rounds

\n", + "\r\n", + "
\r\n", + "

This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.

\n", + "\r\n", + "
Distillation units per round2\r\n", + "

The number of units in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the number of copies for the distillation units per round.

\n", + "\r\n", + "
Distillation units15-to-1 space efficient logical\r\n", + "

The types of distillation units

\n", + "\r\n", + "
\r\n", + "

These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.

\n", + "\r\n", + "
Distillation code distances9\r\n", + "

The code distance in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.

\n", + "\r\n", + "
Number of physical qubits per round6480\r\n", + "

The number of physical qubits used in each round of distillation

\n", + "\r\n", + "
\r\n", + "

The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.

\n", + "\r\n", + "
Runtime per round46us 800ns\r\n", + "

The runtime of each distillation round

\n", + "\r\n", + "
\r\n", + "

The runtime of the T factory is the sum of the runtimes in all rounds.

\n", + "\r\n", + "
Logical T state error rate2.17e-6\r\n", + "

Logical T state error rate

\n", + "\r\n", + "
\r\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 4.46e-6.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Pre-layout logical resources\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Logical qubits (pre-layout)16\r\n", + "

Number of logical qubits in the input quantum program

\n", + "\r\n", + "
\r\n", + "

We determine 45 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", + "\r\n", + "
T gates0\r\n", + "

Number of T gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.

\n", + "\r\n", + "
Rotation gates0\r\n", + "

Number of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.

\n", + "\r\n", + "
Rotation depth0\r\n", + "

Depth of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.

\n", + "\r\n", + "
CCZ gates28\r\n", + "

Number of CCZ-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCZ gates.

\n", + "\r\n", + "
CCiX gates0\r\n", + "

Number of CCiX-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCiX gates, which applies \\(-iX\\) controlled on two control qubits [1212.5069].

\n", + "\r\n", + "
Measurement operations0\r\n", + "

Number of single qubit measurements in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Assumed error budget\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Total error budget1.00e-3\r\n", + "

Total error budget for the algorithm

\n", + "\r\n", + "
\r\n", + "

The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget \\(\\epsilon = \\epsilon_{\\log} + \\epsilon_{\\rm dis} + \\epsilon_{\\rm syn}\\) is uniformly distributed and applies to errors \\(\\epsilon_{\\log}\\) to implement logical qubits, an error budget \\(\\epsilon_{\\rm dis}\\) to produce T states through distillation, and an error budget \\(\\epsilon_{\\rm syn}\\) to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets \\(\\epsilon_{\\rm dis}\\) and \\(\\epsilon_{\\rm syn}\\) are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.

\n", + "\r\n", + "
Logical error probability5.00e-4\r\n", + "

Probability of at least one logical error

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
T distillation error probability5.00e-4\r\n", + "

Probability of at least one faulty T distillation

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
Rotation synthesis error probability0.00e0\r\n", + "

Probability of at least one failed rotation synthesis

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Physical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Qubit namequbit_gate_ns_e3\r\n", + "

Some descriptive name for the qubit model

\n", + "\r\n", + "
\r\n", + "

You can load pre-defined qubit parameters by using the names qubit_gate_ns_e3, qubit_gate_ns_e4, qubit_gate_us_e3, qubit_gate_us_e4, qubit_maj_ns_e4, or qubit_maj_ns_e6. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).

\n", + "\r\n", + "
Instruction setGateBased\r\n", + "

Underlying qubit technology (gate-based or Majorana)

\n", + "\r\n", + "
\r\n", + "

When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either gate-based or Majorana. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.

\n", + "\r\n", + "
Single-qubit measurement time100 ns\r\n", + "

Operation time for single-qubit measurement (t_meas) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.

\n", + "\r\n", + "
Single-qubit gate time50 ns\r\n", + "

Operation time for single-qubit gate (t_gate) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.

\n", + "\r\n", + "
Two-qubit gate time50 ns\r\n", + "

Operation time for two-qubit gate in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.

\n", + "\r\n", + "
T gate time50 ns\r\n", + "

Operation time for a T gate

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to execute a T gate.

\n", + "\r\n", + "
Single-qubit measurement error rate0.001\r\n", + "

Error rate for single-qubit measurement

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit measurement in the Pauli basis may fail.

\n", + "\r\n", + "
Single-qubit error rate0.001\r\n", + "

Error rate for single-qubit Clifford gate (p)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.

\n", + "\r\n", + "
Two-qubit error rate0.001\r\n", + "

Error rate for two-qubit Clifford gate

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.

\n", + "\r\n", + "
T gate error rate0.001\r\n", + "

Error rate to prepare single-qubit T state or apply a T gate (p_T)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which executing a single T gate may fail.

\n", + "\r\n", + "
\n", + "
\r\n", + " Assumptions\r\n", + "
    \n", + "

  • More details on the following lists of assumptions can be found in the paper Accessing requirements for scaling quantum computers and their applications.

    \n", + "
    • \n", + "

  • Uniform independent physical noise. We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.

    \n", + "
    • \n", + "

  • Efficient classical computation. We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.

    \n", + "
    • \n", + "

  • Extraction circuits for planar quantum ISA. We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).

    \n", + "
    • \n", + "

  • Uniform independent logical noise. We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.

    \n", + "
    • \n", + "

  • Negligible Clifford costs for synthesis. We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.

    \n", + "
    • \n", + "

  • Smooth magic state consumption rate. We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.

    \n", + "
    • \n", + "
\n" + ], + "text/plain": [ + "{'errorBudget': {'logical': 0.0005, 'rotations': 0.0, 'tstates': 0.0005},\n", + " 'jobParams': {'errorBudget': 0.001,\n", + " 'qecScheme': {'crossingPrefactor': 0.03,\n", + " 'errorCorrectionThreshold': 0.01,\n", + " 'logicalCycleTime': '(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance',\n", + " 'name': 'surface_code',\n", + " 'physicalQubitsPerLogicalQubit': '2 * codeDistance * codeDistance'},\n", + " 'qubitParams': {'instructionSet': 'GateBased',\n", + " 'name': 'qubit_gate_ns_e3',\n", + " 'oneQubitGateErrorRate': 0.001,\n", + " 'oneQubitGateTime': '50 ns',\n", + " 'oneQubitMeasurementErrorRate': 0.001,\n", + " 'oneQubitMeasurementTime': '100 ns',\n", + " 'tGateErrorRate': 0.001,\n", + " 'tGateTime': '50 ns',\n", + " 'twoQubitGateErrorRate': 0.001,\n", + " 'twoQubitGateTime': '50 ns'}},\n", + " 'logicalCounts': {'ccixCount': 0,\n", + " 'cczCount': 28,\n", + " 'measurementCount': 0,\n", + " 'numQubits': 16,\n", + " 'rotationCount': 0,\n", + " 'rotationDepth': 0,\n", + " 'tCount': 0},\n", + " 'logicalQubit': {'codeDistance': 11,\n", + " 'logicalCycleTime': 4400.0,\n", + " 'logicalErrorRate': 3.000000000000002e-08,\n", + " 'physicalQubits': 242},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 84,\n", + " 'algorithmicLogicalQubits': 45,\n", + " 'cliffordErrorRate': 0.001,\n", + " 'logicalDepth': 84,\n", + " 'numTfactories': 15,\n", + " 'numTfactoryRuns': 8,\n", + " 'numTsPerRotation': None,\n", + " 'numTstates': 112,\n", + " 'physicalQubitsForAlgorithm': 10890,\n", + " 'physicalQubitsForTfactories': 97200,\n", + " 'requiredLogicalQubitErrorRate': 1.3227513227513228e-07,\n", + " 'requiredLogicalTstateErrorRate': 4.464285714285715e-06},\n", + " 'physicalQubits': 108090,\n", + " 'runtime': 369600},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", + " 'errorBudget': '1.00e-3',\n", + " 'errorBudgetLogical': '5.00e-4',\n", + " 'errorBudgetRotations': '0.00e0',\n", + " 'errorBudgetTstates': '5.00e-4',\n", + " 'logicalCycleTime': '4us 400ns',\n", + " 'logicalErrorRate': '3.00e-8',\n", + " 'numTsPerRotation': 'No rotations in algorithm',\n", + " 'numUnitsPerRound': '2',\n", + " 'physicalQubitsForTfactoriesPercentage': '89.93 %',\n", + " 'physicalQubitsPerRound': '6480',\n", + " 'requiredLogicalQubitErrorRate': '1.32e-7',\n", + " 'requiredLogicalTstateErrorRate': '4.46e-6',\n", + " 'runtime': '369us 600ns',\n", + " 'tfactoryRuntime': '46us 800ns',\n", + " 'tfactoryRuntimePerRound': '46us 800ns',\n", + " 'tstateLogicalErrorRate': '2.17e-6',\n", + " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", + " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", + " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", + " '**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.',\n", + " '**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).',\n", + " '**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.',\n", + " '**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.',\n", + " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", + " 'groups': [{'alwaysVisible': True,\n", + " 'entries': [{'description': 'Number of physical qubits',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 10890 physical qubits to implement the algorithm logic, and 97200 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'physicalCounts/physicalQubits'},\n", + " {'description': 'Total runtime',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 84 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/runtime'}],\n", + " 'title': 'Physical resource estimates'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 16$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 45$ logical qubits.',\n", + " 'label': 'Logical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", + " {'description': 'Number of logical cycles for the algorithm',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 0 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 28 CCZ and 0 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'label': 'Algorithmic depth',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", + " {'description': 'Number of logical cycles performed',\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 84. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'label': 'Logical depth',\n", + " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", + " {'description': 'Number of T states consumed by the algorithm',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 28 CCZ and 0 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'label': 'Number of T states',\n", + " 'path': 'physicalCounts/breakdown/numTstates'},\n", + " {'description': \"Number of T factories capable of producing the demanded 112 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 15 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{112\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 369us 600ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " 'label': 'Number of T factories',\n", + " 'path': 'physicalCounts/breakdown/numTfactories'},\n", + " {'description': 'Number of times all T factories are invoked',\n", + " 'explanation': 'In order to prepare the 112 T states, the 15 copies of the T factory are repeatedly invoked 8 times.',\n", + " 'label': 'Number of T factory invocations',\n", + " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", + " {'description': 'Number of physical qubits for the algorithm after layout',\n", + " 'explanation': 'The 10890 are the product of the 45 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.',\n", + " 'label': 'Physical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", + " {'description': 'Number of physical qubits for the T factories',\n", + " 'explanation': 'Each T factory requires 6480 physical qubits and we run 15 in parallel, therefore we need $97200 = 6480 \\\\cdot 15$ qubits.',\n", + " 'label': 'Physical T factory qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", + " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 45 logical qubits and the total cycle count 84.',\n", + " 'label': 'Required logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", + " {'description': 'The minimum T state error rate required for distilled T states',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 112.',\n", + " 'label': 'Required logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", + " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", + " 'explanation': 'The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.',\n", + " 'label': 'Number of T states per rotation',\n", + " 'path': 'physicalCountsFormatted/numTsPerRotation'}],\n", + " 'title': 'Resource estimates breakdown'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Name of QEC scheme',\n", + " 'explanation': 'You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.',\n", + " 'label': 'QEC scheme',\n", + " 'path': 'jobParams/qecScheme/name'},\n", + " {'description': 'Required code distance for error correction',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000013227513227513228)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'label': 'Code distance',\n", + " 'path': 'logicalQubit/codeDistance'},\n", + " {'description': 'Number of physical qubits per logical qubit',\n", + " 'explanation': 'The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'logicalQubit/physicalQubits'},\n", + " {'description': 'Duration of a logical cycle in nanoseconds',\n", + " 'explanation': 'The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.',\n", + " 'label': 'Logical cycle time',\n", + " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", + " {'description': 'Logical qubit error rate',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$',\n", + " 'label': 'Logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", + " {'description': 'Crossing prefactor used in QEC scheme',\n", + " 'explanation': 'The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.',\n", + " 'label': 'Crossing prefactor',\n", + " 'path': 'jobParams/qecScheme/crossingPrefactor'},\n", + " {'description': 'Error correction threshold used in QEC scheme',\n", + " 'explanation': 'The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.',\n", + " 'label': 'Error correction threshold',\n", + " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", + " {'description': 'QEC scheme formula used to compute logical cycle time',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 4us 400ns.',\n", + " 'label': 'Logical cycle time formula',\n", + " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", + " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 242.',\n", + " 'label': 'Physical qubits formula',\n", + " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", + " 'title': 'Logical qubit parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of physical qubits for a single T factory',\n", + " 'explanation': 'This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'tfactory/physicalQubits'},\n", + " {'description': 'Runtime of a single T factory',\n", + " 'explanation': 'The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", + " {'description': 'Number of output T states produced in a single run of T factory',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.',\n", + " 'label': 'Number of output T states per run',\n", + " 'path': 'tfactory/numTstates'},\n", + " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", + " 'explanation': 'This value includes the physical input T states of all copies of the distillation unit in the first round.',\n", + " 'label': 'Number of input T states per run',\n", + " 'path': 'tfactory/numInputTstates'},\n", + " {'description': 'The number of distillation rounds',\n", + " 'explanation': 'This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.',\n", + " 'label': 'Distillation rounds',\n", + " 'path': 'tfactory/numRounds'},\n", + " {'description': 'The number of units in each round of distillation',\n", + " 'explanation': 'This is the number of copies for the distillation units per round.',\n", + " 'label': 'Distillation units per round',\n", + " 'path': 'physicalCountsFormatted/numUnitsPerRound'},\n", + " {'description': 'The types of distillation units',\n", + " 'explanation': 'These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.',\n", + " 'label': 'Distillation units',\n", + " 'path': 'physicalCountsFormatted/unitNamePerRound'},\n", + " {'description': 'The code distance in each round of distillation',\n", + " 'explanation': 'This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.',\n", + " 'label': 'Distillation code distances',\n", + " 'path': 'physicalCountsFormatted/codeDistancePerRound'},\n", + " {'description': 'The number of physical qubits used in each round of distillation',\n", + " 'explanation': 'The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.',\n", + " 'label': 'Number of physical qubits per round',\n", + " 'path': 'physicalCountsFormatted/physicalQubitsPerRound'},\n", + " {'description': 'The runtime of each distillation round',\n", + " 'explanation': 'The runtime of the T factory is the sum of the runtimes in all rounds.',\n", + " 'label': 'Runtime per round',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", + " {'description': 'Logical T state error rate',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 4.46e-6.',\n", + " 'label': 'Logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", + " 'title': 'T factory parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", + " 'explanation': 'We determine 45 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'label': 'Logical qubits (pre-layout)',\n", + " 'path': 'logicalCounts/numQubits'},\n", + " {'description': 'Number of T gates in the input quantum program',\n", + " 'explanation': 'This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.',\n", + " 'label': 'T gates',\n", + " 'path': 'logicalCounts/tCount'},\n", + " {'description': 'Number of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.',\n", + " 'label': 'Rotation gates',\n", + " 'path': 'logicalCounts/rotationCount'},\n", + " {'description': 'Depth of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.',\n", + " 'label': 'Rotation depth',\n", + " 'path': 'logicalCounts/rotationDepth'},\n", + " {'description': 'Number of CCZ-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCZ gates.',\n", + " 'label': 'CCZ gates',\n", + " 'path': 'logicalCounts/cczCount'},\n", + " {'description': 'Number of CCiX-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].',\n", + " 'label': 'CCiX gates',\n", + " 'path': 'logicalCounts/ccixCount'},\n", + " {'description': 'Number of single qubit measurements in the input quantum program',\n", + " 'explanation': 'This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.',\n", + " 'label': 'Measurement operations',\n", + " 'path': 'logicalCounts/measurementCount'}],\n", + " 'title': 'Pre-layout logical resources'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Total error budget for the algorithm',\n", + " 'explanation': \"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\n", + " 'label': 'Total error budget',\n", + " 'path': 'physicalCountsFormatted/errorBudget'},\n", + " {'description': 'Probability of at least one logical error',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'Logical error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetLogical'},\n", + " {'description': 'Probability of at least one faulty T distillation',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'T distillation error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetTstates'},\n", + " {'description': 'Probability of at least one failed rotation synthesis',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3.',\n", + " 'label': 'Rotation synthesis error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetRotations'}],\n", + " 'title': 'Assumed error budget'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Some descriptive name for the qubit model',\n", + " 'explanation': 'You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).',\n", + " 'label': 'Qubit name',\n", + " 'path': 'jobParams/qubitParams/name'},\n", + " {'description': 'Underlying qubit technology (gate-based or Majorana)',\n", + " 'explanation': 'When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.',\n", + " 'label': 'Instruction set',\n", + " 'path': 'jobParams/qubitParams/instructionSet'},\n", + " {'description': 'Operation time for single-qubit measurement (t_meas) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.',\n", + " 'label': 'Single-qubit measurement time',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementTime'},\n", + " {'description': 'Operation time for single-qubit gate (t_gate) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.',\n", + " 'label': 'Single-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateTime'},\n", + " {'description': 'Operation time for two-qubit gate in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.',\n", + " 'label': 'Two-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateTime'},\n", + " {'description': 'Operation time for a T gate',\n", + " 'explanation': 'This is the operation time in nanoseconds to execute a T gate.',\n", + " 'label': 'T gate time',\n", + " 'path': 'jobParams/qubitParams/tGateTime'},\n", + " {'description': 'Error rate for single-qubit measurement',\n", + " 'explanation': 'This is the probability in which a single-qubit measurement in the Pauli basis may fail.',\n", + " 'label': 'Single-qubit measurement error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementErrorRate'},\n", + " {'description': 'Error rate for single-qubit Clifford gate (p)',\n", + " 'explanation': 'This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.',\n", + " 'label': 'Single-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateErrorRate'},\n", + " {'description': 'Error rate for two-qubit Clifford gate',\n", + " 'explanation': 'This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.',\n", + " 'label': 'Two-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateErrorRate'},\n", + " {'description': 'Error rate to prepare single-qubit T state or apply a T gate (p_T)',\n", + " 'explanation': 'This is the probability in which executing a single T gate may fail.',\n", + " 'label': 'T gate error rate',\n", + " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", + " 'title': 'Physical qubit parameters'}]},\n", + " 'status': 'success',\n", + " 'tfactory': {'codeDistancePerRound': [9],\n", + " 'logicalErrorRate': 2.165000000000001e-06,\n", + " 'numInputTstates': 30,\n", + " 'numRounds': 1,\n", + " 'numTstates': 1,\n", + " 'numUnitsPerRound': [2],\n", + " 'physicalQubits': 6480,\n", + " 'physicalQubitsPerRound': [6480],\n", + " 'runtime': 46800.0,\n", + " 'runtimePerRound': [46800.0],\n", + " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", "# result = qsharp.azure.output(\"...\")\n", @@ -367,7 +4915,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, "metadata": { "collapsed": false, "jupyter": { @@ -394,7 +4942,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 14, "metadata": { "collapsed": false, "jupyter": { @@ -407,10 +4955,37 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Logical algorithmic qubits = 45\n", + "Algorithmic depth = 84\n", + "Score = 3780\n" + ] + }, + { + "data": { + "text/plain": [ + "3780" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "evaluate_results(result)" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -418,9 +4993,9 @@ "name": "python3" }, "kernelspec": { - "display_name": "Python 3 [Default]", + "display_name": "Python 3 [Q#]", "language": "python", - "name": "python3" + "name": "python3_qsharp_b54crn" }, "language_info": { "codemirror_mode": { diff --git a/obj/__entrypoint__.dll b/obj/__entrypoint__.dll new file mode 100644 index 0000000000000000000000000000000000000000..6c6e7d3b3c59f1c9228c8f898c3a6524006a0b9a GIT binary patch literal 228352 zcmeEv31FN@b^m<3vTn(i>^MGhe3q3UTSqL}PGTi?EX%SZ@GUux<8`E!^hw@$wJU$S zYggeY}}@@6DT;?KeFjf-$ph^H%`L4^wQ6iif0PGy6jWh zwy!R0KNLym17^I>4EO8Z;aDu5)VmDbOvUs_Oy9h-P4AEQ77f5%oJ zIpOaR(%mV4rZx|nncf@}8oN&1SQ!XbEfk_qh?PrBBr*W2 ziL6TkLjZGDRs@14_y-)Q|JZ?lzyW2E4*cWF!0&SB3Xz+*5DBgnV*aY2xWOt?AW*dk 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zw}W0`{UNvad4#7%j~{VcEV!YcV`n#KThrqQU0(PfjjP9tR;9{qCNPLPNrgsp+_w-38gDJK{UVSF{P-rWt{zwDG3$Pns*d6zd~_MF_)R1woBu~ z&Xb+395}Jf;B#N^YrsNQ!&98_f;;SVv0SjH?3~B1;D+}d%asn>#f*r%;2x7o%2b-XC=lWH{GrT5 zWq}L3B`z%nQ?@TNRnAs5$Q^xc55^9Iu8ERe$h^0zG#?qMEj>CljUWD%Cv6=$2vW^1 zEeou(rBKKh#`1-NJz*9O?*A?jleN8}3obO4&mF~CpD%$XflsAE-m{kK49_DaJ69yuVN>3(52VTHq5J6l z?m~XTE*A5J;Vm8_;ZpFdf+%>r4xTMraz`_Te9oNe%LB=&G&$^(iH7BUgC49(yx+e{ zk1FAdUy(&XslQ@8Rmn4BUpLArHIB}2&SrO{GdVR?oB${6;Ys%gr*EwQj^?Zov!Qc2 S{(_~rVEvFn*>-O`4*Y){ckP-0 literal 0 HcmV?d00001 From aa34d9e78ddff434b973a0681301c05865878450 Mon Sep 17 00:00:00 2001 From: Hamish Hall Date: Sun, 29 Jan 2023 12:07:04 +0000 Subject: [PATCH 2/7] next checkpoint --- iQuHack-challenge-2023-task2.ipynb | 669 ++-- iQuHack-challenge-2023-task3.ipynb | 762 ++--- iQuHack-challenge-2023-task7.ipynb | 4673 +++++++++++++++++++++++++++- obj/__entrypoint__.dll | Bin 228352 -> 321536 bytes obj/__entrypoint__snippets__.dll | Bin 106496 -> 51200 bytes obj/__snippets__.dll | Bin 105984 -> 114688 bytes 6 files changed, 5359 insertions(+), 745 deletions(-) diff --git a/iQuHack-challenge-2023-task2.ipynb b/iQuHack-challenge-2023-task2.ipynb index 01cf0da..267e958 100644 --- a/iQuHack-challenge-2023-task2.ipynb +++ b/iQuHack-challenge-2023-task2.ipynb @@ -34,7 +34,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 11, "metadata": { "collapsed": false, "jupyter": { @@ -52,7 +52,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "\u001b[93mTo sign in, use a web browser to open the page https://microsoft.com/devicelogin and enter the code F88GK2SR2 to authenticate.\u001b[0m\n", + "\u001b[93mTo sign in, use a web browser to open the page https://microsoft.com/devicelogin and enter the code F2JVHXWME to authenticate.\u001b[0m\n", "[\n", " {\n", " \"cloudName\": \"AzureCloud\",\n", @@ -101,7 +101,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 12, "metadata": { "collapsed": false, "jupyter": { @@ -114,16 +114,7 @@ } } }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Preparing Q# environment...\n", - "...." - ] - } - ], + "outputs": [], "source": [ "# Run this code cell to import the modules required to work with Q# and Azure\n", "import qsharp\n", @@ -132,7 +123,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 13, "metadata": { "collapsed": false, "jupyter": { @@ -154,7 +145,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 14, "metadata": { "collapsed": false, "jupyter": { @@ -191,7 +182,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 15, "metadata": { "collapsed": false, "jupyter": { @@ -207,20 +198,13 @@ } } }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "/snippet_.qs(18,9): warning QS3306: Deprecated syntax. Parentheses here are no longer required and will not be supported in the future.\n" - ] - } - ], + "outputs": [], "source": [ "%%qsharp\n", "open Microsoft.Quantum.Canon;\n", "open Microsoft.Quantum.Bitwise;\n", "open Microsoft.Quantum.Diagnostics;\n", + "open Microsoft.Quantum.Arrays;\n", "\n", "// Task 2. Celebrate MIT iQuHack!\n", "// (input will contain 5 qubits)\n", @@ -241,40 +225,34 @@ "\n", "operation Task2(input : Qubit[], target : Qubit) : Unit is Adj {\n", " ControlledOnInt(13, X)(input, target); // M\n", - "\n", - " ControlledOnInt(17, X)(input, target); // Q\n", - " ControlledOnInt(21, X)(input, target); // U\n", + " ControlledOnInt(20, X)(input, target); // T\n", " ControlledOnInt( 8, X)(input, target); // H\n", " ControlledOnInt( 1, X)(input, target); // A\n", - " ControlledOnInt( 3, X)(input, target); // C\n", - " ControlledOnInt(11, X)(input, target); // K\n", + " ControlledOnInt(9, X)([input[0],input[1],input[3],input[4]], target);\n", + " ControlledOnInt(3, X)([input[0],input[1],input[2],input[4]], target);\n", + "}\n", "\n", - " for (index in 0 .. Length(input) - 1) {\n", - " X(input[index]);\n", - " }\n", - " ControlledOnInt(11, X)(input, target); // T (flipped)\n", + "operation QubitArrayWrapperOperation (op : ((Qubit[], Qubit) => Unit is Adj), qs : Qubit[]) : Unit is Adj { \n", + " op(Most(qs), Tail(qs));\n", "}\n", - "\n" + "\n", + "operation TestCompoundGate () : Unit {\n", + " AssertOperationsEqualReferenced(5+1, QubitArrayWrapperOperation(Task2, _), QubitArrayWrapperOperation (old, _));\n", + "}\n" ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 16, "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "UsageError: Cell magic `%%qsharp` not found.\n" - ] - } - ], - "source": [] + "outputs": [], + "source": [ + "TestCompoundGate();" + ] }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 17, "metadata": { "collapsed": false, "jupyter": { @@ -331,7 +309,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 18, "metadata": { "collapsed": false, "jupyter": { @@ -347,7 +325,7 @@ "outputs": [ { "data": { - "application/x-qsharp-data": 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"|000110⟩\t0.17677669529663698 + 0𝑖\n", "|000111⟩\t0 + 0𝑖\n", "|001000⟩\t0.17677669529663698 + 0𝑖\n", @@ -1982,42 +1960,42 @@ "|001011⟩\t0.17677669529663698 + 0𝑖\n", "|001100⟩\t0.17677669529663698 + 0𝑖\n", "|001101⟩\t0 + 0𝑖\n", - "|001110⟩\t0 + 0𝑖\n", - "|001111⟩\t0.17677669529663698 + 0𝑖\n", + "|001110⟩\t0.17677669529663698 + 0𝑖\n", + "|001111⟩\t0 + 0𝑖\n", "|010000⟩\t0.17677669529663698 + 0𝑖\n", "|010001⟩\t0 + 0𝑖\n", - "|010010⟩\t0 + 0𝑖\n", - "|010011⟩\t0.17677669529663698 + 0𝑖\n", - "|010100⟩\t0 + 0𝑖\n", - "|010101⟩\t0.17677669529663698 + 0𝑖\n", + "|010010⟩\t0.17677669529663698 + 0𝑖\n", + "|010011⟩\t0 + 0𝑖\n", + "|010100⟩\t0.17677669529663698 + 0𝑖\n", + "|010101⟩\t0 + 0𝑖\n", "|010110⟩\t0.17677669529663698 + 0𝑖\n", "|010111⟩\t0 + 0𝑖\n", "|011000⟩\t0.17677669529663698 + 0𝑖\n", "|011001⟩\t0 + 0𝑖\n", "|011010⟩\t0.17677669529663698 + 0𝑖\n", "|011011⟩\t0 + 0𝑖\n", - "|011100⟩\t0 + 0𝑖\n", - "|011101⟩\t0.17677669529663698 + 0𝑖\n", - "|011110⟩\t0 + 0𝑖\n", - "|011111⟩\t0.17677669529663698 + 0𝑖\n", - "|100000⟩\t0.17677669529663698 + 0𝑖\n", - "|100001⟩\t0 + 0𝑖\n", - "|100010⟩\t0.17677669529663698 + 0𝑖\n", - "|100011⟩\t0 + 0𝑖\n", + "|011100⟩\t0.17677669529663698 + 0𝑖\n", + "|011101⟩\t0 + 0𝑖\n", + "|011110⟩\t0.17677669529663698 + 0𝑖\n", + "|011111⟩\t0 + 0𝑖\n", + "|100000⟩\t0 + 0𝑖\n", + "|100001⟩\t0.17677669529663698 + 0𝑖\n", + "|100010⟩\t0 + 0𝑖\n", + "|100011⟩\t0.17677669529663698 + 0𝑖\n", "|100100⟩\t0.17677669529663698 + 0𝑖\n", "|100101⟩\t0 + 0𝑖\n", "|100110⟩\t0.17677669529663698 + 0𝑖\n", "|100111⟩\t0 + 0𝑖\n", "|101000⟩\t0.17677669529663698 + 0𝑖\n", "|101001⟩\t0 + 0𝑖\n", - "|101010⟩\t0.17677669529663698 + 0𝑖\n", - "|101011⟩\t0 + 0𝑖\n", - "|101100⟩\t0.17677669529663698 + 0𝑖\n", - "|101101⟩\t0 + 0𝑖\n", + "|101010⟩\t0 + 0𝑖\n", + "|101011⟩\t0.17677669529663698 + 0𝑖\n", + "|101100⟩\t0 + 0𝑖\n", + "|101101⟩\t0.17677669529663698 + 0𝑖\n", "|101110⟩\t0.17677669529663698 + 0𝑖\n", "|101111⟩\t0 + 0𝑖\n", - "|110000⟩\t0.17677669529663698 + 0𝑖\n", - "|110001⟩\t0 + 0𝑖\n", + "|110000⟩\t0 + 0𝑖\n", + "|110001⟩\t0.17677669529663698 + 0𝑖\n", "|110010⟩\t0.17677669529663698 + 0𝑖\n", "|110011⟩\t0 + 0𝑖\n", "|110100⟩\t0 + 0𝑖\n", @@ -2026,8 +2004,8 @@ "|110111⟩\t0 + 0𝑖\n", "|111000⟩\t0.17677669529663698 + 0𝑖\n", "|111001⟩\t0 + 0𝑖\n", - "|111010⟩\t0 + 0𝑖\n", - "|111011⟩\t0.17677669529663698 + 0𝑖\n", + "|111010⟩\t0.17677669529663698 + 0𝑖\n", + "|111011⟩\t0 + 0𝑖\n", "|111100⟩\t0.17677669529663698 + 0𝑖\n", "|111101⟩\t0 + 0𝑖\n", "|111110⟩\t0.17677669529663698 + 0𝑖\n", @@ -2043,7 +2021,7 @@ "()" ] }, - "execution_count": 12, + "execution_count": 18, "metadata": {}, "output_type": "execute_result" } @@ -2072,7 +2050,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 19, "metadata": { "collapsed": false, "jupyter": { @@ -2106,23 +2084,23 @@ { "data": { "text/plain": [ - "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 278400},\n", - " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 408469},\n", + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 175517},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 438370},\n", " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 2},\n", " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", - " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 257411},\n", - " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", - " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 4298},\n", - " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 139},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 169},\n", " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", - " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 257411},\n", - " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", - " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 4298},\n", - " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 139},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 169},\n", " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", @@ -2130,7 +2108,7 @@ " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" ] }, - "execution_count": 13, + "execution_count": 19, "metadata": {}, "output_type": "execute_result" } @@ -2146,7 +2124,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 20, "metadata": { "collapsed": false, "jupyter": { @@ -2174,7 +2152,7 @@ "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" ] }, - "execution_count": 14, + "execution_count": 20, "metadata": {}, "output_type": "execute_result" } @@ -2185,7 +2163,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 21, "metadata": { "collapsed": false, "jupyter": { @@ -2206,10 +2184,9 @@ "Submitting Task2_ResourceEstimationWrapper to target microsoft.estimator...\n", "Job successfully submitted.\n", " Job name: RE for the task 2\n", - " Job ID: 5d90fa2d-f0ad-4caf-a994-eccabd42cb19\n", + " Job ID: f8a7b04a-cd5c-4fea-aec9-ec6f246a8c34\n", "Waiting up to 30 seconds for Azure Quantum job to complete...\n", - "[10:17:52 PM] Current job status: Waiting\n", - "[10:17:57 PM] Current job status: Succeeded\n" + "[11:51:48 AM] Current job status: Succeeded\n" ] } ], @@ -2220,7 +2197,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 22, "metadata": { "collapsed": false, "jupyter": { @@ -2236,7 +2213,7 @@ "outputs": [ { "data": { - "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":24,\"cczCount\":8,\"measurementCount\":24,\"numQubits\":9,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":120,\"algorithmicLogicalQubits\":28,\"cliffordErrorRate\":0.001,\"logicalDepth\":120,\"numTfactories\":12,\"numTfactoryRuns\":11,\"numTsPerRotation\":null,\"numTstates\":128,\"physicalQubitsForAlgorithm\":6776,\"physicalQubitsForTfactories\":77760,\"requiredLogicalQubitErrorRate\":1.4880952380952382E-07,\"requiredLogicalTstateErrorRate\":3.90625E-06},\"physicalQubits\":84536,\"runtime\":528000},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"91.98 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"1.49e-7\",\"requiredLogicalTstateErrorRate\":\"3.91e-6\",\"runtime\":\"528us\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 6776 physical qubits to implement the algorithm logic, and 77760 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 120 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 9$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 28$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 24 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 8 CCZ and 24 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 120. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 8 CCZ and 24 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 128 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{128\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 528us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 128 T states, the 12 copies of the T factory are repeatedly invoked 11 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 6776 are the product of the 28 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 12 in parallel, therefore we need $77760 = 6480 \\\\cdot 12$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 28 logical qubits and the total cycle count 120.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 128.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000014880952380952382)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 3.91e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 28 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or ¬µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":16,\"cczCount\":6,\"measurementCount\":16,\"numQubits\":9,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":82,\"algorithmicLogicalQubits\":28,\"cliffordErrorRate\":0.001,\"logicalDepth\":82,\"numTfactories\":12,\"numTfactoryRuns\":8,\"numTsPerRotation\":null,\"numTstates\":88,\"physicalQubitsForAlgorithm\":6776,\"physicalQubitsForTfactories\":77760,\"requiredLogicalQubitErrorRate\":2.177700348432056E-07,\"requiredLogicalTstateErrorRate\":5.681818181818182E-06},\"physicalQubits\":84536,\"runtime\":360800},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"91.98 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"2.18e-7\",\"requiredLogicalTstateErrorRate\":\"5.68e-6\",\"runtime\":\"360us 800ns\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 6776 physical qubits to implement the algorithm logic, and 77760 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 82 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 9$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 28$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 16 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 6 CCZ and 16 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 82. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 6 CCZ and 16 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 88 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{88\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 360us 800ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 88 T states, the 12 copies of the T factory are repeatedly invoked 8 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 6776 are the product of the 28 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 12 in parallel, therefore we need $77760 = 6480 \\\\cdot 12$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 28 logical qubits and the total cycle count 82.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 88.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.0000002177700348432056)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 5.68e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 28 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or ¬µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", "text/html": [ "\r\n", "
\r\n", @@ -2260,12 +2237,12 @@ "\r\n", "
\r\n", " \r\n", - " \r\n", + " \r\n", " \r\n", " \n", @@ -2292,36 +2269,36 @@ "\r\n", " \r\n", " \r\n", - " \r\n", + " \r\n", " \r\n", " \n", "\r\n", " \r\n", " \r\n", - " \r\n", + " \r\n", " \r\n", " \n", "\r\n", " \r\n", " \r\n", - " \r\n", + " \r\n", " \r\n", " \n", @@ -2330,22 +2307,22 @@ " \r\n", " \r\n", " \r\n", " \n", "\r\n", " \r\n", " \r\n", - " \r\n", + " \r\n", " \r\n", " \n", @@ -2376,24 +2353,24 @@ "\r\n", " \r\n", " \r\n", - " \r\n", + " \r\n", " \r\n", " \n", "\r\n", " \r\n", " \r\n", - " \r\n", + " \r\n", " \r\n", " \n", @@ -2437,7 +2414,7 @@ "

Required code distance for error correction

\n", "\r\n", "
\r\n", - "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000014880952380952382)}{\\log(0.01/0.001)} - 1\\)

\n", + "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.0000002177700348432056)}{\\log(0.01/0.001)} - 1\\)

\n", "\r\n", " \r\n", " \n", @@ -2661,7 +2638,7 @@ "

Logical T state error rate

\n", "\r\n", "
\r\n", - "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 3.91e-6.

\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 5.68e-6.

\n", "\r\n", " \r\n", " \n", @@ -2724,7 +2701,7 @@ "\r\n", " \r\n", " \r\n", - " \r\n", + " \r\n", " \r\n", " \r\n", - " \r\n", + " \r\n", " \r\n", " \r\n", - " \r\n", + " \r\n", " \r\n", " \r\n", @@ -338,12 +351,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -363,12 +376,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -388,12 +401,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -413,12 +426,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -438,12 +451,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -463,12 +476,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -488,12 +501,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -513,12 +526,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -538,12 +551,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -563,12 +576,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -588,12 +601,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -613,12 +626,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -638,12 +651,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -663,12 +676,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -688,12 +701,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -713,12 +726,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -738,12 +751,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -763,12 +776,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -788,12 +801,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -813,12 +826,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -838,12 +851,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -863,12 +876,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -888,12 +901,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -913,12 +926,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -938,12 +951,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -963,12 +976,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -988,12 +1001,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1013,12 +1026,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1038,12 +1051,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1063,12 +1076,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1088,12 +1101,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1113,12 +1126,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1138,12 +1151,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1163,12 +1176,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1188,12 +1201,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1213,12 +1226,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1238,12 +1251,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1263,12 +1276,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1288,12 +1301,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1313,12 +1326,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1338,12 +1351,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1363,12 +1376,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1388,12 +1401,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1413,12 +1426,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1438,12 +1451,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1463,12 +1476,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1488,12 +1501,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1513,12 +1526,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1538,12 +1551,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1563,12 +1576,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1588,12 +1601,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1613,12 +1626,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1638,12 +1651,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1663,12 +1676,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1688,12 +1701,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1713,12 +1726,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1738,12 +1751,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1763,12 +1776,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1788,12 +1801,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1813,12 +1826,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1838,12 +1851,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1863,12 +1876,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1888,12 +1901,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1913,12 +1926,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1938,12 +1951,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1963,12 +1976,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1988,12 +2001,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2013,12 +2026,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2038,12 +2051,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2063,12 +2076,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2088,12 +2101,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2113,12 +2126,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2138,12 +2151,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2163,12 +2176,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2188,12 +2201,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2213,12 +2226,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2238,12 +2251,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2263,12 +2276,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2288,12 +2301,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2313,12 +2326,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2338,12 +2351,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2363,12 +2376,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2388,12 +2401,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2413,12 +2426,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2438,12 +2451,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2463,12 +2476,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2488,12 +2501,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2513,12 +2526,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2538,12 +2551,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2563,12 +2576,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2588,12 +2601,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2613,12 +2626,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2638,12 +2651,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2663,12 +2676,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2688,12 +2701,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2713,12 +2726,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2738,12 +2751,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2763,12 +2776,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2788,12 +2801,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2813,12 +2826,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2838,12 +2851,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2863,12 +2876,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2888,12 +2901,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2913,12 +2926,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2938,12 +2951,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2963,12 +2976,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2988,12 +3001,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3013,12 +3026,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3038,12 +3051,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3063,12 +3076,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3088,12 +3101,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3113,12 +3126,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3138,12 +3151,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3163,12 +3176,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3188,12 +3201,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3213,12 +3226,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3238,12 +3251,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3263,12 +3276,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3288,12 +3301,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3313,12 +3326,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3338,12 +3351,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3363,12 +3376,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3388,12 +3401,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3413,12 +3426,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3438,12 +3451,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3463,12 +3476,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3488,12 +3501,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3644,7 +3657,7 @@ "()" ] }, - "execution_count": 6, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } @@ -3707,8 +3720,8 @@ { "data": { "text/plain": [ - "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 305641},\n", - " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 361199},\n", + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 171513},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 434582},\n", " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 2},\n", " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", @@ -3716,14 +3729,14 @@ " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", - " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 184},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 175},\n", " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", - " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 184},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 175},\n", " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", @@ -3807,10 +3820,9 @@ "Submitting Task3_ResourceEstimationWrapper to target microsoft.estimator...\n", "Job successfully submitted.\n", " Job name: RE for the task 3\n", - " Job ID: 4ac53537-57cd-424e-9937-c6019dacbc0a\n", + " Job ID: 5e58d190-e0a8-4e7c-8a6a-3ffb25f39cd5\n", "Waiting up to 30 seconds for Azure Quantum job to complete...\n", - "[6:25:13 AM] Current job status: Executing\n", - "[6:25:18 AM] Current job status: Succeeded\n" + "[10:42:27 AM] Current job status: Succeeded\n" ] } ], @@ -3837,7 +3849,7 @@ "outputs": [ { "data": { - "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":80,\"cczCount\":20,\"measurementCount\":80,\"numQubits\":11,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":380,\"algorithmicLogicalQubits\":33,\"cliffordErrorRate\":0.001,\"logicalDepth\":380,\"numTfactories\":14,\"numTfactoryRuns\":29,\"numTsPerRotation\":null,\"numTstates\":400,\"physicalQubitsForAlgorithm\":7986,\"physicalQubitsForTfactories\":135520,\"requiredLogicalQubitErrorRate\":3.987240829346092E-08,\"requiredLogicalTstateErrorRate\":1.25E-06},\"physicalQubits\":143506,\"runtime\":1672000},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"11\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"94.44 %\",\"physicalQubitsPerRound\":\"9680\",\"requiredLogicalQubitErrorRate\":\"3.99e-8\",\"requiredLogicalTstateErrorRate\":\"1.25e-6\",\"runtime\":\"1ms 672us\",\"tfactoryRuntime\":\"57us 200ns\",\"tfactoryRuntimePerRound\":\"57us 200ns\",\"tstateLogicalErrorRate\":\"2.48e-7\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 7986 physical qubits to implement the algorithm logic, and 135520 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 380 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 11$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 33$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 80 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 20 CCZ and 80 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 380. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 20 CCZ and 80 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 400 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{400\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 1ms 672us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 400 T states, the 14 copies of the T factory are repeatedly invoked 29 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 7986 are the product of the 33 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 9680 physical qubits and we run 14 in parallel, therefore we need $135520 = 9680 \\\\cdot 14$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 380.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 400.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000003987240829346092)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[11],\"logicalErrorRate\":2.480000000000001E-07,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":9680,\"physicalQubitsPerRound\":[9680],\"runtime\":57200.0,\"runtimePerRound\":[57200.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":1,\"cczCount\":17,\"measurementCount\":1,\"numQubits\":13,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":55,\"algorithmicLogicalQubits\":38,\"cliffordErrorRate\":0.001,\"logicalDepth\":55,\"numTfactories\":14,\"numTfactoryRuns\":6,\"numTsPerRotation\":null,\"numTstates\":72,\"physicalQubitsForAlgorithm\":9196,\"physicalQubitsForTfactories\":90720,\"requiredLogicalQubitErrorRate\":2.3923444976076555E-07,\"requiredLogicalTstateErrorRate\":6.944444444444445E-06},\"physicalQubits\":99916,\"runtime\":242000},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"90.80 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"2.39e-7\",\"requiredLogicalTstateErrorRate\":\"6.94e-6\",\"runtime\":\"242us\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 9196 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 55 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 13$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 38$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 1 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 17 CCZ and 1 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 55. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 17 CCZ and 1 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 72 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{72\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 242us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 72 T states, the 14 copies of the T factory are repeatedly invoked 6 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 9196 are the product of the 38 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\\\cdot 14$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 55.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 72.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000023923444976076555)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.94e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", "text/html": [ "\r\n", "
\r\n", @@ -3849,24 +3861,24 @@ "\r\n", "
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Required code distance for error correction

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The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000003987240829346092)}{\\log(0.01/0.001)} - 1\\)

\n", + "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000023923444976076555)}{\\log(0.01/0.001)} - 1\\)

\n", "\r\n", " \r\n", " \n", @@ -4137,7 +4149,7 @@ "\r\n", " \r\n", " \r\n", - " \r\n", + " \r\n", " \r\n", " \r\n", - " \r\n", + " \r\n", " \r\n", " \n", @@ -4221,7 +4233,7 @@ "\r\n", " \r\n", " \r\n", - " \r\n", + " \r\n", " \r\n", " \r\n", - " \r\n", + " \r\n", " \r\n", " \r\n", - " \r\n", + " \r\n", " \r\n", " \r\n", - " \r\n", + " \r\n", " \r\n", " \n", @@ -4277,12 +4289,12 @@ "\r\n", " \r\n", " \r\n", - " \r\n", + " \r\n", " \r\n", " \n", @@ -4325,7 +4337,7 @@ "\r\n", " \r\n", " \r\n", - " \r\n", + " \r\n", " \r\n", " \r\n", - " \r\n", + " \r\n", " \r\n", " \r\n", - " \r\n", + " \r\n", " \r\n", " \r\n", @@ -357,12 +332,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -382,12 +357,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -407,12 +382,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -432,12 +407,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -457,12 +432,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -482,12 +457,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -507,12 +482,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -532,12 +507,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -557,12 +532,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -582,12 +557,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -607,12 +582,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -632,12 +607,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -657,12 +632,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -682,12 +657,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -707,12 +682,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -732,12 +707,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -757,12 +732,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -782,12 +757,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -807,12 +782,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -832,12 +807,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -857,12 +832,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -882,12 +857,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -907,12 +882,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -932,12 +907,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -957,12 +932,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -982,12 +957,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1007,12 +982,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1032,12 +1007,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1057,12 +1032,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1082,12 +1057,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1107,12 +1082,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1132,12 +1107,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1157,12 +1132,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1182,12 +1157,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1207,12 +1182,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1232,12 +1207,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1257,12 +1232,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1282,12 +1257,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1307,12 +1282,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1332,12 +1307,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1357,12 +1332,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1382,12 +1357,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1407,12 +1382,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1432,12 +1407,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1457,12 +1432,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1482,12 +1457,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1507,12 +1482,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1532,12 +1507,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1557,12 +1532,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1582,12 +1557,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1607,12 +1582,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1632,12 +1607,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1657,12 +1632,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1682,12 +1657,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1707,12 +1682,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1732,12 +1707,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1757,12 +1732,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1782,12 +1757,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1807,12 +1782,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1832,12 +1807,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1857,12 +1832,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1882,12 +1857,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1907,12 +1882,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1932,12 +1907,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1957,12 +1932,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -1982,12 +1957,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2007,12 +1982,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2032,12 +2007,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2057,12 +2032,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2082,12 +2057,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2107,12 +2082,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2132,12 +2107,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2157,12 +2132,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2182,12 +2157,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2207,12 +2182,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2232,12 +2207,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2257,12 +2232,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2282,12 +2257,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2307,12 +2282,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2332,12 +2307,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2357,12 +2332,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2382,12 +2357,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2407,12 +2382,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2432,12 +2407,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2457,12 +2432,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2482,12 +2457,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2507,12 +2482,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2532,12 +2507,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2557,12 +2532,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2582,12 +2557,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2607,12 +2582,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2632,12 +2607,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2657,12 +2632,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2682,12 +2657,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2707,12 +2682,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2732,12 +2707,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2757,12 +2732,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2782,12 +2757,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2807,12 +2782,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2832,12 +2807,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2857,12 +2832,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2882,12 +2857,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2907,12 +2882,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2932,12 +2907,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2957,12 +2932,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -2982,12 +2957,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3007,12 +2982,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3032,12 +3007,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3057,12 +3032,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3082,12 +3057,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3107,12 +3082,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3132,12 +3107,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3157,12 +3132,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3182,12 +3157,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3207,12 +3182,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3232,12 +3207,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3257,12 +3232,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3282,12 +3257,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3307,12 +3282,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3332,12 +3307,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3357,12 +3332,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3382,12 +3357,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3407,12 +3382,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3432,12 +3407,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3457,12 +3432,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3482,12 +3457,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3507,12 +3482,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3532,12 +3507,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3557,12 +3532,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3582,12 +3557,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3607,12 +3582,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3632,12 +3607,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3657,12 +3632,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3682,12 +3657,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3707,12 +3682,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3732,12 +3707,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3757,12 +3732,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3782,12 +3757,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3807,12 +3782,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3832,12 +3807,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3857,12 +3832,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3882,12 +3857,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3907,12 +3882,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3932,12 +3907,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3957,12 +3932,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -3982,12 +3957,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4007,12 +3982,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4032,12 +4007,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4057,12 +4032,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4082,12 +4057,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4107,12 +4082,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4132,12 +4107,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4157,12 +4132,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4182,12 +4157,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4207,12 +4182,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4232,12 +4207,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4257,12 +4232,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4282,12 +4257,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4307,12 +4282,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4332,12 +4307,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4357,12 +4332,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4382,12 +4357,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4407,12 +4382,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4432,12 +4407,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4457,12 +4432,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4482,12 +4457,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4507,12 +4482,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4532,12 +4507,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4557,12 +4532,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4582,12 +4557,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4607,12 +4582,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4632,12 +4607,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4657,12 +4632,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4682,12 +4657,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4707,12 +4682,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4732,12 +4707,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4757,12 +4732,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4782,12 +4757,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4807,12 +4782,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4832,12 +4807,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4857,12 +4832,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4882,12 +4857,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4907,12 +4882,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4932,12 +4907,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4957,12 +4932,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -4982,12 +4957,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5007,12 +4982,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5032,12 +5007,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5057,12 +5032,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5082,12 +5057,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5107,12 +5082,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5132,12 +5107,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5157,12 +5132,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5182,12 +5157,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5207,12 +5182,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5232,12 +5207,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5257,12 +5232,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5282,12 +5257,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5307,12 +5282,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5332,12 +5307,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5357,12 +5332,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5382,12 +5357,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5407,12 +5382,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5432,12 +5407,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5457,12 +5432,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5482,12 +5457,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5507,12 +5482,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5532,12 +5507,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5557,12 +5532,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5582,12 +5557,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5607,12 +5582,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5632,12 +5607,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5657,12 +5632,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5682,12 +5657,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5707,12 +5682,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5732,12 +5707,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5757,12 +5732,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5782,12 +5757,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5807,12 +5782,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5832,12 +5807,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5857,12 +5832,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5882,12 +5857,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5907,12 +5882,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5932,12 +5907,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5957,12 +5932,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -5982,12 +5957,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6007,12 +5982,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6032,12 +6007,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6057,12 +6032,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6082,12 +6057,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6107,12 +6082,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6132,12 +6107,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6157,12 +6132,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6182,12 +6157,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6207,12 +6182,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6232,12 +6207,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6257,12 +6232,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6282,12 +6257,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6307,12 +6282,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6332,12 +6307,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6357,12 +6332,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6382,12 +6357,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6407,12 +6382,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6432,12 +6407,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6457,12 +6432,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6482,12 +6457,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6507,12 +6482,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6532,12 +6507,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6557,12 +6532,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6582,12 +6557,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6607,12 +6582,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6632,12 +6607,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6657,12 +6632,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6682,12 +6657,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6707,12 +6682,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", " \r\n", @@ -6991,7 +6966,7 @@ "()" ] }, - "execution_count": 33, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } @@ -7020,7 +6995,7 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 8, "metadata": { "collapsed": false, "jupyter": { @@ -7054,23 +7029,23 @@ { "data": { "text/plain": [ - "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 47232},\n", - " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 383474},\n", - " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 2},\n", + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 177740},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 321366},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 4},\n", " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", - " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 180},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 166},\n", " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", - " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 180},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 166},\n", " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", @@ -7078,7 +7053,7 @@ " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" ] }, - "execution_count": 34, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -7094,7 +7069,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 9, "metadata": { "collapsed": false, "jupyter": { @@ -7122,7 +7097,7 @@ "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" ] }, - "execution_count": 35, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } @@ -7133,7 +7108,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 10, "metadata": { "collapsed": false, "jupyter": { @@ -7154,9 +7129,9 @@ "Submitting Task6_ResourceEstimationWrapper to target microsoft.estimator...\n", "Job successfully submitted.\n", " Job name: RE for the task 6\n", - " Job ID: c796f8ea-2157-429d-b6d6-9315680622eb\n", + " Job ID: 1678631d-016c-4332-ba1f-61fcb3b081b9\n", "Waiting up to 30 seconds for Azure Quantum job to complete...\n", - "[9:02:21 AM] Current job status: Succeeded\n" + "[12:40:10 PM] Current job status: Succeeded\n" ] } ], @@ -7167,7 +7142,7 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 11, "metadata": { "collapsed": false, "jupyter": { @@ -8220,7 +8195,7 @@ " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" ] }, - "execution_count": 37, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" } @@ -8233,7 +8208,7 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 12, "metadata": { "collapsed": false, "jupyter": { @@ -8260,7 +8235,7 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 13, "metadata": { "collapsed": false, "jupyter": { @@ -8289,7 +8264,7 @@ "1050" ] }, - "execution_count": 39, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" } diff --git a/iQuHack-challenge-2023-task7.ipynb b/iQuHack-challenge-2023-task7.ipynb index c2cd08a..84be853 100644 --- a/iQuHack-challenge-2023-task7.ipynb +++ b/iQuHack-challenge-2023-task7.ipynb @@ -67,7 +67,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": { "collapsed": false, "jupyter": { @@ -80,7 +80,15 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Preparing Q# environment...\n" + ] + } + ], "source": [ "# Run this code cell to import the modules required to work with Q# and Azure\n", "import qsharp\n", @@ -89,7 +97,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": { "collapsed": false, "jupyter": { @@ -104,14 +112,14 @@ }, "outputs": [], "source": [ - "teamname=\"msft_is_the_best\" # Update this field with your team name\n", + "teamname=\"schrodingers-cat\" # Update this field with your team name\n", "task=[\"task7\"]\n", - "slack_id=\"myslackid\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + "slack_id=\"U04L3SFUCQ2\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "metadata": { "collapsed": false, "jupyter": { @@ -148,7 +156,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 4, "metadata": { "collapsed": false, "jupyter": { @@ -180,10 +188,11 @@ "}\n", "\n", "operation Task7(input : Qubit[], target : Qubit) : Unit is Adj {\n", - " ControlledOnInt(9, X)([input[0], input[1], input[2], input[3]], target);\n", - " ControlledOnInt(9, X)([input[1], input[2], input[3], input[4]], target);\n", - " ControlledOnInt(9, X)([input[2], input[3], input[4], input[5]], target);\n", - " ControlledOnInt(9, X)([input[3], input[4], input[5], input[6]], target);\n", + " ControlledOnInt(9, X)([input[6], input[5], input[4], input[3]], target);\n", + " ControlledOnInt(9, X)([input[5], input[4], input[3], input[2]], target);\n", + " ControlledOnInt(9, X)([input[4], input[3], input[2], input[1]], target);\n", + " ControlledOnInt(9, X)([input[3], input[2], input[1], input[0]], target);\n", + " ControlledOnInt(73, X)(input, target);\n", "}\n", "\n", "operation 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$\\left|001111\\right\\rangle$$0.1768 + 0.0000 i$$0.0000 + 0.0000 i$\r\n", " \r\n", " \r\n", - "

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\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", "
$\\left|010010\\right\\rangle$$0.0000 + 0.0000 i$$0.1768 + 0.0000 i$\r\n", " \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", "
$\\left|010011\\right\\rangle$$0.1768 + 0.0000 i$$0.0000 + 0.0000 i$\r\n", " \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", "
$\\left|010100\\right\\rangle$$0.0000 + 0.0000 i$$0.1768 + 0.0000 i$\r\n", " \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", "
$\\left|010101\\right\\rangle$$0.1768 + 0.0000 i$$0.0000 + 0.0000 i$\r\n", " \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", "
$\\left|011100\\right\\rangle$$0.0000 + 0.0000 i$$0.1768 + 0.0000 i$\r\n", " \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", "
$\\left|011101\\right\\rangle$$0.1768 + 0.0000 i$$0.0000 + 0.0000 i$\r\n", " \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", "
$\\left|011110\\right\\rangle$$0.0000 + 0.0000 i$$0.1768 + 0.0000 i$\r\n", " \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", "
$\\left|011111\\right\\rangle$$0.1768 + 0.0000 i$$0.0000 + 0.0000 i$\r\n", " \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", "
$\\left|100000\\right\\rangle$$0.1768 + 0.0000 i$$0.0000 + 0.0000 i$\r\n", " \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", "
$\\left|100001\\right\\rangle$$0.0000 + 0.0000 i$$0.1768 + 0.0000 i$\r\n", " \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", "
$\\left|100010\\right\\rangle$$0.1768 + 0.0000 i$$0.0000 + 0.0000 i$\r\n", " \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", "
$\\left|100011\\right\\rangle$$0.0000 + 0.0000 i$$0.1768 + 0.0000 i$\r\n", " \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", "
$\\left|101010\\right\\rangle$$0.1768 + 0.0000 i$$0.0000 + 0.0000 i$\r\n", " \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", "
$\\left|101011\\right\\rangle$$0.0000 + 0.0000 i$$0.1768 + 0.0000 i$\r\n", " \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", "
$\\left|101100\\right\\rangle$$0.1768 + 0.0000 i$$0.0000 + 0.0000 i$\r\n", " \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", "
$\\left|101101\\right\\rangle$$0.0000 + 0.0000 i$$0.1768 + 0.0000 i$\r\n", " \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", "
$\\left|110000\\right\\rangle$$0.1768 + 0.0000 i$$0.0000 + 0.0000 i$\r\n", " \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", "
$\\left|110001\\right\\rangle$$0.0000 + 0.0000 i$$0.1768 + 0.0000 i$\r\n", " \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", "
$\\left|111010\\right\\rangle$$0.0000 + 0.0000 i$$0.1768 + 0.0000 i$\r\n", " \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", "
$\\left|111011\\right\\rangle$$0.1768 + 0.0000 i$$0.0000 + 0.0000 i$\r\n", " \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", " 		\r\n", - "

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\r\n", " 		\r\n", - "

\r\n", + "

\r\n", "

\r\n", "
Runtime528us360us 800ns\r\n", "

Total runtime

\n", "\r\n", "
\r\n", - "

This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 120 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

\n", + "

This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 82 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

\n", "\r\n", "
Algorithmic depth12082\r\n", "

Number of logical cycles for the algorithm

\n", "\r\n", "
\r\n", - "

To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 24 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 8 CCZ and 24 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

\n", + "

To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 16 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 6 CCZ and 16 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

\n", "\r\n", "
Logical depth12082\r\n", "

Number of logical cycles performed

\n", "\r\n", "
\r\n", - "

This number is usually equal to the logical depth of the algorithm, which is 120. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", + "

This number is usually equal to the logical depth of the algorithm, which is 82. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", "\r\n", "
Number of T states12888\r\n", "

Number of T states consumed by the algorithm

\n", "\r\n", "
\r\n", - "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 8 CCZ and 24 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", + "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 6 CCZ and 16 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", "\r\n", "
Number of T factories12\r\n", - "

Number of T factories capable of producing the demanded 128 T states during the algorithm's runtime

\n", + "

Number of T factories capable of producing the demanded 88 T states during the algorithm's runtime

\n", "\r\n", "
\r\n", - "

The total number of T factories 12 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{128\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 528us\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", + "

The total number of T factories 12 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{88\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 360us 800ns\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", "\r\n", "
Number of T factory invocations118\r\n", "

Number of times all T factories are invoked

\n", "\r\n", "
\r\n", - "

In order to prepare the 128 T states, the 12 copies of the T factory are repeatedly invoked 11 times.

\n", + "

In order to prepare the 88 T states, the 12 copies of the T factory are repeatedly invoked 8 times.

\n", "\r\n", "
Required logical qubit error rate1.49e-72.18e-7\r\n", "

The minimum logical qubit error rate required to run the algorithm within the error budget

\n", "\r\n", "
\r\n", - "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 28 logical qubits and the total cycle count 120.

\n", + "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 28 logical qubits and the total cycle count 82.

\n", "\r\n", "
Required logical T state error rate3.91e-65.68e-6\r\n", "

The minimum T state error rate required for distilled T states

\n", "\r\n", "
\r\n", - "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 128.

\n", + "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 88.

\n", "\r\n", "
CCZ gates86\r\n", "

Number of CCZ-gates in the input quantum program

\n", "\r\n", @@ -2736,7 +2713,7 @@ "\r\n", "
CCiX gates2416\r\n", "

Number of CCiX-gates in the input quantum program

\n", "\r\n", @@ -2748,7 +2725,7 @@ "\r\n", "
Measurement operations2416\r\n", "

Number of single qubit measurements in the input quantum program

\n", "\r\n", @@ -2979,9 +2956,9 @@ " 'tGateTime': '50 ns',\n", " 'twoQubitGateErrorRate': 0.001,\n", " 'twoQubitGateTime': '50 ns'}},\n", - " 'logicalCounts': {'ccixCount': 24,\n", - " 'cczCount': 8,\n", - " 'measurementCount': 24,\n", + " 'logicalCounts': {'ccixCount': 16,\n", + " 'cczCount': 6,\n", + " 'measurementCount': 16,\n", " 'numQubits': 9,\n", " 'rotationCount': 0,\n", " 'rotationDepth': 0,\n", @@ -2990,20 +2967,20 @@ " 'logicalCycleTime': 4400.0,\n", " 'logicalErrorRate': 3.000000000000002e-08,\n", " 'physicalQubits': 242},\n", - " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 120,\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 82,\n", " 'algorithmicLogicalQubits': 28,\n", " 'cliffordErrorRate': 0.001,\n", - " 'logicalDepth': 120,\n", + " 'logicalDepth': 82,\n", " 'numTfactories': 12,\n", - " 'numTfactoryRuns': 11,\n", + " 'numTfactoryRuns': 8,\n", " 'numTsPerRotation': None,\n", - " 'numTstates': 128,\n", + " 'numTstates': 88,\n", " 'physicalQubitsForAlgorithm': 6776,\n", " 'physicalQubitsForTfactories': 77760,\n", - " 'requiredLogicalQubitErrorRate': 1.4880952380952382e-07,\n", - " 'requiredLogicalTstateErrorRate': 3.90625e-06},\n", + " 'requiredLogicalQubitErrorRate': 2.177700348432056e-07,\n", + " 'requiredLogicalTstateErrorRate': 5.681818181818182e-06},\n", " 'physicalQubits': 84536,\n", - " 'runtime': 528000},\n", + " 'runtime': 360800},\n", " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", " 'errorBudget': '1.00e-3',\n", " 'errorBudgetLogical': '5.00e-4',\n", @@ -3015,9 +2992,9 @@ " 'numUnitsPerRound': '2',\n", " 'physicalQubitsForTfactoriesPercentage': '91.98 %',\n", " 'physicalQubitsPerRound': '6480',\n", - " 'requiredLogicalQubitErrorRate': '1.49e-7',\n", - " 'requiredLogicalTstateErrorRate': '3.91e-6',\n", - " 'runtime': '528us',\n", + " 'requiredLogicalQubitErrorRate': '2.18e-7',\n", + " 'requiredLogicalTstateErrorRate': '5.68e-6',\n", + " 'runtime': '360us 800ns',\n", " 'tfactoryRuntime': '46us 800ns',\n", " 'tfactoryRuntimePerRound': '46us 800ns',\n", " 'tstateLogicalErrorRate': '2.17e-6',\n", @@ -3035,7 +3012,7 @@ " 'label': 'Physical qubits',\n", " 'path': 'physicalCounts/physicalQubits'},\n", " {'description': 'Total runtime',\n", - " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 120 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 82 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", " 'label': 'Runtime',\n", " 'path': 'physicalCountsFormatted/runtime'}],\n", " 'title': 'Physical resource estimates'},\n", @@ -3045,23 +3022,23 @@ " 'label': 'Logical algorithmic qubits',\n", " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", " {'description': 'Number of logical cycles for the algorithm',\n", - " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 24 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 8 CCZ and 24 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 16 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 6 CCZ and 16 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", " 'label': 'Algorithmic depth',\n", " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", " {'description': 'Number of logical cycles performed',\n", - " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 120. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 82. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", " 'label': 'Logical depth',\n", " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", " {'description': 'Number of T states consumed by the algorithm',\n", - " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 8 CCZ and 24 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 6 CCZ and 16 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", " 'label': 'Number of T states',\n", " 'path': 'physicalCounts/breakdown/numTstates'},\n", - " {'description': \"Number of T factories capable of producing the demanded 128 T states during the algorithm's runtime\",\n", - " 'explanation': 'The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{128\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 528us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " {'description': \"Number of T factories capable of producing the demanded 88 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{88\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 360us 800ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", " 'label': 'Number of T factories',\n", " 'path': 'physicalCounts/breakdown/numTfactories'},\n", " {'description': 'Number of times all T factories are invoked',\n", - " 'explanation': 'In order to prepare the 128 T states, the 12 copies of the T factory are repeatedly invoked 11 times.',\n", + " 'explanation': 'In order to prepare the 88 T states, the 12 copies of the T factory are repeatedly invoked 8 times.',\n", " 'label': 'Number of T factory invocations',\n", " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", " {'description': 'Number of physical qubits for the algorithm after layout',\n", @@ -3073,11 +3050,11 @@ " 'label': 'Physical T factory qubits',\n", " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", - " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 28 logical qubits and the total cycle count 120.',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 28 logical qubits and the total cycle count 82.',\n", " 'label': 'Required logical qubit error rate',\n", " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", " {'description': 'The minimum T state error rate required for distilled T states',\n", - " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 128.',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 88.',\n", " 'label': 'Required logical T state error rate',\n", " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", @@ -3091,7 +3068,7 @@ " 'label': 'QEC scheme',\n", " 'path': 'jobParams/qecScheme/name'},\n", " {'description': 'Required code distance for error correction',\n", - " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000014880952380952382)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.0000002177700348432056)}{\\\\log(0.01/0.001)} - 1$',\n", " 'label': 'Code distance',\n", " 'path': 'logicalQubit/codeDistance'},\n", " {'description': 'Number of physical qubits per logical qubit',\n", @@ -3165,7 +3142,7 @@ " 'label': 'Runtime per round',\n", " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", " {'description': 'Logical T state error rate',\n", - " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 3.91e-6.',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 5.68e-6.',\n", " 'label': 'Logical T state error rate',\n", " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", " 'title': 'T factory parameters'},\n", @@ -3273,7 +3250,7 @@ " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" ] }, - "execution_count": 16, + "execution_count": 22, "metadata": {}, "output_type": "execute_result" } @@ -3286,7 +3263,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 23, "metadata": { "collapsed": false, "jupyter": { @@ -3313,7 +3290,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 24, "metadata": { "collapsed": false, "jupyter": { @@ -3332,17 +3309,17 @@ "output_type": "stream", "text": [ "Logical algorithmic qubits = 28\n", - "Algorithmic depth = 120\n", - "Score = 3360\n" + "Algorithmic depth = 82\n", + "Score = 2296\n" ] }, { "data": { "text/plain": [ - "3360" + "2296" ] }, - "execution_count": 18, + "execution_count": 24, "metadata": {}, "output_type": "execute_result" } diff --git a/iQuHack-challenge-2023-task3.ipynb b/iQuHack-challenge-2023-task3.ipynb index 77007c4..8133476 100644 --- a/iQuHack-challenge-2023-task3.ipynb +++ b/iQuHack-challenge-2023-task3.ipynb @@ -80,15 +80,7 @@ } } }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Preparing Q# environment...\n" - ] - } - ], + "outputs": [], "source": [ "# Run this code cell to import the modules required to work with Q# and Azure\n", "import qsharp\n", @@ -177,6 +169,7 @@ "%%qsharp\n", "open Microsoft.Quantum.Canon;\n", "open Microsoft.Quantum.Diagnostics;\n", + "open Microsoft.Quantum.Arrays;\n", "\n", "// Task 3. \n", "// (input will contain 6 qubits)\n", @@ -194,24 +187,44 @@ "}\n", "\n", "operation Task3(input : Qubit[], target : Qubit) : Unit is Adj {\n", - " use output = Qubit[Length(input)+1] {\n", - " within {\n", - " output[0] = input[0]\n", - " for i in 1 .. Length(input) - 1 { \n", - " \n", - " }\n", - " } apply {\n", - " ControlledOnInt(3, X)(output, target);\n", - " }\n", - "\n", + " use sumWires = Qubit[4];\n", + " use zero = Qubit[1];\n", + " within{\n", + " //Ebene 1\n", + " CarryN(input[0], input[1], input[2], sumWires[0]);\n", + " CarryN(input[3], input[4], input[5], sumWires[1]);\n", + " //Ebene 2\n", + " CarryN(zero[0], input[2], input[5], sumWires[2]);\n", + " CarryN(sumWires[2], sumWires[0], sumWires[1], sumWires[3]);\n", + " //Outputs: input[5], sumWires[1], sumWires[3]\n", + " // == 3 --> input[5] == 1 && sumWires[1] == 1 && sumWires[3] == 0\n", + " X(sumWires[3]);\n", + " } apply{\n", + " Controlled X([input[5], sumWires[1], sumWires[3]], target);\n", " }\n", "}\n", - "\n" + "\n", + "operation QubitArrayWrapperOperation (op : ((Qubit[], Qubit) => Unit is Adj), qs : Qubit[]) : Unit is Adj { \n", + " op(Most(qs), Tail(qs));\n", + "}\n", + "\n", + "operation TestCompoundGate () : Unit {\n", + " AssertOperationsEqualReferenced(6+1, QubitArrayWrapperOperation(Task3, _), QubitArrayWrapperOperation (original, _));\n", + "}" ] }, { "cell_type": "code", "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "TestCompoundGate();" + ] + }, + { + "cell_type": "code", + "execution_count": 6, "metadata": { "collapsed": false, "jupyter": { @@ -268,7 +281,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 7, "metadata": { "collapsed": false, "jupyter": { @@ -313,12 +326,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " 		\r\n", - "

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Physical qubits14350699916\r\n", "

Number of physical qubits

\n", "\r\n", "
\r\n", - "

This value represents the total number of physical qubits, which is the sum of 7986 physical qubits to implement the algorithm logic, and 135520 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

\n", + "

This value represents the total number of physical qubits, which is the sum of 9196 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

\n", "\r\n", "
Runtime1ms 672us242us\r\n", "

Total runtime

\n", "\r\n", "
\r\n", - "

This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 380 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

\n", + "

This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 55 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

\n", "\r\n", "
Logical algorithmic qubits3338\r\n", "

Number of logical qubits for the algorithm after layout

\n", "\r\n", "
\r\n", - "

Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 11\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 33$ logical qubits.

\n", + "

Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 13\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 38$ logical qubits.

\n", "\r\n", "
Algorithmic depth38055\r\n", "

Number of logical cycles for the algorithm

\n", "\r\n", "
\r\n", - "

To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 80 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 20 CCZ and 80 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

\n", + "

To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 1 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 17 CCZ and 1 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

\n", "\r\n", "
Logical depth38055\r\n", "

Number of logical cycles performed

\n", "\r\n", "
\r\n", - "

This number is usually equal to the logical depth of the algorithm, which is 380. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", + "

This number is usually equal to the logical depth of the algorithm, which is 55. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", "\r\n", "
Number of T states40072\r\n", "

Number of T states consumed by the algorithm

\n", "\r\n", "
\r\n", - "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 20 CCZ and 80 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", + "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 17 CCZ and 1 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", "\r\n", "
Number of T factories14\r\n", - "

Number of T factories capable of producing the demanded 400 T states during the algorithm's runtime

\n", + "

Number of T factories capable of producing the demanded 72 T states during the algorithm's runtime

\n", "\r\n", "
\r\n", - "

The total number of T factories 14 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{400\\;\\text{T states} \\cdot 57us 200ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 1ms 672us\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", + "

The total number of T factories 14 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{72\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 242us\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", "\r\n", "
Number of T factory invocations296\r\n", "

Number of times all T factories are invoked

\n", "\r\n", "
\r\n", - "

In order to prepare the 400 T states, the 14 copies of the T factory are repeatedly invoked 29 times.

\n", + "

In order to prepare the 72 T states, the 14 copies of the T factory are repeatedly invoked 6 times.

\n", "\r\n", "
Physical algorithmic qubits79869196\r\n", "

Number of physical qubits for the algorithm after layout

\n", "\r\n", "
\r\n", - "

The 7986 are the product of the 33 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.

\n", + "

The 9196 are the product of the 38 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.

\n", "\r\n", "
Physical T factory qubits13552090720\r\n", "

Number of physical qubits for the T factories

\n", "\r\n", "
\r\n", - "

Each T factory requires 9680 physical qubits and we run 14 in parallel, therefore we need $135520 = 9680 \\cdot 14$ qubits.

\n", + "

Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\cdot 14$ qubits.

\n", "\r\n", "
Required logical qubit error rate3.99e-82.39e-7\r\n", "

The minimum logical qubit error rate required to run the algorithm within the error budget

\n", "\r\n", "
\r\n", - "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 380.

\n", + "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 55.

\n", "\r\n", "
Required logical T state error rate1.25e-66.94e-6\r\n", "

The minimum T state error rate required for distilled T states

\n", "\r\n", "
\r\n", - "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 400.

\n", + "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 72.

\n", "\r\n", "
Physical qubits96806480\r\n", "

Number of physical qubits for a single T factory

\n", "\r\n", @@ -4149,7 +4161,7 @@ "\r\n", "
Runtime57us 200ns46us 800ns\r\n", "

Runtime of a single T factory

\n", "\r\n", @@ -4166,7 +4178,7 @@ "

Number of output T states produced in a single run of T factory

\n", "\r\n", "
\r\n", - "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.

\n", + "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.

\n", "\r\n", "
Distillation code distances119\r\n", "

The code distance in each round of distillation

\n", "\r\n", @@ -4233,7 +4245,7 @@ "\r\n", "
Number of physical qubits per round96806480\r\n", "

The number of physical qubits used in each round of distillation

\n", "\r\n", @@ -4245,7 +4257,7 @@ "\r\n", "
Runtime per round57us 200ns46us 800ns\r\n", "

The runtime of each distillation round

\n", "\r\n", @@ -4257,12 +4269,12 @@ "\r\n", "
Logical T state error rate2.48e-72.17e-6\r\n", "

Logical T state error rate

\n", "\r\n", "
\r\n", - "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-6.

\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.94e-6.

\n", "\r\n", "
Logical qubits (pre-layout)1113\r\n", "

Number of logical qubits in the input quantum program

\n", "\r\n", "
\r\n", - "

We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", + "

We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", "\r\n", "
CCZ gates2017\r\n", "

Number of CCZ-gates in the input quantum program

\n", "\r\n", @@ -4337,7 +4349,7 @@ "\r\n", "
CCiX gates801\r\n", "

Number of CCiX-gates in the input quantum program

\n", "\r\n", @@ -4349,7 +4361,7 @@ "\r\n", "
Measurement operations801\r\n", "

Number of single qubit measurements in the input quantum program

\n", "\r\n", @@ -4580,10 +4592,10 @@ " 'tGateTime': '50 ns',\n", " 'twoQubitGateErrorRate': 0.001,\n", " 'twoQubitGateTime': '50 ns'}},\n", - " 'logicalCounts': {'ccixCount': 80,\n", - " 'cczCount': 20,\n", - " 'measurementCount': 80,\n", - " 'numQubits': 11,\n", + " 'logicalCounts': {'ccixCount': 1,\n", + " 'cczCount': 17,\n", + " 'measurementCount': 1,\n", + " 'numQubits': 13,\n", " 'rotationCount': 0,\n", " 'rotationDepth': 0,\n", " 'tCount': 0},\n", @@ -4591,21 +4603,21 @@ " 'logicalCycleTime': 4400.0,\n", " 'logicalErrorRate': 3.000000000000002e-08,\n", " 'physicalQubits': 242},\n", - " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 380,\n", - " 'algorithmicLogicalQubits': 33,\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 55,\n", + " 'algorithmicLogicalQubits': 38,\n", " 'cliffordErrorRate': 0.001,\n", - " 'logicalDepth': 380,\n", + " 'logicalDepth': 55,\n", " 'numTfactories': 14,\n", - " 'numTfactoryRuns': 29,\n", + " 'numTfactoryRuns': 6,\n", " 'numTsPerRotation': None,\n", - " 'numTstates': 400,\n", - " 'physicalQubitsForAlgorithm': 7986,\n", - " 'physicalQubitsForTfactories': 135520,\n", - " 'requiredLogicalQubitErrorRate': 3.987240829346092e-08,\n", - " 'requiredLogicalTstateErrorRate': 1.25e-06},\n", - " 'physicalQubits': 143506,\n", - " 'runtime': 1672000},\n", - " 'physicalCountsFormatted': {'codeDistancePerRound': '11',\n", + " 'numTstates': 72,\n", + " 'physicalQubitsForAlgorithm': 9196,\n", + " 'physicalQubitsForTfactories': 90720,\n", + " 'requiredLogicalQubitErrorRate': 2.3923444976076555e-07,\n", + " 'requiredLogicalTstateErrorRate': 6.944444444444445e-06},\n", + " 'physicalQubits': 99916,\n", + " 'runtime': 242000},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", " 'errorBudget': '1.00e-3',\n", " 'errorBudgetLogical': '5.00e-4',\n", " 'errorBudgetRotations': '0.00e0',\n", @@ -4614,14 +4626,14 @@ " 'logicalErrorRate': '3.00e-8',\n", " 'numTsPerRotation': 'No rotations in algorithm',\n", " 'numUnitsPerRound': '2',\n", - " 'physicalQubitsForTfactoriesPercentage': '94.44 %',\n", - " 'physicalQubitsPerRound': '9680',\n", - " 'requiredLogicalQubitErrorRate': '3.99e-8',\n", - " 'requiredLogicalTstateErrorRate': '1.25e-6',\n", - " 'runtime': '1ms 672us',\n", - " 'tfactoryRuntime': '57us 200ns',\n", - " 'tfactoryRuntimePerRound': '57us 200ns',\n", - " 'tstateLogicalErrorRate': '2.48e-7',\n", + " 'physicalQubitsForTfactoriesPercentage': '90.80 %',\n", + " 'physicalQubitsPerRound': '6480',\n", + " 'requiredLogicalQubitErrorRate': '2.39e-7',\n", + " 'requiredLogicalTstateErrorRate': '6.94e-6',\n", + " 'runtime': '242us',\n", + " 'tfactoryRuntime': '46us 800ns',\n", + " 'tfactoryRuntimePerRound': '46us 800ns',\n", + " 'tstateLogicalErrorRate': '2.17e-6',\n", " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", @@ -4632,53 +4644,53 @@ " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", " 'groups': [{'alwaysVisible': True,\n", " 'entries': [{'description': 'Number of physical qubits',\n", - " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 7986 physical qubits to implement the algorithm logic, and 135520 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 9196 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", " 'label': 'Physical qubits',\n", " 'path': 'physicalCounts/physicalQubits'},\n", " {'description': 'Total runtime',\n", - " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 380 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 55 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", " 'label': 'Runtime',\n", " 'path': 'physicalCountsFormatted/runtime'}],\n", " 'title': 'Physical resource estimates'},\n", " {'alwaysVisible': False,\n", " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", - " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 11$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 33$ logical qubits.',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 13$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 38$ logical qubits.',\n", " 'label': 'Logical algorithmic qubits',\n", " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", " {'description': 'Number of logical cycles for the algorithm',\n", - " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 80 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 20 CCZ and 80 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 1 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 17 CCZ and 1 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", " 'label': 'Algorithmic depth',\n", " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", " {'description': 'Number of logical cycles performed',\n", - " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 380. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 55. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", " 'label': 'Logical depth',\n", " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", " {'description': 'Number of T states consumed by the algorithm',\n", - " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 20 CCZ and 80 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 17 CCZ and 1 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", " 'label': 'Number of T states',\n", " 'path': 'physicalCounts/breakdown/numTstates'},\n", - " {'description': \"Number of T factories capable of producing the demanded 400 T states during the algorithm's runtime\",\n", - " 'explanation': 'The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{400\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 1ms 672us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " {'description': \"Number of T factories capable of producing the demanded 72 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{72\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 242us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", " 'label': 'Number of T factories',\n", " 'path': 'physicalCounts/breakdown/numTfactories'},\n", " {'description': 'Number of times all T factories are invoked',\n", - " 'explanation': 'In order to prepare the 400 T states, the 14 copies of the T factory are repeatedly invoked 29 times.',\n", + " 'explanation': 'In order to prepare the 72 T states, the 14 copies of the T factory are repeatedly invoked 6 times.',\n", " 'label': 'Number of T factory invocations',\n", " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", " {'description': 'Number of physical qubits for the algorithm after layout',\n", - " 'explanation': 'The 7986 are the product of the 33 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.',\n", + " 'explanation': 'The 9196 are the product of the 38 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.',\n", " 'label': 'Physical algorithmic qubits',\n", " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", " {'description': 'Number of physical qubits for the T factories',\n", - " 'explanation': 'Each T factory requires 9680 physical qubits and we run 14 in parallel, therefore we need $135520 = 9680 \\\\cdot 14$ qubits.',\n", + " 'explanation': 'Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\\\cdot 14$ qubits.',\n", " 'label': 'Physical T factory qubits',\n", " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", - " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 380.',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 55.',\n", " 'label': 'Required logical qubit error rate',\n", " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", " {'description': 'The minimum T state error rate required for distilled T states',\n", - " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 400.',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 72.',\n", " 'label': 'Required logical T state error rate',\n", " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", @@ -4692,7 +4704,7 @@ " 'label': 'QEC scheme',\n", " 'path': 'jobParams/qecScheme/name'},\n", " {'description': 'Required code distance for error correction',\n", - " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000003987240829346092)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000023923444976076555)}{\\\\log(0.01/0.001)} - 1$',\n", " 'label': 'Code distance',\n", " 'path': 'logicalQubit/codeDistance'},\n", " {'description': 'Number of physical qubits per logical qubit',\n", @@ -4734,7 +4746,7 @@ " 'label': 'Runtime',\n", " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", " {'description': 'Number of output T states produced in a single run of T factory',\n", - " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.',\n", " 'label': 'Number of output T states per run',\n", " 'path': 'tfactory/numTstates'},\n", " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", @@ -4766,13 +4778,13 @@ " 'label': 'Runtime per round',\n", " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", " {'description': 'Logical T state error rate',\n", - " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-6.',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.94e-6.',\n", " 'label': 'Logical T state error rate',\n", " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", " 'title': 'T factory parameters'},\n", " {'alwaysVisible': False,\n", " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", - " 'explanation': 'We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'explanation': 'We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", " 'label': 'Logical qubits (pre-layout)',\n", " 'path': 'logicalCounts/numQubits'},\n", " {'description': 'Number of T gates in the input quantum program',\n", @@ -4861,16 +4873,16 @@ " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", " 'title': 'Physical qubit parameters'}]},\n", " 'status': 'success',\n", - " 'tfactory': {'codeDistancePerRound': [11],\n", - " 'logicalErrorRate': 2.480000000000001e-07,\n", + " 'tfactory': {'codeDistancePerRound': [9],\n", + " 'logicalErrorRate': 2.165000000000001e-06,\n", " 'numInputTstates': 30,\n", " 'numRounds': 1,\n", " 'numTstates': 1,\n", " 'numUnitsPerRound': [2],\n", - " 'physicalQubits': 9680,\n", - " 'physicalQubitsPerRound': [9680],\n", - " 'runtime': 57200.0,\n", - " 'runtimePerRound': [57200.0],\n", + " 'physicalQubits': 6480,\n", + " 'physicalQubitsPerRound': [6480],\n", + " 'runtime': 46800.0,\n", + " 'runtimePerRound': [46800.0],\n", " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" ] }, @@ -4932,15 +4944,15 @@ "name": "stdout", "output_type": "stream", "text": [ - "Logical algorithmic qubits = 33\n", - "Algorithmic depth = 380\n", - "Score = 12540\n" + "Logical algorithmic qubits = 38\n", + "Algorithmic depth = 55\n", + "Score = 2090\n" ] }, { "data": { "text/plain": [ - "12540" + "2090" ] }, "execution_count": 13, diff --git a/iQuHack-challenge-2023-task7.ipynb b/iQuHack-challenge-2023-task7.ipynb index 2670c29..c2cd08a 100644 --- a/iQuHack-challenge-2023-task7.ipynb +++ b/iQuHack-challenge-2023-task7.ipynb @@ -67,7 +67,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": { "collapsed": false, "jupyter": { @@ -89,7 +89,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": { "collapsed": false, "jupyter": { @@ -111,7 +111,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": { "collapsed": false, "jupyter": { @@ -148,7 +148,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 19, "metadata": { "collapsed": false, "jupyter": { @@ -169,19 +169,124 @@ "%%qsharp\n", "open Microsoft.Quantum.Canon;\n", "open Microsoft.Quantum.Diagnostics;\n", + "open Microsoft.Quantum.Arrays;\n", "\n", "// Task 7. \n", "// (input will contain 7 qubits)\n", - "operation Task7(input : Qubit[], target : Qubit) : Unit is Adj {\n", + "operation original(input : Qubit[], target : Qubit) : Unit is Adj {\n", " for i in [9,18,19,25,36,37,38,39,41,50,51,57,72,73,74,75,76,77,78,79,82,83,89,100,101,102,103,105,114,115,121] {\n", " ControlledOnInt(i, X)(input, target);\n", " }\n", - "}" + "}\n", + "\n", + "operation Task7(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " ControlledOnInt(9, X)([input[0], input[1], input[2], input[3]], target);\n", + " ControlledOnInt(9, X)([input[1], input[2], input[3], input[4]], target);\n", + " ControlledOnInt(9, X)([input[2], input[3], input[4], input[5]], target);\n", + " ControlledOnInt(9, X)([input[3], input[4], input[5], input[6]], target);\n", + "}\n", + "\n", + "operation QubitArrayWrapperOperation (op : ((Qubit[], Qubit) => Unit is Adj), qs : Qubit[]) : Unit is Adj { \n", + " op(Most(qs), Tail(qs));\n", + "}\n", + "\n", + "operation TestCompoundGate () : Unit {\n", + " AssertOperationsEqualReferenced(7+1, QubitArrayWrapperOperation(Task7, _), QubitArrayWrapperOperation (original, _));\n", + "}\n" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "\r\n", + "
\r\n", + " \r\n", + " Unhandled exception of type Microsoft.Quantum.Simulation.Core.ExecutionFailException: Qubit in invalid state. Expecting: Zero\n", + "\tExpected:\t0\n", + "\tActual:\t0.007812499999999998\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + "
SourceCallable
/home/jovyan/2023_microsoft/D:\\a\\1\\s\\submodules\\qsharp-runtime\\src\\Simulation\\QSharpFoundation\\Diagnostics\\Assert.qs:0Microsoft.Quantum.Diagnostics.AssertMeasurement
/home/jovyan/2023_microsoft/D:\\a\\1\\s\\submodules\\qsharp-runtime\\src\\Simulation\\QSharpFoundation\\Diagnostics\\AssertQubit.qs:0Microsoft.Quantum.Diagnostics.AssertQubit
/home/jovyan/2023_microsoft/D:\\a\\1\\s\\submodules\\qsharp-runtime\\src\\Simulation\\QSharpFoundation\\Diagnostics\\AssertAllZero.qs:0Microsoft.Quantum.Diagnostics.AssertAllZero
/home/jovyan/2023_microsoft/D:\\a\\1\\s\\submodules\\qsharp-runtime\\src\\Simulation\\TargetDefinitions\\Decompositions\\AssertOperationsEqualReferenced.qs:0Microsoft.Quantum.Diagnostics.AssertOperationsEqualReferenced
(notebook)TestCompoundGate
\r\n", + "
\r\n", + " " + ], + "text/plain": [ + "Unhandled exception. Microsoft.Quantum.Simulation.Core.ExecutionFailException: Qubit in invalid state. Expecting: Zero\n", + "\tExpected:\t0\n", + "\tActual:\t0.007812499999999998\n", + " ---> Microsoft.Quantum.Diagnostics.AssertMeasurement on /home/jovyan/2023_microsoft/D:\\a\\1\\s\\submodules\\qsharp-runtime\\src\\Simulation\\QSharpFoundation\\Diagnostics\\Assert.qs:line 0\n", + " at Microsoft.Quantum.Diagnostics.AssertQubit on /home/jovyan/2023_microsoft/D:\\a\\1\\s\\submodules\\qsharp-runtime\\src\\Simulation\\QSharpFoundation\\Diagnostics\\AssertQubit.qs:line 0\n", + " at Microsoft.Quantum.Diagnostics.AssertAllZero on /home/jovyan/2023_microsoft/D:\\a\\1\\s\\submodules\\qsharp-runtime\\src\\Simulation\\QSharpFoundation\\Diagnostics\\AssertAllZero.qs:line 0\n", + " at Microsoft.Quantum.Diagnostics.AssertOperationsEqualReferenced on /home/jovyan/2023_microsoft/D:\\a\\1\\s\\submodules\\qsharp-runtime\\src\\Simulation\\TargetDefinitions\\Decompositions\\AssertOperationsEqualReferenced.qs:line 0\n", + " at SNIPPET.TestCompoundGate on /snippet_.qs:line 0\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Qubit in invalid state. Expecting: Zero\n", + "\tExpected:\t0\n", + "\tActual:\t0.007812499999999998\n" + ] + } + ], + "source": [ + "TestCompoundGate();" + ] + }, + { + "cell_type": "code", + "execution_count": 8, "metadata": { "collapsed": false, "jupyter": { @@ -238,7 +343,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "metadata": { "collapsed": false, "jupyter": { @@ -251,7 +356,3374 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": 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Qubit IDs0, 1, 2, 3, 4, 5, 6, 7
Basis state (bitstring)AmplitudeMeas. Pr.
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$\\left|00110110\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|01011010\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1001111100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10100000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10100010\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1010010100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1010011100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10101000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10101010\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10101100\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10101110\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10110000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1011001100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10110100\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10110110\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10111000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10111010\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|11000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|11000100\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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"output_type": "execute_result" + } + ], "source": [ "# Note that in the output of this cell the target qubit corresponds to the rightmost bit\n", "qsharp.config[\"dump.basisStateLabelingConvention\"]=\"Bitstring\"\n", @@ -276,7 +3748,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, "metadata": { "collapsed": false, "jupyter": { @@ -289,19 +3761,68 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "\"Connecting to Azure Quantum...\"", + "text/plain": [ + "Connecting to Azure Quantum..." + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Connected to Azure Quantum workspace azure-q in location uksouth.\n" + ] + }, + { + "data": { + "text/plain": [ + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 176176},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 317595},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 2},\n", + " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 168},\n", + " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 168},\n", + " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.qpu.aspen-m-2', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", "# If you're using this notebook in qBraid, keep it\n", "qsharp.azure.connect(\n", - " resourceId=\"...\",\n", - " location=\"...\",\n", + " resourceId=\"/subscriptions/7fc54e95-14cf-4a6f-b50e-d6155c241309/resourceGroups/AzureQuantum/providers/Microsoft.Quantum/Workspaces/azure-q\",\n", + " location=\"UK South\",\n", " credential=\"CLI\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "metadata": { "collapsed": false, "jupyter": { @@ -314,14 +3835,33 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loading package Microsoft.Quantum.Providers.Core and dependencies...\n", + "Active target is now microsoft.estimator\n" + ] + }, + { + "data": { + "text/plain": [ + "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "qsharp.azure.target(\"microsoft.estimator\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, "metadata": { "collapsed": false, "jupyter": { @@ -334,7 +3874,21 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Submitting Task7_ResourceEstimationWrapper to target microsoft.estimator...\n", + "Job successfully submitted.\n", + " Job name: RE for the task 7\n", + " Job ID: 86743ad4-5cca-4ea9-b420-d0b0c93f9a49\n", + "Waiting up to 30 seconds for Azure Quantum job to complete...\n", + "[11:59:38 AM] Current job status: Executing\n", + "[11:59:43 AM] Current job status: Succeeded\n" + ] + } + ], "source": [ "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", "result = qsharp.azure.execute(Task7_ResourceEstimationWrapper, jobName=\"RE for the task 7\")" @@ -342,7 +3896,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 14, "metadata": { "collapsed": false, "jupyter": { @@ -355,7 +3909,1051 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":155,\"cczCount\":31,\"measurementCount\":155,\"numQubits\":13,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":13,\"logicalCycleTime\":5200.0,\"logicalErrorRate\":3.000000000000002E-09,\"physicalQubits\":338},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":713,\"algorithmicLogicalQubits\":38,\"cliffordErrorRate\":0.001,\"logicalDepth\":713,\"numTfactories\":12,\"numTfactoryRuns\":62,\"numTsPerRotation\":null,\"numTstates\":744,\"physicalQubitsForAlgorithm\":12844,\"physicalQubitsForTfactories\":116160,\"requiredLogicalQubitErrorRate\":1.845427031815162E-08,\"requiredLogicalTstateErrorRate\":6.720430107526882E-07},\"physicalQubits\":129004,\"runtime\":3707600},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"11\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"5us 200ns\",\"logicalErrorRate\":\"3.00e-9\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"90.04 %\",\"physicalQubitsPerRound\":\"9680\",\"requiredLogicalQubitErrorRate\":\"1.85e-8\",\"requiredLogicalTstateErrorRate\":\"6.72e-7\",\"runtime\":\"3ms 707us 600ns\",\"tfactoryRuntime\":\"57us 200ns\",\"tfactoryRuntimePerRound\":\"57us 200ns\",\"tstateLogicalErrorRate\":\"2.48e-7\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 12844 physical qubits to implement the algorithm logic, and 116160 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (5us 200ns) multiplied by the 713 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 13$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 38$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 155 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 31 CCZ and 155 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 713. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 31 CCZ and 155 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 744 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{744\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 3ms 707us 600ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 744 T states, the 12 copies of the T factory are repeatedly invoked 62 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 12844 are the product of the 38 logical qubits after layout and the 338 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 9680 physical qubits and we run 12 in parallel, therefore we need $116160 = 9680 \\\\cdot 12$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 713.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 744.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000001845427031815162)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{13 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 5us 200ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 338.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.72e-7.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or ¬µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[11],\"logicalErrorRate\":2.480000000000001E-07,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":9680,\"physicalQubitsPerRound\":[9680],\"runtime\":57200.0,\"runtimePerRound\":[57200.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "text/html": [ + "\r\n", + "
\r\n", + " \r\n", + " Physical resource estimates\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits129004\r\n", + "

Number of physical qubits

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This value represents the total number of physical qubits, which is the sum of 12844 physical qubits to implement the algorithm logic, and 116160 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

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Runtime3ms 707us 600ns\r\n", + "

Total runtime

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This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (5us 200ns) multiplied by the 713 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

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Logical algorithmic qubits38\r\n", + "

Number of logical qubits for the algorithm after layout

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Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 13\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 38$ logical qubits.

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Algorithmic depth713\r\n", + "

Number of logical cycles for the algorithm

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To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 155 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 31 CCZ and 155 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

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Logical depth713\r\n", + "

Number of logical cycles performed

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This number is usually equal to the logical depth of the algorithm, which is 713. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

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Number of T states744\r\n", + "

Number of T states consumed by the algorithm

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To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 31 CCZ and 155 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

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Number of T factories12\r\n", + "

Number of T factories capable of producing the demanded 744 T states during the algorithm's runtime

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The total number of T factories 12 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{744\\;\\text{T states} \\cdot 57us 200ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 3ms 707us 600ns\\;\\text{algorithm runtime}}\\right\\rceil\\)

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Number of T factory invocations62\r\n", + "

Number of times all T factories are invoked

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In order to prepare the 744 T states, the 12 copies of the T factory are repeatedly invoked 62 times.

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Physical algorithmic qubits12844\r\n", + "

Number of physical qubits for the algorithm after layout

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The 12844 are the product of the 38 logical qubits after layout and the 338 physical qubits that encode a single logical qubit.

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Physical T factory qubits116160\r\n", + "

Number of physical qubits for the T factories

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Each T factory requires 9680 physical qubits and we run 12 in parallel, therefore we need $116160 = 9680 \\cdot 12$ qubits.

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Required logical qubit error rate1.85e-8\r\n", + "

The minimum logical qubit error rate required to run the algorithm within the error budget

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The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 713.

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Required logical T state error rate6.72e-7\r\n", + "

The minimum T state error rate required for distilled T states

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The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 744.

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Number of T states per rotationNo rotations in algorithm\r\n", + "

Number of T states to implement a rotation with an arbitrary angle

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The number of T states to implement a rotation with an arbitrary angle is \\(\\lceil 0.53 \\log_2(0 / 0) + 5.3\\rceil\\) [arXiv:2203.10064]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.

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\r\n", + " \r\n", + " Logical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
QEC schemesurface_code\r\n", + "

Name of QEC scheme

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You can load pre-defined QEC schemes by using the name surface_code or floquet_code. The latter only works with Majorana qubits.

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Code distance13\r\n", + "

Required code distance for error correction

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The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000001845427031815162)}{\\log(0.01/0.001)} - 1\\)

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Physical qubits338\r\n", + "

Number of physical qubits per logical qubit

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The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.

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Logical cycle time5us 200ns\r\n", + "

Duration of a logical cycle in nanoseconds

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The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.

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Logical qubit error rate3.00e-9\r\n", + "

Logical qubit error rate

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The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{13 + 1}{2}$

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Crossing prefactor0.03\r\n", + "

Crossing prefactor used in QEC scheme

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The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.

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Error correction threshold0.01\r\n", + "

Error correction threshold used in QEC scheme

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The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.

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Logical cycle time formula(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\r\n", + "

QEC scheme formula used to compute logical cycle time

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This is the formula that is used to compute the logical cycle time 5us 200ns.

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Physical qubits formula2 * codeDistance * codeDistance\r\n", + "

QEC scheme formula used to compute number of physical qubits per logical qubit

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This is the formula that is used to compute the number of physical qubits per logical qubits 338.

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Physical qubits9680\r\n", + "

Number of physical qubits for a single T factory

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This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.

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Runtime57us 200ns\r\n", + "

Runtime of a single T factory

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The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.

\n", + "\r\n", + "
Number of output T states per run1\r\n", + "

Number of output T states produced in a single run of T factory

\n", + "\r\n", + "
\r\n", + "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.

\n", + "\r\n", + "
Number of input T states per run30\r\n", + "

Number of physical input T states consumed in a single run of a T factory

\n", + "\r\n", + "
\r\n", + "

This value includes the physical input T states of all copies of the distillation unit in the first round.

\n", + "\r\n", + "
Distillation rounds1\r\n", + "

The number of distillation rounds

\n", + "\r\n", + "
\r\n", + "

This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.

\n", + "\r\n", + "
Distillation units per round2\r\n", + "

The number of units in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the number of copies for the distillation units per round.

\n", + "\r\n", + "
Distillation units15-to-1 space efficient logical\r\n", + "

The types of distillation units

\n", + "\r\n", + "
\r\n", + "

These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.

\n", + "\r\n", + "
Distillation code distances11\r\n", + "

The code distance in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.

\n", + "\r\n", + "
Number of physical qubits per round9680\r\n", + "

The number of physical qubits used in each round of distillation

\n", + "\r\n", + "
\r\n", + "

The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.

\n", + "\r\n", + "
Runtime per round57us 200ns\r\n", + "

The runtime of each distillation round

\n", + "\r\n", + "
\r\n", + "

The runtime of the T factory is the sum of the runtimes in all rounds.

\n", + "\r\n", + "
Logical T state error rate2.48e-7\r\n", + "

Logical T state error rate

\n", + "\r\n", + "
\r\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.72e-7.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Pre-layout logical resources\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Logical qubits (pre-layout)13\r\n", + "

Number of logical qubits in the input quantum program

\n", + "\r\n", + "
\r\n", + "

We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", + "\r\n", + "
T gates0\r\n", + "

Number of T gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.

\n", + "\r\n", + "
Rotation gates0\r\n", + "

Number of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.

\n", + "\r\n", + "
Rotation depth0\r\n", + "

Depth of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.

\n", + "\r\n", + "
CCZ gates31\r\n", + "

Number of CCZ-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCZ gates.

\n", + "\r\n", + "
CCiX gates155\r\n", + "

Number of CCiX-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCiX gates, which applies \\(-iX\\) controlled on two control qubits [1212.5069].

\n", + "\r\n", + "
Measurement operations155\r\n", + "

Number of single qubit measurements in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Assumed error budget\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Total error budget1.00e-3\r\n", + "

Total error budget for the algorithm

\n", + "\r\n", + "
\r\n", + "

The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget \\(\\epsilon = \\epsilon_{\\log} + \\epsilon_{\\rm dis} + \\epsilon_{\\rm syn}\\) is uniformly distributed and applies to errors \\(\\epsilon_{\\log}\\) to implement logical qubits, an error budget \\(\\epsilon_{\\rm dis}\\) to produce T states through distillation, and an error budget \\(\\epsilon_{\\rm syn}\\) to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets \\(\\epsilon_{\\rm dis}\\) and \\(\\epsilon_{\\rm syn}\\) are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.

\n", + "\r\n", + "
Logical error probability5.00e-4\r\n", + "

Probability of at least one logical error

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
T distillation error probability5.00e-4\r\n", + "

Probability of at least one faulty T distillation

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
Rotation synthesis error probability0.00e0\r\n", + "

Probability of at least one failed rotation synthesis

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Physical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Qubit namequbit_gate_ns_e3\r\n", + "

Some descriptive name for the qubit model

\n", + "\r\n", + "
\r\n", + "

You can load pre-defined qubit parameters by using the names qubit_gate_ns_e3, qubit_gate_ns_e4, qubit_gate_us_e3, qubit_gate_us_e4, qubit_maj_ns_e4, or qubit_maj_ns_e6. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).

\n", + "\r\n", + "
Instruction setGateBased\r\n", + "

Underlying qubit technology (gate-based or Majorana)

\n", + "\r\n", + "
\r\n", + "

When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either gate-based or Majorana. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.

\n", + "\r\n", + "
Single-qubit measurement time100 ns\r\n", + "

Operation time for single-qubit measurement (t_meas) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.

\n", + "\r\n", + "
Single-qubit gate time50 ns\r\n", + "

Operation time for single-qubit gate (t_gate) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.

\n", + "\r\n", + "
Two-qubit gate time50 ns\r\n", + "

Operation time for two-qubit gate in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.

\n", + "\r\n", + "
T gate time50 ns\r\n", + "

Operation time for a T gate

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to execute a T gate.

\n", + "\r\n", + "
Single-qubit measurement error rate0.001\r\n", + "

Error rate for single-qubit measurement

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit measurement in the Pauli basis may fail.

\n", + "\r\n", + "
Single-qubit error rate0.001\r\n", + "

Error rate for single-qubit Clifford gate (p)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.

\n", + "\r\n", + "
Two-qubit error rate0.001\r\n", + "

Error rate for two-qubit Clifford gate

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.

\n", + "\r\n", + "
T gate error rate0.001\r\n", + "

Error rate to prepare single-qubit T state or apply a T gate (p_T)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which executing a single T gate may fail.

\n", + "\r\n", + "
\n", + "
\r\n", + " Assumptions\r\n", + "
    \n", + "

  • More details on the following lists of assumptions can be found in the paper Accessing requirements for scaling quantum computers and their applications.

    \n", + "
    • \n", + "

  • Uniform independent physical noise. We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.

    \n", + "
    • \n", + "

  • Efficient classical computation. We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.

    \n", + "
    • \n", + "

  • Extraction circuits for planar quantum ISA. We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).

    \n", + "
    • \n", + "

  • Uniform independent logical noise. We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.

    \n", + "
    • \n", + "

  • Negligible Clifford costs for synthesis. We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.

    \n", + "
    • \n", + "

  • Smooth magic state consumption rate. We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.

    \n", + "
    • \n", + "
\n" + ], + "text/plain": [ + "{'errorBudget': {'logical': 0.0005, 'rotations': 0.0, 'tstates': 0.0005},\n", + " 'jobParams': {'errorBudget': 0.001,\n", + " 'qecScheme': {'crossingPrefactor': 0.03,\n", + " 'errorCorrectionThreshold': 0.01,\n", + " 'logicalCycleTime': '(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance',\n", + " 'name': 'surface_code',\n", + " 'physicalQubitsPerLogicalQubit': '2 * codeDistance * codeDistance'},\n", + " 'qubitParams': {'instructionSet': 'GateBased',\n", + " 'name': 'qubit_gate_ns_e3',\n", + " 'oneQubitGateErrorRate': 0.001,\n", + " 'oneQubitGateTime': '50 ns',\n", + " 'oneQubitMeasurementErrorRate': 0.001,\n", + " 'oneQubitMeasurementTime': '100 ns',\n", + " 'tGateErrorRate': 0.001,\n", + " 'tGateTime': '50 ns',\n", + " 'twoQubitGateErrorRate': 0.001,\n", + " 'twoQubitGateTime': '50 ns'}},\n", + " 'logicalCounts': {'ccixCount': 155,\n", + " 'cczCount': 31,\n", + " 'measurementCount': 155,\n", + " 'numQubits': 13,\n", + " 'rotationCount': 0,\n", + " 'rotationDepth': 0,\n", + " 'tCount': 0},\n", + " 'logicalQubit': {'codeDistance': 13,\n", + " 'logicalCycleTime': 5200.0,\n", + " 'logicalErrorRate': 3.000000000000002e-09,\n", + " 'physicalQubits': 338},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 713,\n", + " 'algorithmicLogicalQubits': 38,\n", + " 'cliffordErrorRate': 0.001,\n", + " 'logicalDepth': 713,\n", + " 'numTfactories': 12,\n", + " 'numTfactoryRuns': 62,\n", + " 'numTsPerRotation': None,\n", + " 'numTstates': 744,\n", + " 'physicalQubitsForAlgorithm': 12844,\n", + " 'physicalQubitsForTfactories': 116160,\n", + " 'requiredLogicalQubitErrorRate': 1.845427031815162e-08,\n", + " 'requiredLogicalTstateErrorRate': 6.720430107526882e-07},\n", + " 'physicalQubits': 129004,\n", + " 'runtime': 3707600},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '11',\n", + " 'errorBudget': '1.00e-3',\n", + " 'errorBudgetLogical': '5.00e-4',\n", + " 'errorBudgetRotations': '0.00e0',\n", + " 'errorBudgetTstates': '5.00e-4',\n", + " 'logicalCycleTime': '5us 200ns',\n", + " 'logicalErrorRate': '3.00e-9',\n", + " 'numTsPerRotation': 'No rotations in algorithm',\n", + " 'numUnitsPerRound': '2',\n", + " 'physicalQubitsForTfactoriesPercentage': '90.04 %',\n", + " 'physicalQubitsPerRound': '9680',\n", + " 'requiredLogicalQubitErrorRate': '1.85e-8',\n", + " 'requiredLogicalTstateErrorRate': '6.72e-7',\n", + " 'runtime': '3ms 707us 600ns',\n", + " 'tfactoryRuntime': '57us 200ns',\n", + " 'tfactoryRuntimePerRound': '57us 200ns',\n", + " 'tstateLogicalErrorRate': '2.48e-7',\n", + " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", + " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", + " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", + " '**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.',\n", + " '**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).',\n", + " '**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.',\n", + " '**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.',\n", + " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", + " 'groups': [{'alwaysVisible': True,\n", + " 'entries': [{'description': 'Number of physical qubits',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 12844 physical qubits to implement the algorithm logic, and 116160 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'physicalCounts/physicalQubits'},\n", + " {'description': 'Total runtime',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (5us 200ns) multiplied by the 713 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/runtime'}],\n", + " 'title': 'Physical resource estimates'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 13$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 38$ logical qubits.',\n", + " 'label': 'Logical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", + " {'description': 'Number of logical cycles for the algorithm',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 155 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 31 CCZ and 155 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'label': 'Algorithmic depth',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", + " {'description': 'Number of logical cycles performed',\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 713. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'label': 'Logical depth',\n", + " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", + " {'description': 'Number of T states consumed by the algorithm',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 31 CCZ and 155 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'label': 'Number of T states',\n", + " 'path': 'physicalCounts/breakdown/numTstates'},\n", + " {'description': \"Number of T factories capable of producing the demanded 744 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{744\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 3ms 707us 600ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " 'label': 'Number of T factories',\n", + " 'path': 'physicalCounts/breakdown/numTfactories'},\n", + " {'description': 'Number of times all T factories are invoked',\n", + " 'explanation': 'In order to prepare the 744 T states, the 12 copies of the T factory are repeatedly invoked 62 times.',\n", + " 'label': 'Number of T factory invocations',\n", + " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", + " {'description': 'Number of physical qubits for the algorithm after layout',\n", + " 'explanation': 'The 12844 are the product of the 38 logical qubits after layout and the 338 physical qubits that encode a single logical qubit.',\n", + " 'label': 'Physical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", + " {'description': 'Number of physical qubits for the T factories',\n", + " 'explanation': 'Each T factory requires 9680 physical qubits and we run 12 in parallel, therefore we need $116160 = 9680 \\\\cdot 12$ qubits.',\n", + " 'label': 'Physical T factory qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", + " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 713.',\n", + " 'label': 'Required logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", + " {'description': 'The minimum T state error rate required for distilled T states',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 744.',\n", + " 'label': 'Required logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", + " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", + " 'explanation': 'The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.',\n", + " 'label': 'Number of T states per rotation',\n", + " 'path': 'physicalCountsFormatted/numTsPerRotation'}],\n", + " 'title': 'Resource estimates breakdown'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Name of QEC scheme',\n", + " 'explanation': 'You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.',\n", + " 'label': 'QEC scheme',\n", + " 'path': 'jobParams/qecScheme/name'},\n", + " {'description': 'Required code distance for error correction',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000001845427031815162)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'label': 'Code distance',\n", + " 'path': 'logicalQubit/codeDistance'},\n", + " {'description': 'Number of physical qubits per logical qubit',\n", + " 'explanation': 'The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'logicalQubit/physicalQubits'},\n", + " {'description': 'Duration of a logical cycle in nanoseconds',\n", + " 'explanation': 'The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.',\n", + " 'label': 'Logical cycle time',\n", + " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", + " {'description': 'Logical qubit error rate',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{13 + 1}{2}$',\n", + " 'label': 'Logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", + " {'description': 'Crossing prefactor used in QEC scheme',\n", + " 'explanation': 'The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.',\n", + " 'label': 'Crossing prefactor',\n", + " 'path': 'jobParams/qecScheme/crossingPrefactor'},\n", + " {'description': 'Error correction threshold used in QEC scheme',\n", + " 'explanation': 'The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.',\n", + " 'label': 'Error correction threshold',\n", + " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", + " {'description': 'QEC scheme formula used to compute logical cycle time',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 5us 200ns.',\n", + " 'label': 'Logical cycle time formula',\n", + " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", + " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 338.',\n", + " 'label': 'Physical qubits formula',\n", + " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", + " 'title': 'Logical qubit parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of physical qubits for a single T factory',\n", + " 'explanation': 'This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'tfactory/physicalQubits'},\n", + " {'description': 'Runtime of a single T factory',\n", + " 'explanation': 'The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", + " {'description': 'Number of output T states produced in a single run of T factory',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.',\n", + " 'label': 'Number of output T states per run',\n", + " 'path': 'tfactory/numTstates'},\n", + " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", + " 'explanation': 'This value includes the physical input T states of all copies of the distillation unit in the first round.',\n", + " 'label': 'Number of input T states per run',\n", + " 'path': 'tfactory/numInputTstates'},\n", + " {'description': 'The number of distillation rounds',\n", + " 'explanation': 'This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.',\n", + " 'label': 'Distillation rounds',\n", + " 'path': 'tfactory/numRounds'},\n", + " {'description': 'The number of units in each round of distillation',\n", + " 'explanation': 'This is the number of copies for the distillation units per round.',\n", + " 'label': 'Distillation units per round',\n", + " 'path': 'physicalCountsFormatted/numUnitsPerRound'},\n", + " {'description': 'The types of distillation units',\n", + " 'explanation': 'These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.',\n", + " 'label': 'Distillation units',\n", + " 'path': 'physicalCountsFormatted/unitNamePerRound'},\n", + " {'description': 'The code distance in each round of distillation',\n", + " 'explanation': 'This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.',\n", + " 'label': 'Distillation code distances',\n", + " 'path': 'physicalCountsFormatted/codeDistancePerRound'},\n", + " {'description': 'The number of physical qubits used in each round of distillation',\n", + " 'explanation': 'The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.',\n", + " 'label': 'Number of physical qubits per round',\n", + " 'path': 'physicalCountsFormatted/physicalQubitsPerRound'},\n", + " {'description': 'The runtime of each distillation round',\n", + " 'explanation': 'The runtime of the T factory is the sum of the runtimes in all rounds.',\n", + " 'label': 'Runtime per round',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", + " {'description': 'Logical T state error rate',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.72e-7.',\n", + " 'label': 'Logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", + " 'title': 'T factory parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", + " 'explanation': 'We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'label': 'Logical qubits (pre-layout)',\n", + " 'path': 'logicalCounts/numQubits'},\n", + " {'description': 'Number of T gates in the input quantum program',\n", + " 'explanation': 'This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.',\n", + " 'label': 'T gates',\n", + " 'path': 'logicalCounts/tCount'},\n", + " {'description': 'Number of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.',\n", + " 'label': 'Rotation gates',\n", + " 'path': 'logicalCounts/rotationCount'},\n", + " {'description': 'Depth of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.',\n", + " 'label': 'Rotation depth',\n", + " 'path': 'logicalCounts/rotationDepth'},\n", + " {'description': 'Number of CCZ-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCZ gates.',\n", + " 'label': 'CCZ gates',\n", + " 'path': 'logicalCounts/cczCount'},\n", + " {'description': 'Number of CCiX-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].',\n", + " 'label': 'CCiX gates',\n", + " 'path': 'logicalCounts/ccixCount'},\n", + " {'description': 'Number of single qubit measurements in the input quantum program',\n", + " 'explanation': 'This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.',\n", + " 'label': 'Measurement operations',\n", + " 'path': 'logicalCounts/measurementCount'}],\n", + " 'title': 'Pre-layout logical resources'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Total error budget for the algorithm',\n", + " 'explanation': \"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\n", + " 'label': 'Total error budget',\n", + " 'path': 'physicalCountsFormatted/errorBudget'},\n", + " {'description': 'Probability of at least one logical error',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'Logical error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetLogical'},\n", + " {'description': 'Probability of at least one faulty T distillation',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'T distillation error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetTstates'},\n", + " {'description': 'Probability of at least one failed rotation synthesis',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3.',\n", + " 'label': 'Rotation synthesis error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetRotations'}],\n", + " 'title': 'Assumed error budget'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Some descriptive name for the qubit model',\n", + " 'explanation': 'You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).',\n", + " 'label': 'Qubit name',\n", + " 'path': 'jobParams/qubitParams/name'},\n", + " {'description': 'Underlying qubit technology (gate-based or Majorana)',\n", + " 'explanation': 'When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.',\n", + " 'label': 'Instruction set',\n", + " 'path': 'jobParams/qubitParams/instructionSet'},\n", + " {'description': 'Operation time for single-qubit measurement (t_meas) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.',\n", + " 'label': 'Single-qubit measurement time',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementTime'},\n", + " {'description': 'Operation time for single-qubit gate (t_gate) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.',\n", + " 'label': 'Single-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateTime'},\n", + " {'description': 'Operation time for two-qubit gate in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.',\n", + " 'label': 'Two-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateTime'},\n", + " {'description': 'Operation time for a T gate',\n", + " 'explanation': 'This is the operation time in nanoseconds to execute a T gate.',\n", + " 'label': 'T gate time',\n", + " 'path': 'jobParams/qubitParams/tGateTime'},\n", + " {'description': 'Error rate for single-qubit measurement',\n", + " 'explanation': 'This is the probability in which a single-qubit measurement in the Pauli basis may fail.',\n", + " 'label': 'Single-qubit measurement error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementErrorRate'},\n", + " {'description': 'Error rate for single-qubit Clifford gate (p)',\n", + " 'explanation': 'This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.',\n", + " 'label': 'Single-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateErrorRate'},\n", + " {'description': 'Error rate for two-qubit Clifford gate',\n", + " 'explanation': 'This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.',\n", + " 'label': 'Two-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateErrorRate'},\n", + " {'description': 'Error rate to prepare single-qubit T state or apply a T gate (p_T)',\n", + " 'explanation': 'This is the probability in which executing a single T gate may fail.',\n", + " 'label': 'T gate error rate',\n", + " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", + " 'title': 'Physical qubit parameters'}]},\n", + " 'status': 'success',\n", + " 'tfactory': {'codeDistancePerRound': [11],\n", + " 'logicalErrorRate': 2.480000000000001e-07,\n", + " 'numInputTstates': 30,\n", + " 'numRounds': 1,\n", + " 'numTstates': 1,\n", + " 'numUnitsPerRound': [2],\n", + " 'physicalQubits': 9680,\n", + " 'physicalQubitsPerRound': [9680],\n", + " 'runtime': 57200.0,\n", + " 'runtimePerRound': [57200.0],\n", + " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", "# result = qsharp.azure.output(\"...\")\n", @@ -364,7 +4962,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 15, "metadata": { "collapsed": false, "jupyter": { @@ -391,7 +4989,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 16, "metadata": { "collapsed": false, "jupyter": { @@ -404,10 +5002,37 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Logical algorithmic qubits = 38\n", + "Algorithmic depth = 713\n", + "Score = 27094\n" + ] + }, + { + "data": { + "text/plain": [ + "27094" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "evaluate_results(result)" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -415,9 +5040,9 @@ "name": "python3" }, "kernelspec": { - "display_name": "Python 3 [Default]", + "display_name": "Python 3 [Q#]", "language": "python", - "name": "python3" + "name": "python3_qsharp_b54crn" }, "language_info": { "codemirror_mode": { diff --git a/obj/__entrypoint__.dll b/obj/__entrypoint__.dll index 6c6e7d3b3c59f1c9228c8f898c3a6524006a0b9a..a00d44fff70892e84668831d398d9163455199bc 100644 GIT binary patch literal 321536 zcmeEv31C#!_4j#iCX-1*wh1H<5QeZA2*m7RlPv^|vV}#fqG3oT7)UZWldu?~KvC;b zmug*FwJvDYR;$+54Xs$$s@1kwwOZ>|TU%OfwXIs0?|06<@6DT+34&s4zrTUI{O)q@ zx#!+{?s@kuGymvw$wNe5xQ{<3x&tBq%@lvn-ezQHjkqg|ZcBS&MmCq^zkzAYA9 z8;z`rhB|`Hq0Y`oS8!!G813#1wsi*QEL;-oh_r-DGc(giYtoDAiRKw5UEcKTW~;TA zs3@3Wlo7oKu1u90HByLzhzAi8V+IccF?V 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zk1FAdUy(&XslQ@8Rmn4BUpLArHIB}2&SrO{GdVR?oB${6;Ys%gr*EwQj^?Zov!Qc2 S{(_~rVEvFn*>-O`4*Y){ckP-0 From 9b658146067d58ec68e19a7fb2c80d81f889b42e Mon Sep 17 00:00:00 2001 From: Hamish Hall Date: Sun, 29 Jan 2023 12:41:23 +0000 Subject: [PATCH 3/7] 7 done too --- ...Hack-challenge-2023-task6-checkpoint.ipynb | 7928 ++++++++++++++++- ...Hack-challenge-2023-task7-checkpoint.ipynb | 4615 +++++++++- iQuHack-challenge-2023-task6.ipynb | 1091 ++- iQuHack-challenge-2023-task7.ipynb | 870 +- obj/__entrypoint__.dll | Bin 321536 -> 321024 bytes obj/__entrypoint__snippets__.dll | Bin 51200 -> 89600 bytes obj/__snippets__.dll | Bin 114688 -> 89088 bytes 7 files changed, 13427 insertions(+), 1077 deletions(-) diff --git a/.ipynb_checkpoints/iQuHack-challenge-2023-task6-checkpoint.ipynb b/.ipynb_checkpoints/iQuHack-challenge-2023-task6-checkpoint.ipynb index 4d2f2c8..7babc33 100644 --- a/.ipynb_checkpoints/iQuHack-challenge-2023-task6-checkpoint.ipynb +++ b/.ipynb_checkpoints/iQuHack-challenge-2023-task6-checkpoint.ipynb @@ -67,7 +67,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "collapsed": false, "jupyter": { @@ -89,7 +89,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": { "collapsed": false, "jupyter": { @@ -104,14 +104,14 @@ }, "outputs": [], "source": [ - "teamname=\"msft_is_the_best\" # Update this field with your team name\n", + "teamname=\"schrodingers-duck\" # Update this field with your team name\n", "task=[\"task6\"]\n", - "slack_id=\"myslackid\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + "slack_id=\"U04L3SFUCQ2\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": { "collapsed": false, "jupyter": { @@ -148,7 +148,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": { "collapsed": false, "jupyter": { @@ -169,19 +169,43 @@ "%%qsharp\n", "open Microsoft.Quantum.Canon;\n", "open Microsoft.Quantum.Diagnostics;\n", + "open Microsoft.Quantum.Arrays;\n", "\n", "// Task 6. \n", "// (input will contain 8 qubits)\n", - "operation Task6(input : Qubit[], target : Qubit) : Unit is Adj {\n", + "operation original(input : Qubit[], target : Qubit) : Unit is Adj {\n", " for i in [144, 145, 148, 149, 152, 153, 156, 157, 208, 209, 212, 213, 216, 217, 220, 221] {\n", " ControlledOnInt(i, X)(input, target);\n", " }\n", + "}\n", + "\n", + "operation Task6(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " for i in [20,22] {\n", + " ControlledOnInt(i, X)([input[1],input[2],input[4], input[5], input[7]], target);\n", + " }\n", + "}\n", + "\n", + "operation QubitArrayWrapperOperation (op : ((Qubit[], Qubit) => Unit is Adj), qs : Qubit[]) : Unit is Adj { \n", + " op(Most(qs), Tail(qs));\n", + "}\n", + "\n", + "operation TestCompoundGate () : Unit {\n", + " AssertOperationsEqualReferenced(8+1, QubitArrayWrapperOperation(Task6, _), QubitArrayWrapperOperation (original, _));\n", "}" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "TestCompoundGate();" + ] + }, + { + "cell_type": "code", + "execution_count": 6, "metadata": { "collapsed": false, "jupyter": { @@ -238,7 +262,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "metadata": { "collapsed": false, "jupyter": { @@ -251,7 +275,6702 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": 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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

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    \r\n", + "

    \r\n", + "
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    \r\n", + "

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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

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    \r\n", + "

    \r\n", + "
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    \r\n", + "

    \r\n", + "
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    \r\n", + "

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    \r\n", + "

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    \r\n", + "

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"output_type": "execute_result" + } + ], "source": [ "# Note that in the output of this cell the target qubit corresponds to the rightmost bit\n", "qsharp.config[\"dump.basisStateLabelingConvention\"]=\"Bitstring\"\n", @@ -276,7 +6995,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, "metadata": { "collapsed": false, "jupyter": { @@ -289,19 +7008,68 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "\"Connecting to Azure Quantum...\"", + "text/plain": [ + "Connecting to Azure Quantum..." + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Connected to Azure Quantum workspace azure-q in location uksouth.\n" + ] + }, + { + "data": { + "text/plain": [ + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 177740},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 321366},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 4},\n", + " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 166},\n", + " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 166},\n", + " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.qpu.aspen-m-2', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", "# If you're using this notebook in qBraid, keep it\n", "qsharp.azure.connect(\n", - " resourceId=\"...\",\n", - " location=\"...\",\n", + " resourceId=\"/subscriptions/7fc54e95-14cf-4a6f-b50e-d6155c241309/resourceGroups/AzureQuantum/providers/Microsoft.Quantum/Workspaces/azure-q\",\n", + " location=\"UK South\",\n", " credential=\"CLI\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "metadata": { "collapsed": false, "jupyter": { @@ -314,14 +7082,33 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loading package Microsoft.Quantum.Providers.Core and dependencies...\n", + "Active target is now microsoft.estimator\n" + ] + }, + { + "data": { + "text/plain": [ + "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "qsharp.azure.target(\"microsoft.estimator\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "metadata": { "collapsed": false, "jupyter": { @@ -334,7 +7121,20 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Submitting Task6_ResourceEstimationWrapper to target microsoft.estimator...\n", + "Job successfully submitted.\n", + " Job name: RE for the task 6\n", + " Job ID: 1678631d-016c-4332-ba1f-61fcb3b081b9\n", + "Waiting up to 30 seconds for Azure Quantum job to complete...\n", + "[12:40:10 PM] Current job status: Succeeded\n" + ] + } + ], "source": [ "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", "result = qsharp.azure.execute(Task6_ResourceEstimationWrapper, jobName=\"RE for the task 6\")" @@ -342,7 +7142,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, "metadata": { "collapsed": false, "jupyter": { @@ -355,7 +7155,1051 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":6,\"cczCount\":2,\"measurementCount\":6,\"numQubits\":12,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":9,\"logicalCycleTime\":3600.0,\"logicalErrorRate\":3.0000000000000015E-07,\"physicalQubits\":162},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":30,\"algorithmicLogicalQubits\":35,\"cliffordErrorRate\":0.001,\"logicalDepth\":30,\"numTfactories\":14,\"numTfactoryRuns\":3,\"numTsPerRotation\":null,\"numTstates\":32,\"physicalQubitsForAlgorithm\":5670,\"physicalQubitsForTfactories\":90720,\"requiredLogicalQubitErrorRate\":4.761904761904762E-07,\"requiredLogicalTstateErrorRate\":1.5625E-05},\"physicalQubits\":96390,\"runtime\":108000},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"3us 600ns\",\"logicalErrorRate\":\"3.00e-7\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"94.12 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"4.76e-7\",\"requiredLogicalTstateErrorRate\":\"1.56e-5\",\"runtime\":\"108us\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 5670 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 30 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 12$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 35$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 6 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 2 CCZ and 6 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 30. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 2 CCZ and 6 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 32 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{32\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 108us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 32 T states, the 14 copies of the T factory are repeatedly invoked 3 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 5670 are the product of the 35 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\\\cdot 14$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 35 logical qubits and the total cycle count 30.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 32.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.0000004761904761904762)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{9 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 3us 600ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 162.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.56e-5.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 35 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or ¬µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "text/html": [ + "\r\n", + "

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    \n", + "\r\n", + "
    \n", + "\r\n", + "
    \r\n", + " \r\n", + " Resource estimates breakdown\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
    Logical algorithmic qubits35\r\n", + "

    Number of logical qubits for the algorithm after layout

    \n", + "    \r\n", + "
    \r\n", + "

    Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 12\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 35$ logical qubits.

    \n", + "\r\n", + "
    Algorithmic depth30\r\n", + "

    Number of logical cycles for the algorithm

    \n", + "    \r\n", + "
    \r\n", + "

    To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 6 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 2 CCZ and 6 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

    \n", + "\r\n", + "
    Logical depth30\r\n", + "

    Number of logical cycles performed

    \n", + "    \r\n", + "
    \r\n", + "

    This number is usually equal to the logical depth of the algorithm, which is 30. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

    \n", + "\r\n", + "
    Number of T states32\r\n", + "

    Number of T states consumed by the algorithm

    \n", + "    \r\n", + "
    \r\n", + "

    To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 2 CCZ and 6 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

    \n", + "\r\n", + "
    Number of T factories14\r\n", + "

    Number of T factories capable of producing the demanded 32 T states during the algorithm's runtime

    \n", + "    \r\n", + "
    \r\n", + "

    The total number of T factories 14 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{32\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 108us\\;\\text{algorithm runtime}}\\right\\rceil\\)

    \n", + "\r\n", + "
    Number of T factory invocations3\r\n", + "

    Number of times all T factories are invoked

    \n", + "    \r\n", + "
    \r\n", + "

    In order to prepare the 32 T states, the 14 copies of the T factory are repeatedly invoked 3 times.

    \n", + "\r\n", + "
    Physical algorithmic qubits5670\r\n", + "

    Number of physical qubits for the algorithm after layout

    \n", + "    \r\n", + "
    \r\n", + "

    The 5670 are the product of the 35 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.

    \n", + "\r\n", + "
    Physical T factory qubits90720\r\n", + "

    Number of physical qubits for the T factories

    \n", + "    \r\n", + "
    \r\n", + "

    Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\cdot 14$ qubits.

    \n", + "\r\n", + "
    Required logical qubit error rate4.76e-7\r\n", + "

    The minimum logical qubit error rate required to run the algorithm within the error budget

    \n", + "    \r\n", + "
    \r\n", + "

    The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 35 logical qubits and the total cycle count 30.

    \n", + "\r\n", + "
    Required logical T state error rate1.56e-5\r\n", + "

    The minimum T state error rate required for distilled T states

    \n", + "    \r\n", + "
    \r\n", + "

    The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 32.

    \n", + "\r\n", + "
    Number of T states per rotationNo rotations in algorithm\r\n", + "

    Number of T states to implement a rotation with an arbitrary angle

    \n", + "    \r\n", + "
    \r\n", + "

    The number of T states to implement a rotation with an arbitrary angle is \\(\\lceil 0.53 \\log_2(0 / 0) + 5.3\\rceil\\) [arXiv:2203.10064]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.

    \n", + "\r\n", + "
    \n", + "\r\n", + "
    \r\n", + " \r\n", + " Logical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
    QEC schemesurface_code\r\n", + "

    Name of QEC scheme

    \n", + "    \r\n", + "
    \r\n", + "

    You can load pre-defined QEC schemes by using the name surface_code or floquet_code. The latter only works with Majorana qubits.

    \n", + "\r\n", + "
    Code distance9\r\n", + "

    Required code distance for error correction

    \n", + "    \r\n", + "
    \r\n", + "

    The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.0000004761904761904762)}{\\log(0.01/0.001)} - 1\\)

    \n", + "\r\n", + "
    Physical qubits162\r\n", + "

    Number of physical qubits per logical qubit

    \n", + "    \r\n", + "
    \r\n", + "

    The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.

    \n", + "\r\n", + "
    Logical cycle time3us 600ns\r\n", + "

    Duration of a logical cycle in nanoseconds

    \n", + "    \r\n", + "
    \r\n", + "

    The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.

    \n", + "\r\n", + "
    Logical qubit error rate3.00e-7\r\n", + "

    Logical qubit error rate

    \n", + "    \r\n", + "
    \r\n", + "

    The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{9 + 1}{2}$

    \n", + "\r\n", + "
    Crossing prefactor0.03\r\n", + "

    Crossing prefactor used in QEC scheme

    \n", + "    \r\n", + "
    \r\n", + "

    The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.

    \n", + "\r\n", + "
    Error correction threshold0.01\r\n", + "

    Error correction threshold used in QEC scheme

    \n", + "    \r\n", + "
    \r\n", + "

    The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.

    \n", + "\r\n", + "
    Logical cycle time formula(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\r\n", + "

    QEC scheme formula used to compute logical cycle time

    \n", + "    \r\n", + "
    \r\n", + "

    This is the formula that is used to compute the logical cycle time 3us 600ns.

    \n", + "\r\n", + "
    Physical qubits formula2 * codeDistance * codeDistance\r\n", + "

    QEC scheme formula used to compute number of physical qubits per logical qubit

    \n", + "    \r\n", + "
    \r\n", + "

    This is the formula that is used to compute the number of physical qubits per logical qubits 162.

    \n", + "\r\n", + "
    \n", + "\r\n", + "
    \r\n", + " \r\n", + " T factory parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
    Physical qubits6480\r\n", + "

    Number of physical qubits for a single T factory

    \n", + "    \r\n", + "
    \r\n", + "

    This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.

    \n", + "\r\n", + "
    Runtime46us 800ns\r\n", + "

    Runtime of a single T factory

    \n", + "    \r\n", + "
    \r\n", + "

    The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.

    \n", + "\r\n", + "
    Number of output T states per run1\r\n", + "

    Number of output T states produced in a single run of T factory

    \n", + "    \r\n", + "
    \r\n", + "

    The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.

    \n", + "\r\n", + "
    Number of input T states per run30\r\n", + "

    Number of physical input T states consumed in a single run of a T factory

    \n", + "    \r\n", + "
    \r\n", + "

    This value includes the physical input T states of all copies of the distillation unit in the first round.

    \n", + "\r\n", + "
    Distillation rounds1\r\n", + "

    The number of distillation rounds

    \n", + "    \r\n", + "
    \r\n", + "

    This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.

    \n", + "\r\n", + "
    Distillation units per round2\r\n", + "

    The number of units in each round of distillation

    \n", + "    \r\n", + "
    \r\n", + "

    This is the number of copies for the distillation units per round.

    \n", + "\r\n", + "
    Distillation units15-to-1 space efficient logical\r\n", + "

    The types of distillation units

    \n", + "    \r\n", + "
    \r\n", + "

    These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.

    \n", + "\r\n", + "
    Distillation code distances9\r\n", + "

    The code distance in each round of distillation

    \n", + "    \r\n", + "
    \r\n", + "

    This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.

    \n", + "\r\n", + "
    Number of physical qubits per round6480\r\n", + "

    The number of physical qubits used in each round of distillation

    \n", + "    \r\n", + "
    \r\n", + "

    The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.

    \n", + "\r\n", + "
    Runtime per round46us 800ns\r\n", + "

    The runtime of each distillation round

    \n", + "    \r\n", + "
    \r\n", + "

    The runtime of the T factory is the sum of the runtimes in all rounds.

    \n", + "\r\n", + "
    Logical T state error rate2.17e-6\r\n", + "

    Logical T state error rate

    \n", + "    \r\n", + "
    \r\n", + "

    This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.56e-5.

    \n", + "\r\n", + "
    \n", + "\r\n", + "
    \r\n", + " \r\n", + " Pre-layout logical resources\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
    Logical qubits (pre-layout)12\r\n", + "

    Number of logical qubits in the input quantum program

    \n", + "    \r\n", + "
    \r\n", + "

    We determine 35 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

    \n", + "\r\n", + "
    T gates0\r\n", + "

    Number of T gates in the input quantum program

    \n", + "    \r\n", + "
    \r\n", + "

    This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.

    \n", + "\r\n", + "
    Rotation gates0\r\n", + "

    Number of rotation gates in the input quantum program

    \n", + "    \r\n", + "
    \r\n", + "

    This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.

    \n", + "\r\n", + "
    Rotation depth0\r\n", + "

    Depth of rotation gates in the input quantum program

    \n", + "    \r\n", + "
    \r\n", + "

    This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.

    \n", + "\r\n", + "
    CCZ gates2\r\n", + "

    Number of CCZ-gates in the input quantum program

    \n", + "    \r\n", + "
    \r\n", + "

    This is the number of CCZ gates.

    \n", + "\r\n", + "
    CCiX gates6\r\n", + "

    Number of CCiX-gates in the input quantum program

    \n", + "    \r\n", + "
    \r\n", + "

    This is the number of CCiX gates, which applies \\(-iX\\) controlled on two control qubits [1212.5069].

    \n", + "\r\n", + "
    Measurement operations6\r\n", + "

    Number of single qubit measurements in the input quantum program

    \n", + "    \r\n", + "
    \r\n", + "

    This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.

    \n", + "\r\n", + "
    \n", + "\r\n", + "
    \r\n", + " \r\n", + " Assumed error budget\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
    Total error budget1.00e-3\r\n", + "

    Total error budget for the algorithm

    \n", + "    \r\n", + "
    \r\n", + "

    The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget \\(\\epsilon = \\epsilon_{\\log} + \\epsilon_{\\rm dis} + \\epsilon_{\\rm syn}\\) is uniformly distributed and applies to errors \\(\\epsilon_{\\log}\\) to implement logical qubits, an error budget \\(\\epsilon_{\\rm dis}\\) to produce T states through distillation, and an error budget \\(\\epsilon_{\\rm syn}\\) to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets \\(\\epsilon_{\\rm dis}\\) and \\(\\epsilon_{\\rm syn}\\) are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.

    \n", + "\r\n", + "
    Logical error probability5.00e-4\r\n", + "

    Probability of at least one logical error

    \n", + "    \r\n", + "
    \r\n", + "

    This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

    \n", + "\r\n", + "
    T distillation error probability5.00e-4\r\n", + "

    Probability of at least one faulty T distillation

    \n", + "    \r\n", + "
    \r\n", + "

    This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

    \n", + "\r\n", + "
    Rotation synthesis error probability0.00e0\r\n", + "

    Probability of at least one failed rotation synthesis

    \n", + "    \r\n", + "
    \r\n", + "

    This is one third of the total error budget 1.00e-3.

    \n", + "\r\n", + "
    \n", + "\r\n", + "
    \r\n", + " \r\n", + " Physical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
    Qubit namequbit_gate_ns_e3\r\n", + "

    Some descriptive name for the qubit model

    \n", + "    \r\n", + "
    \r\n", + "

    You can load pre-defined qubit parameters by using the names qubit_gate_ns_e3, qubit_gate_ns_e4, qubit_gate_us_e3, qubit_gate_us_e4, qubit_maj_ns_e4, or qubit_maj_ns_e6. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).

    \n", + "\r\n", + "
    Instruction setGateBased\r\n", + "

    Underlying qubit technology (gate-based or Majorana)

    \n", + "    \r\n", + "
    \r\n", + "

    When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either gate-based or Majorana. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.

    \n", + "\r\n", + "
    Single-qubit measurement time100 ns\r\n", + "

    Operation time for single-qubit measurement (t_meas) in ns

    \n", + "    \r\n", + "
    \r\n", + "

    This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.

    \n", + "\r\n", + "
    Single-qubit gate time50 ns\r\n", + "

    Operation time for single-qubit gate (t_gate) in ns

    \n", + "    \r\n", + "
    \r\n", + "

    This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.

    \n", + "\r\n", + "
    Two-qubit gate time50 ns\r\n", + "

    Operation time for two-qubit gate in ns

    \n", + "    \r\n", + "
    \r\n", + "

    This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.

    \n", + "\r\n", + "
    T gate time50 ns\r\n", + "

    Operation time for a T gate

    \n", + "    \r\n", + "
    \r\n", + "

    This is the operation time in nanoseconds to execute a T gate.

    \n", + "\r\n", + "
    Single-qubit measurement error rate0.001\r\n", + "

    Error rate for single-qubit measurement

    \n", + "    \r\n", + "
    \r\n", + "

    This is the probability in which a single-qubit measurement in the Pauli basis may fail.

    \n", + "\r\n", + "
    Single-qubit error rate0.001\r\n", + "

    Error rate for single-qubit Clifford gate (p)

    \n", + "    \r\n", + "
    \r\n", + "

    This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.

    \n", + "\r\n", + "
    Two-qubit error rate0.001\r\n", + "

    Error rate for two-qubit Clifford gate

    \n", + "    \r\n", + "
    \r\n", + "

    This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.

    \n", + "\r\n", + "
    T gate error rate0.001\r\n", + "

    Error rate to prepare single-qubit T state or apply a T gate (p_T)

    \n", + "    \r\n", + "
    \r\n", + "

    This is the probability in which executing a single T gate may fail.

    \n", + "\r\n", + "
    \n", + "
    \r\n", + " Assumptions\r\n", + "
      \n", + "

    • More details on the following lists of assumptions can be found in the paper Accessing requirements for scaling quantum computers and their applications.

      \n", + "
      • \n", + "

    • Uniform independent physical noise. We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.

      \n", + "
      • \n", + "

    • Efficient classical computation. We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.

      \n", + "
      • \n", + "

    • Extraction circuits for planar quantum ISA. We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).

      \n", + "
      • \n", + "

    • Uniform independent logical noise. We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.

      \n", + "
      • \n", + "

    • Negligible Clifford costs for synthesis. We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.

      \n", + "
      • \n", + "

    • Smooth magic state consumption rate. We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.

      \n", + "
      • \n", + "
    \n" + ], + "text/plain": [ + "{'errorBudget': {'logical': 0.0005, 'rotations': 0.0, 'tstates': 0.0005},\n", + " 'jobParams': {'errorBudget': 0.001,\n", + " 'qecScheme': {'crossingPrefactor': 0.03,\n", + " 'errorCorrectionThreshold': 0.01,\n", + " 'logicalCycleTime': '(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance',\n", + " 'name': 'surface_code',\n", + " 'physicalQubitsPerLogicalQubit': '2 * codeDistance * codeDistance'},\n", + " 'qubitParams': {'instructionSet': 'GateBased',\n", + " 'name': 'qubit_gate_ns_e3',\n", + " 'oneQubitGateErrorRate': 0.001,\n", + " 'oneQubitGateTime': '50 ns',\n", + " 'oneQubitMeasurementErrorRate': 0.001,\n", + " 'oneQubitMeasurementTime': '100 ns',\n", + " 'tGateErrorRate': 0.001,\n", + " 'tGateTime': '50 ns',\n", + " 'twoQubitGateErrorRate': 0.001,\n", + " 'twoQubitGateTime': '50 ns'}},\n", + " 'logicalCounts': {'ccixCount': 6,\n", + " 'cczCount': 2,\n", + " 'measurementCount': 6,\n", + " 'numQubits': 12,\n", + " 'rotationCount': 0,\n", + " 'rotationDepth': 0,\n", + " 'tCount': 0},\n", + " 'logicalQubit': {'codeDistance': 9,\n", + " 'logicalCycleTime': 3600.0,\n", + " 'logicalErrorRate': 3.0000000000000015e-07,\n", + " 'physicalQubits': 162},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 30,\n", + " 'algorithmicLogicalQubits': 35,\n", + " 'cliffordErrorRate': 0.001,\n", + " 'logicalDepth': 30,\n", + " 'numTfactories': 14,\n", + " 'numTfactoryRuns': 3,\n", + " 'numTsPerRotation': None,\n", + " 'numTstates': 32,\n", + " 'physicalQubitsForAlgorithm': 5670,\n", + " 'physicalQubitsForTfactories': 90720,\n", + " 'requiredLogicalQubitErrorRate': 4.761904761904762e-07,\n", + " 'requiredLogicalTstateErrorRate': 1.5625e-05},\n", + " 'physicalQubits': 96390,\n", + " 'runtime': 108000},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", + " 'errorBudget': '1.00e-3',\n", + " 'errorBudgetLogical': '5.00e-4',\n", + " 'errorBudgetRotations': '0.00e0',\n", + " 'errorBudgetTstates': '5.00e-4',\n", + " 'logicalCycleTime': '3us 600ns',\n", + " 'logicalErrorRate': '3.00e-7',\n", + " 'numTsPerRotation': 'No rotations in algorithm',\n", + " 'numUnitsPerRound': '2',\n", + " 'physicalQubitsForTfactoriesPercentage': '94.12 %',\n", + " 'physicalQubitsPerRound': '6480',\n", + " 'requiredLogicalQubitErrorRate': '4.76e-7',\n", + " 'requiredLogicalTstateErrorRate': '1.56e-5',\n", + " 'runtime': '108us',\n", + " 'tfactoryRuntime': '46us 800ns',\n", + " 'tfactoryRuntimePerRound': '46us 800ns',\n", + " 'tstateLogicalErrorRate': '2.17e-6',\n", + " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", + " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", + " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", + " '**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.',\n", + " '**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).',\n", + " '**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.',\n", + " '**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.',\n", + " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", + " 'groups': [{'alwaysVisible': True,\n", + " 'entries': [{'description': 'Number of physical qubits',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 5670 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'physicalCounts/physicalQubits'},\n", + " {'description': 'Total runtime',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 30 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/runtime'}],\n", + " 'title': 'Physical resource estimates'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 12$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 35$ logical qubits.',\n", + " 'label': 'Logical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", + " {'description': 'Number of logical cycles for the algorithm',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 6 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 2 CCZ and 6 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'label': 'Algorithmic depth',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", + " {'description': 'Number of logical cycles performed',\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 30. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'label': 'Logical depth',\n", + " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", + " {'description': 'Number of T states consumed by the algorithm',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 2 CCZ and 6 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'label': 'Number of T states',\n", + " 'path': 'physicalCounts/breakdown/numTstates'},\n", + " {'description': \"Number of T factories capable of producing the demanded 32 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{32\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 108us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " 'label': 'Number of T factories',\n", + " 'path': 'physicalCounts/breakdown/numTfactories'},\n", + " {'description': 'Number of times all T factories are invoked',\n", + " 'explanation': 'In order to prepare the 32 T states, the 14 copies of the T factory are repeatedly invoked 3 times.',\n", + " 'label': 'Number of T factory invocations',\n", + " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", + " {'description': 'Number of physical qubits for the algorithm after layout',\n", + " 'explanation': 'The 5670 are the product of the 35 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.',\n", + " 'label': 'Physical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", + " {'description': 'Number of physical qubits for the T factories',\n", + " 'explanation': 'Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\\\cdot 14$ qubits.',\n", + " 'label': 'Physical T factory qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", + " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 35 logical qubits and the total cycle count 30.',\n", + " 'label': 'Required logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", + " {'description': 'The minimum T state error rate required for distilled T states',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 32.',\n", + " 'label': 'Required logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", + " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", + " 'explanation': 'The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.',\n", + " 'label': 'Number of T states per rotation',\n", + " 'path': 'physicalCountsFormatted/numTsPerRotation'}],\n", + " 'title': 'Resource estimates breakdown'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Name of QEC scheme',\n", + " 'explanation': 'You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.',\n", + " 'label': 'QEC scheme',\n", + " 'path': 'jobParams/qecScheme/name'},\n", + " {'description': 'Required code distance for error correction',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.0000004761904761904762)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'label': 'Code distance',\n", + " 'path': 'logicalQubit/codeDistance'},\n", + " {'description': 'Number of physical qubits per logical qubit',\n", + " 'explanation': 'The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'logicalQubit/physicalQubits'},\n", + " {'description': 'Duration of a logical cycle in nanoseconds',\n", + " 'explanation': 'The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.',\n", + " 'label': 'Logical cycle time',\n", + " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", + " {'description': 'Logical qubit error rate',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{9 + 1}{2}$',\n", + " 'label': 'Logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", + " {'description': 'Crossing prefactor used in QEC scheme',\n", + " 'explanation': 'The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.',\n", + " 'label': 'Crossing prefactor',\n", + " 'path': 'jobParams/qecScheme/crossingPrefactor'},\n", + " {'description': 'Error correction threshold used in QEC scheme',\n", + " 'explanation': 'The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.',\n", + " 'label': 'Error correction threshold',\n", + " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", + " {'description': 'QEC scheme formula used to compute logical cycle time',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 3us 600ns.',\n", + " 'label': 'Logical cycle time formula',\n", + " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", + " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 162.',\n", + " 'label': 'Physical qubits formula',\n", + " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", + " 'title': 'Logical qubit parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of physical qubits for a single T factory',\n", + " 'explanation': 'This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'tfactory/physicalQubits'},\n", + " {'description': 'Runtime of a single T factory',\n", + " 'explanation': 'The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", + " {'description': 'Number of output T states produced in a single run of T factory',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.',\n", + " 'label': 'Number of output T states per run',\n", + " 'path': 'tfactory/numTstates'},\n", + " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", + " 'explanation': 'This value includes the physical input T states of all copies of the distillation unit in the first round.',\n", + " 'label': 'Number of input T states per run',\n", + " 'path': 'tfactory/numInputTstates'},\n", + " {'description': 'The number of distillation rounds',\n", + " 'explanation': 'This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.',\n", + " 'label': 'Distillation rounds',\n", + " 'path': 'tfactory/numRounds'},\n", + " {'description': 'The number of units in each round of distillation',\n", + " 'explanation': 'This is the number of copies for the distillation units per round.',\n", + " 'label': 'Distillation units per round',\n", + " 'path': 'physicalCountsFormatted/numUnitsPerRound'},\n", + " {'description': 'The types of distillation units',\n", + " 'explanation': 'These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.',\n", + " 'label': 'Distillation units',\n", + " 'path': 'physicalCountsFormatted/unitNamePerRound'},\n", + " {'description': 'The code distance in each round of distillation',\n", + " 'explanation': 'This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.',\n", + " 'label': 'Distillation code distances',\n", + " 'path': 'physicalCountsFormatted/codeDistancePerRound'},\n", + " {'description': 'The number of physical qubits used in each round of distillation',\n", + " 'explanation': 'The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.',\n", + " 'label': 'Number of physical qubits per round',\n", + " 'path': 'physicalCountsFormatted/physicalQubitsPerRound'},\n", + " {'description': 'The runtime of each distillation round',\n", + " 'explanation': 'The runtime of the T factory is the sum of the runtimes in all rounds.',\n", + " 'label': 'Runtime per round',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", + " {'description': 'Logical T state error rate',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.56e-5.',\n", + " 'label': 'Logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", + " 'title': 'T factory parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", + " 'explanation': 'We determine 35 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'label': 'Logical qubits (pre-layout)',\n", + " 'path': 'logicalCounts/numQubits'},\n", + " {'description': 'Number of T gates in the input quantum program',\n", + " 'explanation': 'This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.',\n", + " 'label': 'T gates',\n", + " 'path': 'logicalCounts/tCount'},\n", + " {'description': 'Number of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.',\n", + " 'label': 'Rotation gates',\n", + " 'path': 'logicalCounts/rotationCount'},\n", + " {'description': 'Depth of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.',\n", + " 'label': 'Rotation depth',\n", + " 'path': 'logicalCounts/rotationDepth'},\n", + " {'description': 'Number of CCZ-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCZ gates.',\n", + " 'label': 'CCZ gates',\n", + " 'path': 'logicalCounts/cczCount'},\n", + " {'description': 'Number of CCiX-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].',\n", + " 'label': 'CCiX gates',\n", + " 'path': 'logicalCounts/ccixCount'},\n", + " {'description': 'Number of single qubit measurements in the input quantum program',\n", + " 'explanation': 'This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.',\n", + " 'label': 'Measurement operations',\n", + " 'path': 'logicalCounts/measurementCount'}],\n", + " 'title': 'Pre-layout logical resources'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Total error budget for the algorithm',\n", + " 'explanation': \"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\n", + " 'label': 'Total error budget',\n", + " 'path': 'physicalCountsFormatted/errorBudget'},\n", + " {'description': 'Probability of at least one logical error',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'Logical error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetLogical'},\n", + " {'description': 'Probability of at least one faulty T distillation',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'T distillation error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetTstates'},\n", + " {'description': 'Probability of at least one failed rotation synthesis',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3.',\n", + " 'label': 'Rotation synthesis error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetRotations'}],\n", + " 'title': 'Assumed error budget'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Some descriptive name for the qubit model',\n", + " 'explanation': 'You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).',\n", + " 'label': 'Qubit name',\n", + " 'path': 'jobParams/qubitParams/name'},\n", + " {'description': 'Underlying qubit technology (gate-based or Majorana)',\n", + " 'explanation': 'When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.',\n", + " 'label': 'Instruction set',\n", + " 'path': 'jobParams/qubitParams/instructionSet'},\n", + " {'description': 'Operation time for single-qubit measurement (t_meas) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.',\n", + " 'label': 'Single-qubit measurement time',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementTime'},\n", + " {'description': 'Operation time for single-qubit gate (t_gate) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.',\n", + " 'label': 'Single-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateTime'},\n", + " {'description': 'Operation time for two-qubit gate in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.',\n", + " 'label': 'Two-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateTime'},\n", + " {'description': 'Operation time for a T gate',\n", + " 'explanation': 'This is the operation time in nanoseconds to execute a T gate.',\n", + " 'label': 'T gate time',\n", + " 'path': 'jobParams/qubitParams/tGateTime'},\n", + " {'description': 'Error rate for single-qubit measurement',\n", + " 'explanation': 'This is the probability in which a single-qubit measurement in the Pauli basis may fail.',\n", + " 'label': 'Single-qubit measurement error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementErrorRate'},\n", + " {'description': 'Error rate for single-qubit Clifford gate (p)',\n", + " 'explanation': 'This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.',\n", + " 'label': 'Single-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateErrorRate'},\n", + " {'description': 'Error rate for two-qubit Clifford gate',\n", + " 'explanation': 'This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.',\n", + " 'label': 'Two-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateErrorRate'},\n", + " {'description': 'Error rate to prepare single-qubit T state or apply a T gate (p_T)',\n", + " 'explanation': 'This is the probability in which executing a single T gate may fail.',\n", + " 'label': 'T gate error rate',\n", + " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", + " 'title': 'Physical qubit parameters'}]},\n", + " 'status': 'success',\n", + " 'tfactory': {'codeDistancePerRound': [9],\n", + " 'logicalErrorRate': 2.165000000000001e-06,\n", + " 'numInputTstates': 30,\n", + " 'numRounds': 1,\n", + " 'numTstates': 1,\n", + " 'numUnitsPerRound': [2],\n", + " 'physicalQubits': 6480,\n", + " 'physicalQubitsPerRound': [6480],\n", + " 'runtime': 46800.0,\n", + " 'runtimePerRound': [46800.0],\n", + " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", "# result = qsharp.azure.output(\"...\")\n", @@ -364,7 +8208,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "metadata": { "collapsed": false, "jupyter": { @@ -391,7 +8235,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, "metadata": { "collapsed": false, "jupyter": { @@ -404,10 +8248,44 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Logical algorithmic qubits = 35\n", + "Algorithmic depth = 30\n", + "Score = 1050\n" + ] + }, + { + "data": { + "text/plain": [ + "1050" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "evaluate_results(result)" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -415,9 +8293,9 @@ "name": "python3" }, "kernelspec": { - "display_name": "Python 3 [Default]", + "display_name": "Python 3 [Q#]", "language": "python", - "name": "python3" + "name": "python3_qsharp_b54crn" }, "language_info": { "codemirror_mode": { diff --git a/.ipynb_checkpoints/iQuHack-challenge-2023-task7-checkpoint.ipynb b/.ipynb_checkpoints/iQuHack-challenge-2023-task7-checkpoint.ipynb index 2670c29..84be853 100644 --- a/.ipynb_checkpoints/iQuHack-challenge-2023-task7-checkpoint.ipynb +++ b/.ipynb_checkpoints/iQuHack-challenge-2023-task7-checkpoint.ipynb @@ -67,7 +67,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "collapsed": false, "jupyter": { @@ -80,7 +80,15 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Preparing Q# environment...\n" + ] + } + ], "source": [ "# Run this code cell to import the modules required to work with Q# and Azure\n", "import qsharp\n", @@ -89,7 +97,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": { "collapsed": false, "jupyter": { @@ -104,14 +112,14 @@ }, "outputs": [], "source": [ - "teamname=\"msft_is_the_best\" # Update this field with your team name\n", + "teamname=\"schrodingers-cat\" # Update this field with your team name\n", "task=[\"task7\"]\n", - "slack_id=\"myslackid\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + "slack_id=\"U04L3SFUCQ2\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": { "collapsed": false, "jupyter": { @@ -148,7 +156,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": { "collapsed": false, "jupyter": { @@ -169,19 +177,45 @@ "%%qsharp\n", "open Microsoft.Quantum.Canon;\n", "open Microsoft.Quantum.Diagnostics;\n", + "open Microsoft.Quantum.Arrays;\n", "\n", "// Task 7. \n", "// (input will contain 7 qubits)\n", - "operation Task7(input : Qubit[], target : Qubit) : Unit is Adj {\n", + "operation original(input : Qubit[], target : Qubit) : Unit is Adj {\n", " for i in [9,18,19,25,36,37,38,39,41,50,51,57,72,73,74,75,76,77,78,79,82,83,89,100,101,102,103,105,114,115,121] {\n", " ControlledOnInt(i, X)(input, target);\n", " }\n", - "}" + "}\n", + "\n", + "operation Task7(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " ControlledOnInt(9, X)([input[6], input[5], input[4], input[3]], target);\n", + " ControlledOnInt(9, X)([input[5], input[4], input[3], input[2]], target);\n", + " ControlledOnInt(9, X)([input[4], input[3], input[2], input[1]], target);\n", + " ControlledOnInt(9, X)([input[3], input[2], input[1], input[0]], target);\n", + " ControlledOnInt(73, X)(input, target);\n", + "}\n", + "\n", + "operation QubitArrayWrapperOperation (op : ((Qubit[], Qubit) => Unit is Adj), qs : Qubit[]) : Unit is Adj { \n", + " op(Most(qs), Tail(qs));\n", + "}\n", + "\n", + "operation TestCompoundGate () : Unit {\n", + " AssertOperationsEqualReferenced(7+1, QubitArrayWrapperOperation(Task7, _), QubitArrayWrapperOperation (original, _));\n", + "}\n" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "TestCompoundGate();" + ] + }, + { + "cell_type": "code", + "execution_count": 6, "metadata": { "collapsed": false, "jupyter": { @@ -238,7 +272,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "metadata": { "collapsed": false, "jupyter": { @@ -251,7 +285,3374 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": 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"output_type": "execute_result" + } + ], "source": [ "# Note that in the output of this cell the target qubit corresponds to the rightmost bit\n", "qsharp.config[\"dump.basisStateLabelingConvention\"]=\"Bitstring\"\n", @@ -276,7 +3677,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, "metadata": { "collapsed": false, "jupyter": { @@ -289,19 +3690,68 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "\"Connecting to Azure Quantum...\"", + "text/plain": [ + "Connecting to Azure Quantum..." + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Connected to Azure Quantum workspace azure-q in location uksouth.\n" + ] + }, + { + "data": { + "text/plain": [ + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 176914},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 423509},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 4},\n", + " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 166},\n", + " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 166},\n", + " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.qpu.aspen-m-2', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", "# If you're using this notebook in qBraid, keep it\n", "qsharp.azure.connect(\n", - " resourceId=\"...\",\n", - " location=\"...\",\n", + " resourceId=\"/subscriptions/7fc54e95-14cf-4a6f-b50e-d6155c241309/resourceGroups/AzureQuantum/providers/Microsoft.Quantum/Workspaces/azure-q\",\n", + " location=\"UK South\",\n", " credential=\"CLI\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "metadata": { "collapsed": false, "jupyter": { @@ -314,14 +3764,33 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loading package Microsoft.Quantum.Providers.Core and dependencies...\n", + "Active target is now microsoft.estimator\n" + ] + }, + { + "data": { + "text/plain": [ + "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "qsharp.azure.target(\"microsoft.estimator\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "metadata": { "collapsed": false, "jupyter": { @@ -334,7 +3803,21 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Submitting Task7_ResourceEstimationWrapper to target microsoft.estimator...\n", + "Job successfully submitted.\n", + " Job name: RE for the task 7\n", + " Job ID: fd0504b4-d2d0-4bfc-a151-f6708f20d5ce\n", + "Waiting up to 30 seconds for Azure Quantum job to complete...\n", + "[12:35:59 PM] Current job status: Waiting\n", + "[12:36:04 PM] Current job status: Succeeded\n" + ] + } + ], "source": [ "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", "result = qsharp.azure.execute(Task7_ResourceEstimationWrapper, jobName=\"RE for the task 7\")" @@ -342,7 +3825,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, "metadata": { "collapsed": false, "jupyter": { @@ -355,7 +3838,1051 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":13,\"cczCount\":5,\"measurementCount\":13,\"numQubits\":13,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":67,\"algorithmicLogicalQubits\":38,\"cliffordErrorRate\":0.001,\"logicalDepth\":67,\"numTfactories\":12,\"numTfactoryRuns\":6,\"numTsPerRotation\":null,\"numTstates\":72,\"physicalQubitsForAlgorithm\":9196,\"physicalQubitsForTfactories\":77760,\"requiredLogicalQubitErrorRate\":1.9638648860958366E-07,\"requiredLogicalTstateErrorRate\":6.944444444444445E-06},\"physicalQubits\":86956,\"runtime\":294800},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"89.42 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"1.96e-7\",\"requiredLogicalTstateErrorRate\":\"6.94e-6\",\"runtime\":\"294us 800ns\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 9196 physical qubits to implement the algorithm logic, and 77760 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 67 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 13$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 38$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 13 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 5 CCZ and 13 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 67. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 5 CCZ and 13 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 72 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{72\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 294us 800ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 72 T states, the 12 copies of the T factory are repeatedly invoked 6 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 9196 are the product of the 38 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 12 in parallel, therefore we need $77760 = 6480 \\\\cdot 12$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 67.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 72.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000019638648860958366)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.94e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or ¬µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "text/html": [ + "\r\n", + "
    \r\n", + " \r\n", + " Physical resource estimates\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
    Physical qubits86956\r\n", + "

    Number of physical qubits

    \n", + "    \r\n", + "
    \r\n", + "

    This value represents the total number of physical qubits, which is the sum of 9196 physical qubits to implement the algorithm logic, and 77760 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

    \n", + "\r\n", + "
    Runtime294us 800ns\r\n", + "

    Total runtime

    \n", + "    \r\n", + "
    \r\n", + "

    This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 67 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

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    \r\n", + " \r\n", + " Resource estimates breakdown\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
    Logical algorithmic qubits38\r\n", + "

    Number of logical qubits for the algorithm after layout

    \n", + "    \r\n", + "
    \r\n", + "

    Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 13\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 38$ logical qubits.

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    Algorithmic depth67\r\n", + "

    Number of logical cycles for the algorithm

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    \r\n", + "

    To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 13 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 5 CCZ and 13 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

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    Logical depth67\r\n", + "

    Number of logical cycles performed

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    \r\n", + "

    This number is usually equal to the logical depth of the algorithm, which is 67. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

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    Number of T states72\r\n", + "

    Number of T states consumed by the algorithm

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    \r\n", + "

    To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 5 CCZ and 13 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

    \n", + "\r\n", + "
    Number of T factories12\r\n", + "

    Number of T factories capable of producing the demanded 72 T states during the algorithm's runtime

    \n", + "    \r\n", + "
    \r\n", + "

    The total number of T factories 12 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{72\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 294us 800ns\\;\\text{algorithm runtime}}\\right\\rceil\\)

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    Number of T factory invocations6\r\n", + "

    Number of times all T factories are invoked

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    In order to prepare the 72 T states, the 12 copies of the T factory are repeatedly invoked 6 times.

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    Physical algorithmic qubits9196\r\n", + "

    Number of physical qubits for the algorithm after layout

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    The 9196 are the product of the 38 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.

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    Physical T factory qubits77760\r\n", + "

    Number of physical qubits for the T factories

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    \r\n", + "

    Each T factory requires 6480 physical qubits and we run 12 in parallel, therefore we need $77760 = 6480 \\cdot 12$ qubits.

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    Required logical qubit error rate1.96e-7\r\n", + "

    The minimum logical qubit error rate required to run the algorithm within the error budget

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    The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 67.

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    Required logical T state error rate6.94e-6\r\n", + "

    The minimum T state error rate required for distilled T states

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    The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 72.

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    Number of T states per rotationNo rotations in algorithm\r\n", + "

    Number of T states to implement a rotation with an arbitrary angle

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    \r\n", + "

    The number of T states to implement a rotation with an arbitrary angle is \\(\\lceil 0.53 \\log_2(0 / 0) + 5.3\\rceil\\) [arXiv:2203.10064]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.

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    \r\n", + " \r\n", + " Logical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
    QEC schemesurface_code\r\n", + "

    Name of QEC scheme

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    \r\n", + "

    You can load pre-defined QEC schemes by using the name surface_code or floquet_code. The latter only works with Majorana qubits.

    \n", + "\r\n", + "
    Code distance11\r\n", + "

    Required code distance for error correction

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    \r\n", + "

    The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000019638648860958366)}{\\log(0.01/0.001)} - 1\\)

    \n", + "\r\n", + "
    Physical qubits242\r\n", + "

    Number of physical qubits per logical qubit

    \n", + "    \r\n", + "
    \r\n", + "

    The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.

    \n", + "\r\n", + "
    Logical cycle time4us 400ns\r\n", + "

    Duration of a logical cycle in nanoseconds

    \n", + "    \r\n", + "
    \r\n", + "

    The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.

    \n", + "\r\n", + "
    Logical qubit error rate3.00e-8\r\n", + "

    Logical qubit error rate

    \n", + "    \r\n", + "
    \r\n", + "

    The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{11 + 1}{2}$

    \n", + "\r\n", + "
    Crossing prefactor0.03\r\n", + "

    Crossing prefactor used in QEC scheme

    \n", + "    \r\n", + "
    \r\n", + "

    The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.

    \n", + "\r\n", + "
    Error correction threshold0.01\r\n", + "

    Error correction threshold used in QEC scheme

    \n", + "    \r\n", + "
    \r\n", + "

    The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.

    \n", + "\r\n", + "
    Logical cycle time formula(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\r\n", + "

    QEC scheme formula used to compute logical cycle time

    \n", + "    \r\n", + "
    \r\n", + "

    This is the formula that is used to compute the logical cycle time 4us 400ns.

    \n", + "\r\n", + "
    Physical qubits formula2 * codeDistance * codeDistance\r\n", + "

    QEC scheme formula used to compute number of physical qubits per logical qubit

    \n", + "    \r\n", + "
    \r\n", + "

    This is the formula that is used to compute the number of physical qubits per logical qubits 242.

    \n", + "\r\n", + "
    \n", + "\r\n", + "
    \r\n", + " \r\n", + " T factory parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
    Physical qubits6480\r\n", + "

    Number of physical qubits for a single T factory

    \n", + "    \r\n", + "
    \r\n", + "

    This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.

    \n", + "\r\n", + "
    Runtime46us 800ns\r\n", + "

    Runtime of a single T factory

    \n", + "    \r\n", + "
    \r\n", + "

    The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.

    \n", + "\r\n", + "
    Number of output T states per run1\r\n", + "

    Number of output T states produced in a single run of T factory

    \n", + "    \r\n", + "
    \r\n", + "

    The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.

    \n", + "\r\n", + "
    Number of input T states per run30\r\n", + "

    Number of physical input T states consumed in a single run of a T factory

    \n", + "    \r\n", + "
    \r\n", + "

    This value includes the physical input T states of all copies of the distillation unit in the first round.

    \n", + "\r\n", + "
    Distillation rounds1\r\n", + "

    The number of distillation rounds

    \n", + "    \r\n", + "
    \r\n", + "

    This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.

    \n", + "\r\n", + "
    Distillation units per round2\r\n", + "

    The number of units in each round of distillation

    \n", + "    \r\n", + "
    \r\n", + "

    This is the number of copies for the distillation units per round.

    \n", + "\r\n", + "
    Distillation units15-to-1 space efficient logical\r\n", + "

    The types of distillation units

    \n", + "    \r\n", + "
    \r\n", + "

    These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.

    \n", + "\r\n", + "
    Distillation code distances9\r\n", + "

    The code distance in each round of distillation

    \n", + "    \r\n", + "
    \r\n", + "

    This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.

    \n", + "\r\n", + "
    Number of physical qubits per round6480\r\n", + "

    The number of physical qubits used in each round of distillation

    \n", + "    \r\n", + "
    \r\n", + "

    The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.

    \n", + "\r\n", + "
    Runtime per round46us 800ns\r\n", + "

    The runtime of each distillation round

    \n", + "    \r\n", + "
    \r\n", + "

    The runtime of the T factory is the sum of the runtimes in all rounds.

    \n", + "\r\n", + "
    Logical T state error rate2.17e-6\r\n", + "

    Logical T state error rate

    \n", + "    \r\n", + "
    \r\n", + "

    This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.94e-6.

    \n", + "\r\n", + "
    \n", + "\r\n", + "
    \r\n", + " \r\n", + " Pre-layout logical resources\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
    Logical qubits (pre-layout)13\r\n", + "

    Number of logical qubits in the input quantum program

    \n", + "    \r\n", + "
    \r\n", + "

    We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

    \n", + "\r\n", + "
    T gates0\r\n", + "

    Number of T gates in the input quantum program

    \n", + "    \r\n", + "
    \r\n", + "

    This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.

    \n", + "\r\n", + "
    Rotation gates0\r\n", + "

    Number of rotation gates in the input quantum program

    \n", + "    \r\n", + "
    \r\n", + "

    This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.

    \n", + "\r\n", + "
    Rotation depth0\r\n", + "

    Depth of rotation gates in the input quantum program

    \n", + "    \r\n", + "
    \r\n", + "

    This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.

    \n", + "\r\n", + "
    CCZ gates5\r\n", + "

    Number of CCZ-gates in the input quantum program

    \n", + "    \r\n", + "
    \r\n", + "

    This is the number of CCZ gates.

    \n", + "\r\n", + "
    CCiX gates13\r\n", + "

    Number of CCiX-gates in the input quantum program

    \n", + "    \r\n", + "
    \r\n", + "

    This is the number of CCiX gates, which applies \\(-iX\\) controlled on two control qubits [1212.5069].

    \n", + "\r\n", + "
    Measurement operations13\r\n", + "

    Number of single qubit measurements in the input quantum program

    \n", + "    \r\n", + "
    \r\n", + "

    This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.

    \n", + "\r\n", + "
    \n", + "\r\n", + "
    \r\n", + " \r\n", + " Assumed error budget\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
    Total error budget1.00e-3\r\n", + "

    Total error budget for the algorithm

    \n", + "    \r\n", + "
    \r\n", + "

    The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget \\(\\epsilon = \\epsilon_{\\log} + \\epsilon_{\\rm dis} + \\epsilon_{\\rm syn}\\) is uniformly distributed and applies to errors \\(\\epsilon_{\\log}\\) to implement logical qubits, an error budget \\(\\epsilon_{\\rm dis}\\) to produce T states through distillation, and an error budget \\(\\epsilon_{\\rm syn}\\) to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets \\(\\epsilon_{\\rm dis}\\) and \\(\\epsilon_{\\rm syn}\\) are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.

    \n", + "\r\n", + "
    Logical error probability5.00e-4\r\n", + "

    Probability of at least one logical error

    \n", + "    \r\n", + "
    \r\n", + "

    This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

    \n", + "\r\n", + "
    T distillation error probability5.00e-4\r\n", + "

    Probability of at least one faulty T distillation

    \n", + "    \r\n", + "
    \r\n", + "

    This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

    \n", + "\r\n", + "
    Rotation synthesis error probability0.00e0\r\n", + "

    Probability of at least one failed rotation synthesis

    \n", + "    \r\n", + "
    \r\n", + "

    This is one third of the total error budget 1.00e-3.

    \n", + "\r\n", + "
    \n", + "\r\n", + "
    \r\n", + " \r\n", + " Physical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
    Qubit namequbit_gate_ns_e3\r\n", + "

    Some descriptive name for the qubit model

    \n", + "    \r\n", + "
    \r\n", + "

    You can load pre-defined qubit parameters by using the names qubit_gate_ns_e3, qubit_gate_ns_e4, qubit_gate_us_e3, qubit_gate_us_e4, qubit_maj_ns_e4, or qubit_maj_ns_e6. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).

    \n", + "\r\n", + "
    Instruction setGateBased\r\n", + "

    Underlying qubit technology (gate-based or Majorana)

    \n", + "    \r\n", + "
    \r\n", + "

    When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either gate-based or Majorana. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.

    \n", + "\r\n", + "
    Single-qubit measurement time100 ns\r\n", + "

    Operation time for single-qubit measurement (t_meas) in ns

    \n", + "    \r\n", + "
    \r\n", + "

    This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.

    \n", + "\r\n", + "
    Single-qubit gate time50 ns\r\n", + "

    Operation time for single-qubit gate (t_gate) in ns

    \n", + "    \r\n", + "
    \r\n", + "

    This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.

    \n", + "\r\n", + "
    Two-qubit gate time50 ns\r\n", + "

    Operation time for two-qubit gate in ns

    \n", + "    \r\n", + "
    \r\n", + "

    This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.

    \n", + "\r\n", + "
    T gate time50 ns\r\n", + "

    Operation time for a T gate

    \n", + "    \r\n", + "
    \r\n", + "

    This is the operation time in nanoseconds to execute a T gate.

    \n", + "\r\n", + "
    Single-qubit measurement error rate0.001\r\n", + "

    Error rate for single-qubit measurement

    \n", + "    \r\n", + "
    \r\n", + "

    This is the probability in which a single-qubit measurement in the Pauli basis may fail.

    \n", + "\r\n", + "
    Single-qubit error rate0.001\r\n", + "

    Error rate for single-qubit Clifford gate (p)

    \n", + "    \r\n", + "
    \r\n", + "

    This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.

    \n", + "\r\n", + "
    Two-qubit error rate0.001\r\n", + "

    Error rate for two-qubit Clifford gate

    \n", + "    \r\n", + "
    \r\n", + "

    This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.

    \n", + "\r\n", + "
    T gate error rate0.001\r\n", + "

    Error rate to prepare single-qubit T state or apply a T gate (p_T)

    \n", + "    \r\n", + "
    \r\n", + "

    This is the probability in which executing a single T gate may fail.

    \n", + "\r\n", + "
    \n", + "
    \r\n", + " Assumptions\r\n", + "
      \n", + "

    • More details on the following lists of assumptions can be found in the paper Accessing requirements for scaling quantum computers and their applications.

      \n", + "
      • \n", + "

    • Uniform independent physical noise. We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.

      \n", + "
      • \n", + "

    • Efficient classical computation. We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.

      \n", + "
      • \n", + "

    • Extraction circuits for planar quantum ISA. We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).

      \n", + "
      • \n", + "

    • Uniform independent logical noise. We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.

      \n", + "
      • \n", + "

    • Negligible Clifford costs for synthesis. We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.

      \n", + "
      • \n", + "

    • Smooth magic state consumption rate. We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.

      \n", + "
      • \n", + "
    \n" + ], + "text/plain": [ + "{'errorBudget': {'logical': 0.0005, 'rotations': 0.0, 'tstates': 0.0005},\n", + " 'jobParams': {'errorBudget': 0.001,\n", + " 'qecScheme': {'crossingPrefactor': 0.03,\n", + " 'errorCorrectionThreshold': 0.01,\n", + " 'logicalCycleTime': '(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance',\n", + " 'name': 'surface_code',\n", + " 'physicalQubitsPerLogicalQubit': '2 * codeDistance * codeDistance'},\n", + " 'qubitParams': {'instructionSet': 'GateBased',\n", + " 'name': 'qubit_gate_ns_e3',\n", + " 'oneQubitGateErrorRate': 0.001,\n", + " 'oneQubitGateTime': '50 ns',\n", + " 'oneQubitMeasurementErrorRate': 0.001,\n", + " 'oneQubitMeasurementTime': '100 ns',\n", + " 'tGateErrorRate': 0.001,\n", + " 'tGateTime': '50 ns',\n", + " 'twoQubitGateErrorRate': 0.001,\n", + " 'twoQubitGateTime': '50 ns'}},\n", + " 'logicalCounts': {'ccixCount': 13,\n", + " 'cczCount': 5,\n", + " 'measurementCount': 13,\n", + " 'numQubits': 13,\n", + " 'rotationCount': 0,\n", + " 'rotationDepth': 0,\n", + " 'tCount': 0},\n", + " 'logicalQubit': {'codeDistance': 11,\n", + " 'logicalCycleTime': 4400.0,\n", + " 'logicalErrorRate': 3.000000000000002e-08,\n", + " 'physicalQubits': 242},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 67,\n", + " 'algorithmicLogicalQubits': 38,\n", + " 'cliffordErrorRate': 0.001,\n", + " 'logicalDepth': 67,\n", + " 'numTfactories': 12,\n", + " 'numTfactoryRuns': 6,\n", + " 'numTsPerRotation': None,\n", + " 'numTstates': 72,\n", + " 'physicalQubitsForAlgorithm': 9196,\n", + " 'physicalQubitsForTfactories': 77760,\n", + " 'requiredLogicalQubitErrorRate': 1.9638648860958366e-07,\n", + " 'requiredLogicalTstateErrorRate': 6.944444444444445e-06},\n", + " 'physicalQubits': 86956,\n", + " 'runtime': 294800},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", + " 'errorBudget': '1.00e-3',\n", + " 'errorBudgetLogical': '5.00e-4',\n", + " 'errorBudgetRotations': '0.00e0',\n", + " 'errorBudgetTstates': '5.00e-4',\n", + " 'logicalCycleTime': '4us 400ns',\n", + " 'logicalErrorRate': '3.00e-8',\n", + " 'numTsPerRotation': 'No rotations in algorithm',\n", + " 'numUnitsPerRound': '2',\n", + " 'physicalQubitsForTfactoriesPercentage': '89.42 %',\n", + " 'physicalQubitsPerRound': '6480',\n", + " 'requiredLogicalQubitErrorRate': '1.96e-7',\n", + " 'requiredLogicalTstateErrorRate': '6.94e-6',\n", + " 'runtime': '294us 800ns',\n", + " 'tfactoryRuntime': '46us 800ns',\n", + " 'tfactoryRuntimePerRound': '46us 800ns',\n", + " 'tstateLogicalErrorRate': '2.17e-6',\n", + " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", + " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", + " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", + " '**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.',\n", + " '**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).',\n", + " '**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.',\n", + " '**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.',\n", + " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", + " 'groups': [{'alwaysVisible': True,\n", + " 'entries': [{'description': 'Number of physical qubits',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 9196 physical qubits to implement the algorithm logic, and 77760 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'physicalCounts/physicalQubits'},\n", + " {'description': 'Total runtime',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 67 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/runtime'}],\n", + " 'title': 'Physical resource estimates'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 13$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 38$ logical qubits.',\n", + " 'label': 'Logical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", + " {'description': 'Number of logical cycles for the algorithm',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 13 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 5 CCZ and 13 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'label': 'Algorithmic depth',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", + " {'description': 'Number of logical cycles performed',\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 67. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'label': 'Logical depth',\n", + " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", + " {'description': 'Number of T states consumed by the algorithm',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 5 CCZ and 13 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'label': 'Number of T states',\n", + " 'path': 'physicalCounts/breakdown/numTstates'},\n", + " {'description': \"Number of T factories capable of producing the demanded 72 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{72\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 294us 800ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " 'label': 'Number of T factories',\n", + " 'path': 'physicalCounts/breakdown/numTfactories'},\n", + " {'description': 'Number of times all T factories are invoked',\n", + " 'explanation': 'In order to prepare the 72 T states, the 12 copies of the T factory are repeatedly invoked 6 times.',\n", + " 'label': 'Number of T factory invocations',\n", + " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", + " {'description': 'Number of physical qubits for the algorithm after layout',\n", + " 'explanation': 'The 9196 are the product of the 38 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.',\n", + " 'label': 'Physical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", + " {'description': 'Number of physical qubits for the T factories',\n", + " 'explanation': 'Each T factory requires 6480 physical qubits and we run 12 in parallel, therefore we need $77760 = 6480 \\\\cdot 12$ qubits.',\n", + " 'label': 'Physical T factory qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", + " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 67.',\n", + " 'label': 'Required logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", + " {'description': 'The minimum T state error rate required for distilled T states',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 72.',\n", + " 'label': 'Required logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", + " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", + " 'explanation': 'The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.',\n", + " 'label': 'Number of T states per rotation',\n", + " 'path': 'physicalCountsFormatted/numTsPerRotation'}],\n", + " 'title': 'Resource estimates breakdown'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Name of QEC scheme',\n", + " 'explanation': 'You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.',\n", + " 'label': 'QEC scheme',\n", + " 'path': 'jobParams/qecScheme/name'},\n", + " {'description': 'Required code distance for error correction',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000019638648860958366)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'label': 'Code distance',\n", + " 'path': 'logicalQubit/codeDistance'},\n", + " {'description': 'Number of physical qubits per logical qubit',\n", + " 'explanation': 'The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'logicalQubit/physicalQubits'},\n", + " {'description': 'Duration of a logical cycle in nanoseconds',\n", + " 'explanation': 'The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.',\n", + " 'label': 'Logical cycle time',\n", + " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", + " {'description': 'Logical qubit error rate',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$',\n", + " 'label': 'Logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", + " {'description': 'Crossing prefactor used in QEC scheme',\n", + " 'explanation': 'The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.',\n", + " 'label': 'Crossing prefactor',\n", + " 'path': 'jobParams/qecScheme/crossingPrefactor'},\n", + " {'description': 'Error correction threshold used in QEC scheme',\n", + " 'explanation': 'The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.',\n", + " 'label': 'Error correction threshold',\n", + " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", + " {'description': 'QEC scheme formula used to compute logical cycle time',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 4us 400ns.',\n", + " 'label': 'Logical cycle time formula',\n", + " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", + " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 242.',\n", + " 'label': 'Physical qubits formula',\n", + " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", + " 'title': 'Logical qubit parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of physical qubits for a single T factory',\n", + " 'explanation': 'This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'tfactory/physicalQubits'},\n", + " {'description': 'Runtime of a single T factory',\n", + " 'explanation': 'The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", + " {'description': 'Number of output T states produced in a single run of T factory',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.',\n", + " 'label': 'Number of output T states per run',\n", + " 'path': 'tfactory/numTstates'},\n", + " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", + " 'explanation': 'This value includes the physical input T states of all copies of the distillation unit in the first round.',\n", + " 'label': 'Number of input T states per run',\n", + " 'path': 'tfactory/numInputTstates'},\n", + " {'description': 'The number of distillation rounds',\n", + " 'explanation': 'This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.',\n", + " 'label': 'Distillation rounds',\n", + " 'path': 'tfactory/numRounds'},\n", + " {'description': 'The number of units in each round of distillation',\n", + " 'explanation': 'This is the number of copies for the distillation units per round.',\n", + " 'label': 'Distillation units per round',\n", + " 'path': 'physicalCountsFormatted/numUnitsPerRound'},\n", + " {'description': 'The types of distillation units',\n", + " 'explanation': 'These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.',\n", + " 'label': 'Distillation units',\n", + " 'path': 'physicalCountsFormatted/unitNamePerRound'},\n", + " {'description': 'The code distance in each round of distillation',\n", + " 'explanation': 'This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.',\n", + " 'label': 'Distillation code distances',\n", + " 'path': 'physicalCountsFormatted/codeDistancePerRound'},\n", + " {'description': 'The number of physical qubits used in each round of distillation',\n", + " 'explanation': 'The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.',\n", + " 'label': 'Number of physical qubits per round',\n", + " 'path': 'physicalCountsFormatted/physicalQubitsPerRound'},\n", + " {'description': 'The runtime of each distillation round',\n", + " 'explanation': 'The runtime of the T factory is the sum of the runtimes in all rounds.',\n", + " 'label': 'Runtime per round',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", + " {'description': 'Logical T state error rate',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.94e-6.',\n", + " 'label': 'Logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", + " 'title': 'T factory parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", + " 'explanation': 'We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'label': 'Logical qubits (pre-layout)',\n", + " 'path': 'logicalCounts/numQubits'},\n", + " {'description': 'Number of T gates in the input quantum program',\n", + " 'explanation': 'This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.',\n", + " 'label': 'T gates',\n", + " 'path': 'logicalCounts/tCount'},\n", + " {'description': 'Number of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.',\n", + " 'label': 'Rotation gates',\n", + " 'path': 'logicalCounts/rotationCount'},\n", + " {'description': 'Depth of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.',\n", + " 'label': 'Rotation depth',\n", + " 'path': 'logicalCounts/rotationDepth'},\n", + " {'description': 'Number of CCZ-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCZ gates.',\n", + " 'label': 'CCZ gates',\n", + " 'path': 'logicalCounts/cczCount'},\n", + " {'description': 'Number of CCiX-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].',\n", + " 'label': 'CCiX gates',\n", + " 'path': 'logicalCounts/ccixCount'},\n", + " {'description': 'Number of single qubit measurements in the input quantum program',\n", + " 'explanation': 'This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.',\n", + " 'label': 'Measurement operations',\n", + " 'path': 'logicalCounts/measurementCount'}],\n", + " 'title': 'Pre-layout logical resources'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Total error budget for the algorithm',\n", + " 'explanation': \"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\n", + " 'label': 'Total error budget',\n", + " 'path': 'physicalCountsFormatted/errorBudget'},\n", + " {'description': 'Probability of at least one logical error',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'Logical error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetLogical'},\n", + " {'description': 'Probability of at least one faulty T distillation',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'T distillation error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetTstates'},\n", + " {'description': 'Probability of at least one failed rotation synthesis',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3.',\n", + " 'label': 'Rotation synthesis error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetRotations'}],\n", + " 'title': 'Assumed error budget'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Some descriptive name for the qubit model',\n", + " 'explanation': 'You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).',\n", + " 'label': 'Qubit name',\n", + " 'path': 'jobParams/qubitParams/name'},\n", + " {'description': 'Underlying qubit technology (gate-based or Majorana)',\n", + " 'explanation': 'When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.',\n", + " 'label': 'Instruction set',\n", + " 'path': 'jobParams/qubitParams/instructionSet'},\n", + " {'description': 'Operation time for single-qubit measurement (t_meas) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.',\n", + " 'label': 'Single-qubit measurement time',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementTime'},\n", + " {'description': 'Operation time for single-qubit gate (t_gate) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.',\n", + " 'label': 'Single-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateTime'},\n", + " {'description': 'Operation time for two-qubit gate in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.',\n", + " 'label': 'Two-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateTime'},\n", + " {'description': 'Operation time for a T gate',\n", + " 'explanation': 'This is the operation time in nanoseconds to execute a T gate.',\n", + " 'label': 'T gate time',\n", + " 'path': 'jobParams/qubitParams/tGateTime'},\n", + " {'description': 'Error rate for single-qubit measurement',\n", + " 'explanation': 'This is the probability in which a single-qubit measurement in the Pauli basis may fail.',\n", + " 'label': 'Single-qubit measurement error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementErrorRate'},\n", + " {'description': 'Error rate for single-qubit Clifford gate (p)',\n", + " 'explanation': 'This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.',\n", + " 'label': 'Single-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateErrorRate'},\n", + " {'description': 'Error rate for two-qubit Clifford gate',\n", + " 'explanation': 'This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.',\n", + " 'label': 'Two-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateErrorRate'},\n", + " {'description': 'Error rate to prepare single-qubit T state or apply a T gate (p_T)',\n", + " 'explanation': 'This is the probability in which executing a single T gate may fail.',\n", + " 'label': 'T gate error rate',\n", + " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", + " 'title': 'Physical qubit parameters'}]},\n", + " 'status': 'success',\n", + " 'tfactory': {'codeDistancePerRound': [9],\n", + " 'logicalErrorRate': 2.165000000000001e-06,\n", + " 'numInputTstates': 30,\n", + " 'numRounds': 1,\n", + " 'numTstates': 1,\n", + " 'numUnitsPerRound': [2],\n", + " 'physicalQubits': 6480,\n", + " 'physicalQubitsPerRound': [6480],\n", + " 'runtime': 46800.0,\n", + " 'runtimePerRound': [46800.0],\n", + " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", "# result = qsharp.azure.output(\"...\")\n", @@ -364,7 +4891,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "metadata": { "collapsed": false, "jupyter": { @@ -391,7 +4918,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, "metadata": { "collapsed": false, "jupyter": { @@ -404,10 +4931,44 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Logical algorithmic qubits = 38\n", + "Algorithmic depth = 67\n", + "Score = 2546\n" + ] + }, + { + "data": { + "text/plain": [ + "2546" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "evaluate_results(result)" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -415,9 +4976,9 @@ "name": "python3" }, "kernelspec": { - "display_name": "Python 3 [Default]", + "display_name": "Python 3 [Q#]", "language": "python", - "name": "python3" + "name": "python3_qsharp_b54crn" }, "language_info": { "codemirror_mode": { diff --git a/iQuHack-challenge-2023-task6.ipynb b/iQuHack-challenge-2023-task6.ipynb index 5205348..7babc33 100644 --- a/iQuHack-challenge-2023-task6.ipynb +++ b/iQuHack-challenge-2023-task6.ipynb @@ -198,39 +198,14 @@ "cell_type": "code", "execution_count": 5, "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Traceback (most recent call last):\n", - " File \"/opt/conda/lib/python3.9/runpy.py\", line 197, in _run_module_as_main\n", - " return _run_code(code, main_globals, None,\n", - " File \"/opt/conda/lib/python3.9/runpy.py\", line 87, in _run_code\n", - " exec(code, run_globals)\n", - " File \"/opt/conda/lib/python3.9/site-packages/ipykernel_launcher.py\", line 17, in \n", - " app.launch_new_instance()\n", - " File \"/opt/conda/lib/python3.9/site-packages/traitlets/config/application.py\", line 1041, in launch_instance\n", - " app.start()\n", - " File \"/opt/conda/lib/python3.9/site-packages/ipykernel/kernelapp.py\", line 724, in start\n", - " self.io_loop.start()\n", - " File \"/opt/conda/lib/python3.9/site-packages/tornado/platform/asyncio.py\", line 199, in start\n", - " self.asyncio_loop.run_forever()\n", - " File \"/opt/conda/lib/python3.9/asyncio/base_events.py\", line 596, in run_forever\n", - " self._run_once()\n", - " File \"/opt/conda/lib/python3.9/asyncio/base_events.py\", line 1875, in _run_once\n", - " handle = self._ready.popleft()\n", - "IndexError: pop from an empty deque\n" - ] - } - ], + "outputs": [], "source": [ "TestCompoundGate();" ] }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 6, "metadata": { "collapsed": false, "jupyter": { @@ -287,7 +262,7 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 7, "metadata": { "collapsed": false, "jupyter": { @@ -332,12 +307,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", "
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/home/jovyan/2023_microsoft/D:\\a\\1\\s\\submodules\\qsharp-runtime\\src\\Simulation\\QSharpFoundation\\Diagnostics\\AssertQubit.qs:0Microsoft.Quantum.Diagnostics.AssertQubit
/home/jovyan/2023_microsoft/D:\\a\\1\\s\\submodules\\qsharp-runtime\\src\\Simulation\\QSharpFoundation\\Diagnostics\\AssertAllZero.qs:0Microsoft.Quantum.Diagnostics.AssertAllZero
/home/jovyan/2023_microsoft/D:\\a\\1\\s\\submodules\\qsharp-runtime\\src\\Simulation\\TargetDefinitions\\Decompositions\\AssertOperationsEqualReferenced.qs:0Microsoft.Quantum.Diagnostics.AssertOperationsEqualReferenced
(notebook)TestCompoundGate
\r\n", - " \r\n", - " " - ], - "text/plain": [ - "Unhandled exception. Microsoft.Quantum.Simulation.Core.ExecutionFailException: Qubit in invalid state. Expecting: Zero\n", - "\tExpected:\t0\n", - "\tActual:\t0.007812499999999998\n", - " ---> Microsoft.Quantum.Diagnostics.AssertMeasurement on /home/jovyan/2023_microsoft/D:\\a\\1\\s\\submodules\\qsharp-runtime\\src\\Simulation\\QSharpFoundation\\Diagnostics\\Assert.qs:line 0\n", - " at Microsoft.Quantum.Diagnostics.AssertQubit on /home/jovyan/2023_microsoft/D:\\a\\1\\s\\submodules\\qsharp-runtime\\src\\Simulation\\QSharpFoundation\\Diagnostics\\AssertQubit.qs:line 0\n", - " at Microsoft.Quantum.Diagnostics.AssertAllZero on /home/jovyan/2023_microsoft/D:\\a\\1\\s\\submodules\\qsharp-runtime\\src\\Simulation\\QSharpFoundation\\Diagnostics\\AssertAllZero.qs:line 0\n", - " at Microsoft.Quantum.Diagnostics.AssertOperationsEqualReferenced on /home/jovyan/2023_microsoft/D:\\a\\1\\s\\submodules\\qsharp-runtime\\src\\Simulation\\TargetDefinitions\\Decompositions\\AssertOperationsEqualReferenced.qs:line 0\n", - " at SNIPPET.TestCompoundGate on /snippet_.qs:line 0\n" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Qubit in invalid state. Expecting: Zero\n", - "\tExpected:\t0\n", - "\tActual:\t0.007812499999999998\n" - ] - } - ], + "outputs": [], "source": [ "TestCompoundGate();" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 6, "metadata": { "collapsed": false, "jupyter": { @@ -343,7 +272,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 7, "metadata": { "collapsed": false, "jupyter": { @@ -388,12 +317,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -413,12 +342,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -438,12 +367,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -463,12 +392,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -488,12 +417,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -513,12 +442,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -538,12 +467,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -563,12 +492,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -588,12 +517,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -613,12 +542,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -638,12 +567,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -663,12 +592,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -688,12 +617,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -713,12 +642,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -738,12 +667,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -763,12 +692,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -788,12 +717,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -813,12 +742,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -838,12 +767,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -863,12 +792,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -888,12 +817,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -913,12 +842,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -938,12 +867,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -963,12 +892,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -988,12 +917,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1013,12 +942,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1038,12 +967,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1063,12 +992,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1088,12 +1017,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1113,12 +1042,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1138,12 +1067,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1163,12 +1092,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1188,12 +1117,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1213,12 +1142,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1238,12 +1167,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1263,12 +1192,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1288,12 +1217,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1313,12 +1242,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1338,12 +1267,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1363,12 +1292,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1388,12 +1317,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1413,12 +1342,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1438,12 +1367,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1463,12 +1392,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1488,12 +1417,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1513,12 +1442,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1538,12 +1467,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1563,12 +1492,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1588,12 +1517,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1613,12 +1542,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1638,12 +1567,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1663,12 +1592,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1688,12 +1617,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1713,12 +1642,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1738,12 +1667,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1763,12 +1692,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1788,12 +1717,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1813,12 +1742,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1838,12 +1767,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1863,12 +1792,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1888,12 +1817,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1913,12 +1842,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1938,12 +1867,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1963,12 +1892,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1988,12 +1917,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2013,12 +1942,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2038,12 +1967,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2063,12 +1992,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2088,12 +2017,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2113,12 +2042,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2138,12 +2067,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2163,12 +2092,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2188,12 +2117,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2213,12 +2142,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2238,12 +2167,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2263,12 +2192,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2288,12 +2217,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2313,12 +2242,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2338,12 +2267,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2363,12 +2292,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2388,12 +2317,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2413,12 +2342,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2438,12 +2367,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2463,12 +2392,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2488,12 +2417,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2513,12 +2442,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2538,12 +2467,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2563,12 +2492,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2588,12 +2517,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2613,12 +2542,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2638,12 +2567,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2663,12 +2592,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2688,12 +2617,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2713,12 +2642,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2738,12 +2667,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2763,12 +2692,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2788,12 +2717,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2813,12 +2742,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2838,12 +2767,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -2863,12 +2792,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -2888,12 +2817,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -2913,12 +2842,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -2938,12 +2867,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -2963,12 +2892,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -2988,12 +2917,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -3013,12 +2942,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -3038,12 +2967,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -3063,12 +2992,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -3088,12 +3017,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -3113,12 +3042,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -3138,12 +3067,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -3163,12 +3092,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -3188,12 +3117,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -3213,12 +3142,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -3238,12 +3167,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -3263,12 +3192,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -3288,12 +3217,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -3313,12 +3242,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -3338,12 +3267,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -3363,12 +3292,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -3388,12 +3317,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -3438,12 +3367,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -3463,12 +3392,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -3719,7 +3648,7 @@ "()" ] }, - "execution_count": 9, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } @@ -3748,7 +3677,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 8, "metadata": { "collapsed": false, "jupyter": { @@ -3782,23 +3711,23 @@ { "data": { "text/plain": [ - "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 176176},\n", - " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 317595},\n", - " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 2},\n", + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 176914},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 423509},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 4},\n", " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", - " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 168},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 166},\n", " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", - " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 168},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 166},\n", " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", @@ -3806,7 +3735,7 @@ " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" ] }, - "execution_count": 11, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -3822,7 +3751,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 9, "metadata": { "collapsed": false, "jupyter": { @@ -3850,7 +3779,7 @@ "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" ] }, - "execution_count": 12, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } @@ -3861,7 +3790,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 10, "metadata": { "collapsed": false, "jupyter": { @@ -3882,10 +3811,10 @@ "Submitting Task7_ResourceEstimationWrapper to target microsoft.estimator...\n", "Job successfully submitted.\n", " Job name: RE for the task 7\n", - " Job ID: 86743ad4-5cca-4ea9-b420-d0b0c93f9a49\n", + " Job ID: fd0504b4-d2d0-4bfc-a151-f6708f20d5ce\n", "Waiting up to 30 seconds for Azure Quantum job to complete...\n", - "[11:59:38 AM] Current job status: Executing\n", - "[11:59:43 AM] Current job status: Succeeded\n" + "[12:35:59 PM] Current job status: Waiting\n", + "[12:36:04 PM] Current job status: Succeeded\n" ] } ], @@ -3896,7 +3825,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 11, "metadata": { "collapsed": false, "jupyter": { @@ -3912,7 +3841,7 @@ "outputs": [ { "data": { - "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":155,\"cczCount\":31,\"measurementCount\":155,\"numQubits\":13,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":13,\"logicalCycleTime\":5200.0,\"logicalErrorRate\":3.000000000000002E-09,\"physicalQubits\":338},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":713,\"algorithmicLogicalQubits\":38,\"cliffordErrorRate\":0.001,\"logicalDepth\":713,\"numTfactories\":12,\"numTfactoryRuns\":62,\"numTsPerRotation\":null,\"numTstates\":744,\"physicalQubitsForAlgorithm\":12844,\"physicalQubitsForTfactories\":116160,\"requiredLogicalQubitErrorRate\":1.845427031815162E-08,\"requiredLogicalTstateErrorRate\":6.720430107526882E-07},\"physicalQubits\":129004,\"runtime\":3707600},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"11\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"5us 200ns\",\"logicalErrorRate\":\"3.00e-9\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"90.04 %\",\"physicalQubitsPerRound\":\"9680\",\"requiredLogicalQubitErrorRate\":\"1.85e-8\",\"requiredLogicalTstateErrorRate\":\"6.72e-7\",\"runtime\":\"3ms 707us 600ns\",\"tfactoryRuntime\":\"57us 200ns\",\"tfactoryRuntimePerRound\":\"57us 200ns\",\"tstateLogicalErrorRate\":\"2.48e-7\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 12844 physical qubits to implement the algorithm logic, and 116160 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (5us 200ns) multiplied by the 713 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 13$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 38$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 155 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 31 CCZ and 155 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 713. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 31 CCZ and 155 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 744 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{744\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 3ms 707us 600ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 744 T states, the 12 copies of the T factory are repeatedly invoked 62 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 12844 are the product of the 38 logical qubits after layout and the 338 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 9680 physical qubits and we run 12 in parallel, therefore we need $116160 = 9680 \\\\cdot 12$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 713.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 744.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000001845427031815162)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{13 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 5us 200ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 338.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.72e-7.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[11],\"logicalErrorRate\":2.480000000000001E-07,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":9680,\"physicalQubitsPerRound\":[9680],\"runtime\":57200.0,\"runtimePerRound\":[57200.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":13,\"cczCount\":5,\"measurementCount\":13,\"numQubits\":13,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":67,\"algorithmicLogicalQubits\":38,\"cliffordErrorRate\":0.001,\"logicalDepth\":67,\"numTfactories\":12,\"numTfactoryRuns\":6,\"numTsPerRotation\":null,\"numTstates\":72,\"physicalQubitsForAlgorithm\":9196,\"physicalQubitsForTfactories\":77760,\"requiredLogicalQubitErrorRate\":1.9638648860958366E-07,\"requiredLogicalTstateErrorRate\":6.944444444444445E-06},\"physicalQubits\":86956,\"runtime\":294800},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"89.42 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"1.96e-7\",\"requiredLogicalTstateErrorRate\":\"6.94e-6\",\"runtime\":\"294us 800ns\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 9196 physical qubits to implement the algorithm logic, and 77760 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 67 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 13$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 38$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 13 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 5 CCZ and 13 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 67. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 5 CCZ and 13 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 72 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{72\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 294us 800ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 72 T states, the 12 copies of the T factory are repeatedly invoked 6 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 9196 are the product of the 38 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 12 in parallel, therefore we need $77760 = 6480 \\\\cdot 12$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 67.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 72.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000019638648860958366)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.94e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", "text/html": [ "\r\n", "
\r\n", @@ -3924,24 +3853,24 @@ "\r\n", " \r\n", " Physical qubits\r\n", - " 129004\r\n", + " 86956\r\n", " \r\n", "

Number of physical qubits

\n", "\r\n", "
\r\n", - "

This value represents the total number of physical qubits, which is the sum of 12844 physical qubits to implement the algorithm logic, and 116160 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

\n", + "

This value represents the total number of physical qubits, which is the sum of 9196 physical qubits to implement the algorithm logic, and 77760 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Runtime\r\n", - " 3ms 707us 600ns\r\n", + " 294us 800ns\r\n", " \r\n", "

Total runtime

\n", "\r\n", "
\r\n", - "

This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (5us 200ns) multiplied by the 713 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

\n", + "

This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 67 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

\n", "\r\n", " \r\n", " \n", @@ -3968,36 +3897,36 @@ "\r\n", " \r\n", " Algorithmic depth\r\n", - " 713\r\n", + " 67\r\n", " \r\n", "

Number of logical cycles for the algorithm

\n", "\r\n", "
\r\n", - "

To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 155 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 31 CCZ and 155 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

\n", + "

To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 13 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 5 CCZ and 13 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Logical depth\r\n", - " 713\r\n", + " 67\r\n", " \r\n", "

Number of logical cycles performed

\n", "\r\n", "
\r\n", - "

This number is usually equal to the logical depth of the algorithm, which is 713. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", + "

This number is usually equal to the logical depth of the algorithm, which is 67. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Number of T states\r\n", - " 744\r\n", + " 72\r\n", " \r\n", "

Number of T states consumed by the algorithm

\n", "\r\n", "
\r\n", - "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 31 CCZ and 155 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", + "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 5 CCZ and 13 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", "\r\n", " \r\n", " \n", @@ -4006,70 +3935,70 @@ " Number of T factories\r\n", " 12\r\n", " \r\n", - "

Number of T factories capable of producing the demanded 744 T states during the algorithm's runtime

\n", + "

Number of T factories capable of producing the demanded 72 T states during the algorithm's runtime

\n", "\r\n", "
\r\n", - "

The total number of T factories 12 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{744\\;\\text{T states} \\cdot 57us 200ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 3ms 707us 600ns\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", + "

The total number of T factories 12 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{72\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 294us 800ns\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Number of T factory invocations\r\n", - " 62\r\n", + " 6\r\n", " \r\n", "

Number of times all T factories are invoked

\n", "\r\n", "
\r\n", - "

In order to prepare the 744 T states, the 12 copies of the T factory are repeatedly invoked 62 times.

\n", + "

In order to prepare the 72 T states, the 12 copies of the T factory are repeatedly invoked 6 times.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Physical algorithmic qubits\r\n", - " 12844\r\n", + " 9196\r\n", " \r\n", "

Number of physical qubits for the algorithm after layout

\n", "\r\n", "
\r\n", - "

The 12844 are the product of the 38 logical qubits after layout and the 338 physical qubits that encode a single logical qubit.

\n", + "

The 9196 are the product of the 38 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Physical T factory qubits\r\n", - " 116160\r\n", + " 77760\r\n", " \r\n", "

Number of physical qubits for the T factories

\n", "\r\n", "
\r\n", - "

Each T factory requires 9680 physical qubits and we run 12 in parallel, therefore we need $116160 = 9680 \\cdot 12$ qubits.

\n", + "

Each T factory requires 6480 physical qubits and we run 12 in parallel, therefore we need $77760 = 6480 \\cdot 12$ qubits.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Required logical qubit error rate\r\n", - " 1.85e-8\r\n", + " 1.96e-7\r\n", " \r\n", "

The minimum logical qubit error rate required to run the algorithm within the error budget

\n", "\r\n", "
\r\n", - "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 713.

\n", + "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 67.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Required logical T state error rate\r\n", - " 6.72e-7\r\n", + " 6.94e-6\r\n", " \r\n", "

The minimum T state error rate required for distilled T states

\n", "\r\n", "
\r\n", - "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 744.

\n", + "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 72.

\n", "\r\n", " \r\n", " \n", @@ -4108,19 +4037,19 @@ "\r\n", " \r\n", " Code distance\r\n", - " 13\r\n", + " 11\r\n", " \r\n", "

Required code distance for error correction

\n", "\r\n", "
\r\n", - "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000001845427031815162)}{\\log(0.01/0.001)} - 1\\)

\n", + "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000019638648860958366)}{\\log(0.01/0.001)} - 1\\)

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Physical qubits\r\n", - " 338\r\n", + " 242\r\n", " \r\n", "

Number of physical qubits per logical qubit

\n", "\r\n", @@ -4132,7 +4061,7 @@ "\r\n", " \r\n", " Logical cycle time\r\n", - " 5us 200ns\r\n", + " 4us 400ns\r\n", " \r\n", "

Duration of a logical cycle in nanoseconds

\n", "\r\n", @@ -4144,12 +4073,12 @@ "\r\n", " \r\n", " Logical qubit error rate\r\n", - " 3.00e-9\r\n", + " 3.00e-8\r\n", " \r\n", "

Logical qubit error rate

\n", "\r\n", "
\r\n", - "

The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{13 + 1}{2}$

\n", + "

The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{11 + 1}{2}$

\n", "\r\n", " \r\n", " \n", @@ -4185,7 +4114,7 @@ "

QEC scheme formula used to compute logical cycle time

\n", "\r\n", "
\r\n", - "

This is the formula that is used to compute the logical cycle time 5us 200ns.

\n", + "

This is the formula that is used to compute the logical cycle time 4us 400ns.

\n", "\r\n", " \r\n", " \n", @@ -4197,7 +4126,7 @@ "

QEC scheme formula used to compute number of physical qubits per logical qubit

\n", "\r\n", "
\r\n", - "

This is the formula that is used to compute the number of physical qubits per logical qubits 338.

\n", + "

This is the formula that is used to compute the number of physical qubits per logical qubits 242.

\n", "\r\n", " \r\n", " \n", @@ -4212,7 +4141,7 @@ "\r\n", " \r\n", " Physical qubits\r\n", - " 9680\r\n", + " 6480\r\n", " \r\n", "

Number of physical qubits for a single T factory

\n", "\r\n", @@ -4224,7 +4153,7 @@ "\r\n", " \r\n", " Runtime\r\n", - " 57us 200ns\r\n", + " 46us 800ns\r\n", " \r\n", "

Runtime of a single T factory

\n", "\r\n", @@ -4241,7 +4170,7 @@ "

Number of output T states produced in a single run of T factory

\n", "\r\n", "
\r\n", - "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.

\n", + "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.

\n", "\r\n", " \r\n", " \n", @@ -4296,7 +4225,7 @@ "\r\n", " \r\n", " Distillation code distances\r\n", - " 11\r\n", + " 9\r\n", " \r\n", "

The code distance in each round of distillation

\n", "\r\n", @@ -4308,7 +4237,7 @@ "\r\n", " \r\n", " Number of physical qubits per round\r\n", - " 9680\r\n", + " 6480\r\n", " \r\n", "

The number of physical qubits used in each round of distillation

\n", "\r\n", @@ -4320,7 +4249,7 @@ "\r\n", " \r\n", " Runtime per round\r\n", - " 57us 200ns\r\n", + " 46us 800ns\r\n", " \r\n", "

The runtime of each distillation round

\n", "\r\n", @@ -4332,12 +4261,12 @@ "\r\n", " \r\n", " Logical T state error rate\r\n", - " 2.48e-7\r\n", + " 2.17e-6\r\n", " \r\n", "

Logical T state error rate

\n", "\r\n", "
\r\n", - "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.72e-7.

\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.94e-6.

\n", "\r\n", " \r\n", " \n", @@ -4400,7 +4329,7 @@ "\r\n", " \r\n", " CCZ gates\r\n", - " 31\r\n", + " 5\r\n", " \r\n", "

Number of CCZ-gates in the input quantum program

\n", "\r\n", @@ -4412,7 +4341,7 @@ "\r\n", " \r\n", " CCiX gates\r\n", - " 155\r\n", + " 13\r\n", " \r\n", "

Number of CCiX-gates in the input quantum program

\n", "\r\n", @@ -4424,7 +4353,7 @@ "\r\n", " \r\n", " Measurement operations\r\n", - " 155\r\n", + " 13\r\n", " \r\n", "

Number of single qubit measurements in the input quantum program

\n", "\r\n", @@ -4655,48 +4584,48 @@ " 'tGateTime': '50 ns',\n", " 'twoQubitGateErrorRate': 0.001,\n", " 'twoQubitGateTime': '50 ns'}},\n", - " 'logicalCounts': {'ccixCount': 155,\n", - " 'cczCount': 31,\n", - " 'measurementCount': 155,\n", + " 'logicalCounts': {'ccixCount': 13,\n", + " 'cczCount': 5,\n", + " 'measurementCount': 13,\n", " 'numQubits': 13,\n", " 'rotationCount': 0,\n", " 'rotationDepth': 0,\n", " 'tCount': 0},\n", - " 'logicalQubit': {'codeDistance': 13,\n", - " 'logicalCycleTime': 5200.0,\n", - " 'logicalErrorRate': 3.000000000000002e-09,\n", - " 'physicalQubits': 338},\n", - " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 713,\n", + " 'logicalQubit': {'codeDistance': 11,\n", + " 'logicalCycleTime': 4400.0,\n", + " 'logicalErrorRate': 3.000000000000002e-08,\n", + " 'physicalQubits': 242},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 67,\n", " 'algorithmicLogicalQubits': 38,\n", " 'cliffordErrorRate': 0.001,\n", - " 'logicalDepth': 713,\n", + " 'logicalDepth': 67,\n", " 'numTfactories': 12,\n", - " 'numTfactoryRuns': 62,\n", + " 'numTfactoryRuns': 6,\n", " 'numTsPerRotation': None,\n", - " 'numTstates': 744,\n", - " 'physicalQubitsForAlgorithm': 12844,\n", - " 'physicalQubitsForTfactories': 116160,\n", - " 'requiredLogicalQubitErrorRate': 1.845427031815162e-08,\n", - " 'requiredLogicalTstateErrorRate': 6.720430107526882e-07},\n", - " 'physicalQubits': 129004,\n", - " 'runtime': 3707600},\n", - " 'physicalCountsFormatted': {'codeDistancePerRound': '11',\n", + " 'numTstates': 72,\n", + " 'physicalQubitsForAlgorithm': 9196,\n", + " 'physicalQubitsForTfactories': 77760,\n", + " 'requiredLogicalQubitErrorRate': 1.9638648860958366e-07,\n", + " 'requiredLogicalTstateErrorRate': 6.944444444444445e-06},\n", + " 'physicalQubits': 86956,\n", + " 'runtime': 294800},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", " 'errorBudget': '1.00e-3',\n", " 'errorBudgetLogical': '5.00e-4',\n", " 'errorBudgetRotations': '0.00e0',\n", " 'errorBudgetTstates': '5.00e-4',\n", - " 'logicalCycleTime': '5us 200ns',\n", - " 'logicalErrorRate': '3.00e-9',\n", + " 'logicalCycleTime': '4us 400ns',\n", + " 'logicalErrorRate': '3.00e-8',\n", " 'numTsPerRotation': 'No rotations in algorithm',\n", " 'numUnitsPerRound': '2',\n", - " 'physicalQubitsForTfactoriesPercentage': '90.04 %',\n", - " 'physicalQubitsPerRound': '9680',\n", - " 'requiredLogicalQubitErrorRate': '1.85e-8',\n", - " 'requiredLogicalTstateErrorRate': '6.72e-7',\n", - " 'runtime': '3ms 707us 600ns',\n", - " 'tfactoryRuntime': '57us 200ns',\n", - " 'tfactoryRuntimePerRound': '57us 200ns',\n", - " 'tstateLogicalErrorRate': '2.48e-7',\n", + " 'physicalQubitsForTfactoriesPercentage': '89.42 %',\n", + " 'physicalQubitsPerRound': '6480',\n", + " 'requiredLogicalQubitErrorRate': '1.96e-7',\n", + " 'requiredLogicalTstateErrorRate': '6.94e-6',\n", + " 'runtime': '294us 800ns',\n", + " 'tfactoryRuntime': '46us 800ns',\n", + " 'tfactoryRuntimePerRound': '46us 800ns',\n", + " 'tstateLogicalErrorRate': '2.17e-6',\n", " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", @@ -4707,11 +4636,11 @@ " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", " 'groups': [{'alwaysVisible': True,\n", " 'entries': [{'description': 'Number of physical qubits',\n", - " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 12844 physical qubits to implement the algorithm logic, and 116160 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 9196 physical qubits to implement the algorithm logic, and 77760 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", " 'label': 'Physical qubits',\n", " 'path': 'physicalCounts/physicalQubits'},\n", " {'description': 'Total runtime',\n", - " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (5us 200ns) multiplied by the 713 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 67 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", " 'label': 'Runtime',\n", " 'path': 'physicalCountsFormatted/runtime'}],\n", " 'title': 'Physical resource estimates'},\n", @@ -4721,39 +4650,39 @@ " 'label': 'Logical algorithmic qubits',\n", " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", " {'description': 'Number of logical cycles for the algorithm',\n", - " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 155 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 31 CCZ and 155 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 13 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 5 CCZ and 13 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", " 'label': 'Algorithmic depth',\n", " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", " {'description': 'Number of logical cycles performed',\n", - " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 713. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 67. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", " 'label': 'Logical depth',\n", " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", " {'description': 'Number of T states consumed by the algorithm',\n", - " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 31 CCZ and 155 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 5 CCZ and 13 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", " 'label': 'Number of T states',\n", " 'path': 'physicalCounts/breakdown/numTstates'},\n", - " {'description': \"Number of T factories capable of producing the demanded 744 T states during the algorithm's runtime\",\n", - " 'explanation': 'The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{744\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 3ms 707us 600ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " {'description': \"Number of T factories capable of producing the demanded 72 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{72\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 294us 800ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", " 'label': 'Number of T factories',\n", " 'path': 'physicalCounts/breakdown/numTfactories'},\n", " {'description': 'Number of times all T factories are invoked',\n", - " 'explanation': 'In order to prepare the 744 T states, the 12 copies of the T factory are repeatedly invoked 62 times.',\n", + " 'explanation': 'In order to prepare the 72 T states, the 12 copies of the T factory are repeatedly invoked 6 times.',\n", " 'label': 'Number of T factory invocations',\n", " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", " {'description': 'Number of physical qubits for the algorithm after layout',\n", - " 'explanation': 'The 12844 are the product of the 38 logical qubits after layout and the 338 physical qubits that encode a single logical qubit.',\n", + " 'explanation': 'The 9196 are the product of the 38 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.',\n", " 'label': 'Physical algorithmic qubits',\n", " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", " {'description': 'Number of physical qubits for the T factories',\n", - " 'explanation': 'Each T factory requires 9680 physical qubits and we run 12 in parallel, therefore we need $116160 = 9680 \\\\cdot 12$ qubits.',\n", + " 'explanation': 'Each T factory requires 6480 physical qubits and we run 12 in parallel, therefore we need $77760 = 6480 \\\\cdot 12$ qubits.',\n", " 'label': 'Physical T factory qubits',\n", " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", - " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 713.',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 67.',\n", " 'label': 'Required logical qubit error rate',\n", " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", " {'description': 'The minimum T state error rate required for distilled T states',\n", - " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 744.',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 72.',\n", " 'label': 'Required logical T state error rate',\n", " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", @@ -4767,7 +4696,7 @@ " 'label': 'QEC scheme',\n", " 'path': 'jobParams/qecScheme/name'},\n", " {'description': 'Required code distance for error correction',\n", - " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000001845427031815162)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000019638648860958366)}{\\\\log(0.01/0.001)} - 1$',\n", " 'label': 'Code distance',\n", " 'path': 'logicalQubit/codeDistance'},\n", " {'description': 'Number of physical qubits per logical qubit',\n", @@ -4779,7 +4708,7 @@ " 'label': 'Logical cycle time',\n", " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", " {'description': 'Logical qubit error rate',\n", - " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{13 + 1}{2}$',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$',\n", " 'label': 'Logical qubit error rate',\n", " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", " {'description': 'Crossing prefactor used in QEC scheme',\n", @@ -4791,11 +4720,11 @@ " 'label': 'Error correction threshold',\n", " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", " {'description': 'QEC scheme formula used to compute logical cycle time',\n", - " 'explanation': 'This is the formula that is used to compute the logical cycle time 5us 200ns.',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 4us 400ns.',\n", " 'label': 'Logical cycle time formula',\n", " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", - " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 338.',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 242.',\n", " 'label': 'Physical qubits formula',\n", " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", " 'title': 'Logical qubit parameters'},\n", @@ -4809,7 +4738,7 @@ " 'label': 'Runtime',\n", " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", " {'description': 'Number of output T states produced in a single run of T factory',\n", - " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.',\n", " 'label': 'Number of output T states per run',\n", " 'path': 'tfactory/numTstates'},\n", " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", @@ -4841,7 +4770,7 @@ " 'label': 'Runtime per round',\n", " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", " {'description': 'Logical T state error rate',\n", - " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.72e-7.',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.94e-6.',\n", " 'label': 'Logical T state error rate',\n", " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", " 'title': 'T factory parameters'},\n", @@ -4936,20 +4865,20 @@ " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", " 'title': 'Physical qubit parameters'}]},\n", " 'status': 'success',\n", - " 'tfactory': {'codeDistancePerRound': [11],\n", - " 'logicalErrorRate': 2.480000000000001e-07,\n", + " 'tfactory': {'codeDistancePerRound': [9],\n", + " 'logicalErrorRate': 2.165000000000001e-06,\n", " 'numInputTstates': 30,\n", " 'numRounds': 1,\n", " 'numTstates': 1,\n", " 'numUnitsPerRound': [2],\n", - " 'physicalQubits': 9680,\n", - " 'physicalQubitsPerRound': [9680],\n", - " 'runtime': 57200.0,\n", - " 'runtimePerRound': [57200.0],\n", + " 'physicalQubits': 6480,\n", + " 'physicalQubitsPerRound': [6480],\n", + " 'runtime': 46800.0,\n", + " 'runtimePerRound': [46800.0],\n", " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" ] }, - "execution_count": 14, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" } @@ -4962,7 +4891,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 12, "metadata": { "collapsed": false, "jupyter": { @@ -4989,7 +4918,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 13, "metadata": { "collapsed": false, "jupyter": { @@ -5008,17 +4937,17 @@ "output_type": "stream", "text": [ "Logical algorithmic qubits = 38\n", - "Algorithmic depth = 713\n", - "Score = 27094\n" + "Algorithmic depth = 67\n", + "Score = 2546\n" ] }, { "data": { "text/plain": [ - "27094" + "2546" ] }, - "execution_count": 16, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" } @@ -5027,6 +4956,13 @@ "evaluate_results(result)" ] }, 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From a02ee8f23fbe87100aec4905a1897b97fb9390b3 Mon Sep 17 00:00:00 2001 From: Hamish Hall Date: Sun, 29 Jan 2023 13:30:25 +0000 Subject: [PATCH 4/7] close to final submission --- ...Hack-challenge-2023-task1-checkpoint.ipynb | 1522 +++- ...Hack-challenge-2023-task3-checkpoint.ipynb | 4620 +++++++++- ...Hack-challenge-2023-task6-checkpoint.ipynb | 1289 +-- iQuHack-challenge-2023-task1.ipynb | 86 +- iQuHack-challenge-2023-task2.ipynb | 412 +- iQuHack-challenge-2023-task3.ipynb | 747 +- iQuHack-challenge-2023-task6.ipynb | 1289 +-- iQuHack-challenge-2023-task7.ipynb | 576 +- iQuHack-challenge-2023-task9.ipynb | 7903 ++++++++++++++++- obj/__entrypoint__.dll | Bin 321024 -> 321536 bytes obj/__entrypoint__snippets__.dll | Bin 89600 -> 121344 bytes obj/__snippets__.dll | Bin 89088 -> 120832 bytes 12 files changed, 16164 insertions(+), 2280 deletions(-) diff --git a/.ipynb_checkpoints/iQuHack-challenge-2023-task1-checkpoint.ipynb b/.ipynb_checkpoints/iQuHack-challenge-2023-task1-checkpoint.ipynb index 6042c2b..cb5da8d 100644 --- a/.ipynb_checkpoints/iQuHack-challenge-2023-task1-checkpoint.ipynb +++ b/.ipynb_checkpoints/iQuHack-challenge-2023-task1-checkpoint.ipynb @@ -34,7 +34,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "collapsed": false, "jupyter": { @@ -47,7 +47,41 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\u001b[93mTo sign in, use a web browser to open the page https://microsoft.com/devicelogin and enter the code RGGYKHPB3 to authenticate.\u001b[0m\n", + "[\n", + " {\n", + " \"cloudName\": \"AzureCloud\",\n", + " \"homeTenantId\": \"b4e518fe-3bdc-4371-a4be-7f3d83d7acbd\",\n", + " \"id\": \"7fc54e95-14cf-4a6f-b50e-d6155c241309\",\n", + " \"isDefault\": true,\n", + " \"managedByTenants\": [\n", + " {\n", + " \"tenantId\": \"d0ecd01b-d782-448e-bae0-c3cad0e0543a\"\n", + " },\n", + " {\n", + " \"tenantId\": \"94c4857e-1130-4ab8-8eac-069b40c9db20\"\n", + " },\n", + " {\n", + " \"tenantId\": \"f702a9dc-ae48-4dc7-8f0a-8155a6dfa4e5\"\n", + " }\n", + " ],\n", + " \"name\": \"Azure subscription 1\",\n", + " \"state\": \"Enabled\",\n", + " \"tenantId\": \"b4e518fe-3bdc-4371-a4be-7f3d83d7acbd\",\n", + " \"user\": {\n", + " \"name\": \"hachall@hotmail.com\",\n", + " \"type\": \"user\"\n", + " }\n", + " }\n", + "]\n" + ] + } + ], "source": [ "!az login" ] @@ -67,7 +101,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "collapsed": false, "jupyter": { @@ -89,7 +123,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": { "collapsed": false, "jupyter": { @@ -104,14 +138,14 @@ }, "outputs": [], "source": [ - "teamname=\"msft_is_the_best\" # Update this field with your team name\n", + "teamname=\"schrodingers-duck\" # Update this field with your team name\n", "task=[\"task1\"]\n", - "slack_id=\"myslackid\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + "slack_id=\"U04L3SFUCQ2\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": { "collapsed": false, "jupyter": { @@ -148,7 +182,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": { "collapsed": false, "jupyter": { @@ -169,10 +203,11 @@ "%%qsharp\n", "open Microsoft.Quantum.Canon;\n", "open Microsoft.Quantum.Diagnostics;\n", + "open Microsoft.Quantum.Arrays;\n", "\n", "// Task 1. Warm up with simple bit manipulation\n", "// (input will contain 3 qubits)\n", - "operation Task1(input : Qubit[], target : Qubit) : Unit is Adj {\n", + "operation original(input : Qubit[], target : Qubit) : Unit is Adj {\n", " let N = Length(input);\n", " use aux = Qubit[N - 1];\n", " within {\n", @@ -183,12 +218,37 @@ " } apply {\n", " Controlled X(aux, target);\n", " }\n", + "}\n", + "\n", + "operation Task1(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " CNOT(input[1], input[0]);\n", + " CNOT(input[1], input[2]);\n", + " CCNOT(input[0], input[2], target);\n", + " CNOT(input[1], input[0]);\n", + " CNOT(input[1], input[2]);\n", + "}\n", + "\n", + "operation QubitArrayWrapperOperation (op : ((Qubit[], Qubit) => Unit is Adj), qs : Qubit[]) : Unit is Adj { \n", + " op(Most(qs), Tail(qs));\n", + "}\n", + "\n", + "operation TestCompoundGate () : Unit {\n", + " AssertOperationsEqualReferenced(3+1, QubitArrayWrapperOperation(Task1, _), QubitArrayWrapperOperation (original, _));\n", "}" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "TestCompoundGate();" + ] + }, + { + "cell_type": "code", + "execution_count": 6, "metadata": { "collapsed": false, "jupyter": { @@ -245,7 +305,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "metadata": { "collapsed": false, "jupyter": { @@ -258,13 +318,260 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1,2,3],\"n_qubits\":4,\"amplitudes\":{\"0\":{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},\"1\":{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},\"2\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"3\":{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},\"4\":{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},\"5\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"6\":{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},\"7\":{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},\"8\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"9\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"10\":{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},\"11\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"12\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"13\":{\"Real\":0.35355339059327384,\"Imaginary\":0.0,\"Magnitude\":0.35355339059327384,\"Phase\":0.0},\"14\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"15\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0}}}", + "text/html": [ + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + "
Qubit IDs0, 1, 2, 3
Basis state (bitstring)AmplitudeMeas. Pr.
$\\left|0000\\right\\rangle$$0.3536 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0010\\right\\rangle$$0.3536 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0101\\right\\rangle$$0.3536 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0110\\right\\rangle$$0.3536 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1000\\right\\rangle$$0.3536 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1011\\right\\rangle$$0.3536 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1100\\right\\rangle$$0.3536 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1110\\right\\rangle$$0.3536 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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" + ], + "text/plain": [ + "|0000⟩\t0.35355339059327384 + 0𝑖\n", + "|0010⟩\t0.35355339059327384 + 0𝑖\n", + "|0101⟩\t0.35355339059327384 + 0𝑖\n", + "|0110⟩\t0.35355339059327384 + 0𝑖\n", + "|1000⟩\t0.35355339059327384 + 0𝑖\n", + "|1011⟩\t0.35355339059327384 + 0𝑖\n", + "|1100⟩\t0.35355339059327384 + 0𝑖\n", + "|1110⟩\t0.35355339059327384 + 0𝑖" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "()" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# Note that in the output of this cell the target qubit corresponds to the rightmost bit\n", "qsharp.config[\"dump.basisStateLabelingConvention\"]=\"Bitstring\"\n", "qsharp.config[\"dump.phaseDisplayStyle\"]=\"None\"\n", "# Uncomment the following line if you want to see only the entries with non-zero amplitudes\n", - "# qsharp.config[\"dump.truncateSmallAmplitudes\"]=True\n", + "qsharp.config[\"dump.truncateSmallAmplitudes\"]=True\n", "Task1_DumpMachineWrapper.simulate()" ] }, @@ -283,7 +590,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, "metadata": { "collapsed": false, "jupyter": { @@ -296,19 +603,68 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "\"Connecting to Azure Quantum...\"", + "text/plain": [ + "Connecting to Azure Quantum..." + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Connected to Azure Quantum workspace azure-q in location uksouth.\n" + ] + }, + { + "data": { + "text/plain": [ + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 177969},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 303174},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 4},\n", + " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 166},\n", + " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 166},\n", + " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.qpu.aspen-m-2', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", "# If you're using this notebook in qBraid, keep it\n", "qsharp.azure.connect(\n", - " resourceId=\"...\",\n", - " location=\"...\",\n", + " resourceId=\"/subscriptions/7fc54e95-14cf-4a6f-b50e-d6155c241309/resourceGroups/AzureQuantum/providers/Microsoft.Quantum/Workspaces/azure-q\",\n", + " location=\"UK South\",\n", " credential=\"CLI\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "metadata": { "collapsed": false, "jupyter": { @@ -321,14 +677,33 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loading package Microsoft.Quantum.Providers.Core and dependencies...\n", + "Active target is now microsoft.estimator\n" + ] + }, + { + "data": { + "text/plain": [ + "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "qsharp.azure.target(\"microsoft.estimator\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "metadata": { "collapsed": false, "jupyter": { @@ -341,7 +716,20 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Submitting Task1_ResourceEstimationWrapper to target microsoft.estimator...\n", + "Job successfully submitted.\n", + " Job name: RE for the task 1\n", + " Job ID: e139e938-3193-4d04-8a64-e5451930285f\n", + "Waiting up to 30 seconds for Azure Quantum job to complete...\n", + "[12:49:16 PM] Current job status: Succeeded\n" + ] + } + ], "source": [ "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", "result = qsharp.azure.execute(Task1_ResourceEstimationWrapper, jobName=\"RE for the task 1\")" @@ -349,7 +737,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, "metadata": { "collapsed": false, "jupyter": { @@ -362,7 +750,1051 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":0,\"cczCount\":1,\"measurementCount\":0,\"numQubits\":4,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":9,\"logicalCycleTime\":3600.0,\"logicalErrorRate\":3.0000000000000015E-07,\"physicalQubits\":162},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":3,\"algorithmicLogicalQubits\":15,\"cliffordErrorRate\":0.001,\"logicalDepth\":13,\"numTfactories\":4,\"numTfactoryRuns\":1,\"numTsPerRotation\":null,\"numTstates\":4,\"physicalQubitsForAlgorithm\":2430,\"physicalQubitsForTfactories\":15680,\"requiredLogicalQubitErrorRate\":2.564102564102564E-06,\"requiredLogicalTstateErrorRate\":0.000125},\"physicalQubits\":18110,\"runtime\":46800},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"7\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"3us 600ns\",\"logicalErrorRate\":\"3.00e-7\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"86.58 %\",\"physicalQubitsPerRound\":\"3920\",\"requiredLogicalQubitErrorRate\":\"2.56e-6\",\"requiredLogicalTstateErrorRate\":\"1.25e-4\",\"runtime\":\"46us 800ns\",\"tfactoryRuntime\":\"36us 400ns\",\"tfactoryRuntimePerRound\":\"36us 400ns\",\"tstateLogicalErrorRate\":\"2.13e-5\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 2430 physical qubits to implement the algorithm logic, and 15680 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 3 logical cycles to run the algorithm. If however the duration of a single T factory (here: 36us 400ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 4$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 15$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 0 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 1 CCZ and 0 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 3. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 1 CCZ and 0 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 4 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 4 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{4\\\\;\\\\text{T states} \\\\cdot 36us 400ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 46us 800ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 4 T states, the 4 copies of the T factory are repeatedly invoked 1 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 2430 are the product of the 15 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 3920 physical qubits and we run 4 in parallel, therefore we need $15680 = 3920 \\\\cdot 4$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 15 logical qubits and the total cycle count 13.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 4.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.000002564102564102564)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{9 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 3us 600ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 162.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.13e-5.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-4.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 15 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or ¬µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[7],\"logicalErrorRate\":2.133500000000001E-05,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":3920,\"physicalQubitsPerRound\":[3920],\"runtime\":36400.0,\"runtimePerRound\":[36400.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "text/html": [ + "\r\n", + "

\r\n", + " \r\n", + " Physical resource estimates\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits18110\r\n", + "

Number of physical qubits

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This value represents the total number of physical qubits, which is the sum of 2430 physical qubits to implement the algorithm logic, and 15680 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

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Runtime46us 800ns\r\n", + "

Total runtime

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This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 3 logical cycles to run the algorithm. If however the duration of a single T factory (here: 36us 400ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

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\r\n", + " \r\n", + " Resource estimates breakdown\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Logical algorithmic qubits15\r\n", + "

Number of logical qubits for the algorithm after layout

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Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 4\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 15$ logical qubits.

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Algorithmic depth3\r\n", + "

Number of logical cycles for the algorithm

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To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 0 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 1 CCZ and 0 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

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Logical depth13\r\n", + "

Number of logical cycles performed

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This number is usually equal to the logical depth of the algorithm, which is 3. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

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Number of T states4\r\n", + "

Number of T states consumed by the algorithm

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To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 1 CCZ and 0 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

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Number of T factories4\r\n", + "

Number of T factories capable of producing the demanded 4 T states during the algorithm's runtime

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The total number of T factories 4 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{4\\;\\text{T states} \\cdot 36us 400ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 46us 800ns\\;\\text{algorithm runtime}}\\right\\rceil\\)

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Number of T factory invocations1\r\n", + "

Number of times all T factories are invoked

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In order to prepare the 4 T states, the 4 copies of the T factory are repeatedly invoked 1 times.

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Physical algorithmic qubits2430\r\n", + "

Number of physical qubits for the algorithm after layout

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The 2430 are the product of the 15 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.

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Physical T factory qubits15680\r\n", + "

Number of physical qubits for the T factories

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Each T factory requires 3920 physical qubits and we run 4 in parallel, therefore we need $15680 = 3920 \\cdot 4$ qubits.

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Required logical qubit error rate2.56e-6\r\n", + "

The minimum logical qubit error rate required to run the algorithm within the error budget

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The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 15 logical qubits and the total cycle count 13.

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Required logical T state error rate1.25e-4\r\n", + "

The minimum T state error rate required for distilled T states

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The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 4.

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Number of T states per rotationNo rotations in algorithm\r\n", + "

Number of T states to implement a rotation with an arbitrary angle

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The number of T states to implement a rotation with an arbitrary angle is \\(\\lceil 0.53 \\log_2(0 / 0) + 5.3\\rceil\\) [arXiv:2203.10064]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Logical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
QEC schemesurface_code\r\n", + "

Name of QEC scheme

\n", + "\r\n", + "
\r\n", + "

You can load pre-defined QEC schemes by using the name surface_code or floquet_code. The latter only works with Majorana qubits.

\n", + "\r\n", + "
Code distance9\r\n", + "

Required code distance for error correction

\n", + "\r\n", + "
\r\n", + "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.000002564102564102564)}{\\log(0.01/0.001)} - 1\\)

\n", + "\r\n", + "
Physical qubits162\r\n", + "

Number of physical qubits per logical qubit

\n", + "\r\n", + "
\r\n", + "

The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.

\n", + "\r\n", + "
Logical cycle time3us 600ns\r\n", + "

Duration of a logical cycle in nanoseconds

\n", + "\r\n", + "
\r\n", + "

The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.

\n", + "\r\n", + "
Logical qubit error rate3.00e-7\r\n", + "

Logical qubit error rate

\n", + "\r\n", + "
\r\n", + "

The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{9 + 1}{2}$

\n", + "\r\n", + "
Crossing prefactor0.03\r\n", + "

Crossing prefactor used in QEC scheme

\n", + "\r\n", + "
\r\n", + "

The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.

\n", + "\r\n", + "
Error correction threshold0.01\r\n", + "

Error correction threshold used in QEC scheme

\n", + "\r\n", + "
\r\n", + "

The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.

\n", + "\r\n", + "
Logical cycle time formula(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\r\n", + "

QEC scheme formula used to compute logical cycle time

\n", + "\r\n", + "
\r\n", + "

This is the formula that is used to compute the logical cycle time 3us 600ns.

\n", + "\r\n", + "
Physical qubits formula2 * codeDistance * codeDistance\r\n", + "

QEC scheme formula used to compute number of physical qubits per logical qubit

\n", + "\r\n", + "
\r\n", + "

This is the formula that is used to compute the number of physical qubits per logical qubits 162.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " T factory parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits3920\r\n", + "

Number of physical qubits for a single T factory

\n", + "\r\n", + "
\r\n", + "

This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.

\n", + "\r\n", + "
Runtime36us 400ns\r\n", + "

Runtime of a single T factory

\n", + "\r\n", + "
\r\n", + "

The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.

\n", + "\r\n", + "
Number of output T states per run1\r\n", + "

Number of output T states produced in a single run of T factory

\n", + "\r\n", + "
\r\n", + "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.13e-5.

\n", + "\r\n", + "
Number of input T states per run30\r\n", + "

Number of physical input T states consumed in a single run of a T factory

\n", + "\r\n", + "
\r\n", + "

This value includes the physical input T states of all copies of the distillation unit in the first round.

\n", + "\r\n", + "
Distillation rounds1\r\n", + "

The number of distillation rounds

\n", + "\r\n", + "
\r\n", + "

This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.

\n", + "\r\n", + "
Distillation units per round2\r\n", + "

The number of units in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the number of copies for the distillation units per round.

\n", + "\r\n", + "
Distillation units15-to-1 space efficient logical\r\n", + "

The types of distillation units

\n", + "\r\n", + "
\r\n", + "

These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.

\n", + "\r\n", + "
Distillation code distances7\r\n", + "

The code distance in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.

\n", + "\r\n", + "
Number of physical qubits per round3920\r\n", + "

The number of physical qubits used in each round of distillation

\n", + "\r\n", + "
\r\n", + "

The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.

\n", + "\r\n", + "
Runtime per round36us 400ns\r\n", + "

The runtime of each distillation round

\n", + "\r\n", + "
\r\n", + "

The runtime of the T factory is the sum of the runtimes in all rounds.

\n", + "\r\n", + "
Logical T state error rate2.13e-5\r\n", + "

Logical T state error rate

\n", + "\r\n", + "
\r\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-4.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Pre-layout logical resources\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Logical qubits (pre-layout)4\r\n", + "

Number of logical qubits in the input quantum program

\n", + "\r\n", + "
\r\n", + "

We determine 15 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", + "\r\n", + "
T gates0\r\n", + "

Number of T gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.

\n", + "\r\n", + "
Rotation gates0\r\n", + "

Number of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.

\n", + "\r\n", + "
Rotation depth0\r\n", + "

Depth of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.

\n", + "\r\n", + "
CCZ gates1\r\n", + "

Number of CCZ-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCZ gates.

\n", + "\r\n", + "
CCiX gates0\r\n", + "

Number of CCiX-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCiX gates, which applies \\(-iX\\) controlled on two control qubits [1212.5069].

\n", + "\r\n", + "
Measurement operations0\r\n", + "

Number of single qubit measurements in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Assumed error budget\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Total error budget1.00e-3\r\n", + "

Total error budget for the algorithm

\n", + "\r\n", + "
\r\n", + "

The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget \\(\\epsilon = \\epsilon_{\\log} + \\epsilon_{\\rm dis} + \\epsilon_{\\rm syn}\\) is uniformly distributed and applies to errors \\(\\epsilon_{\\log}\\) to implement logical qubits, an error budget \\(\\epsilon_{\\rm dis}\\) to produce T states through distillation, and an error budget \\(\\epsilon_{\\rm syn}\\) to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets \\(\\epsilon_{\\rm dis}\\) and \\(\\epsilon_{\\rm syn}\\) are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.

\n", + "\r\n", + "
Logical error probability5.00e-4\r\n", + "

Probability of at least one logical error

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
T distillation error probability5.00e-4\r\n", + "

Probability of at least one faulty T distillation

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
Rotation synthesis error probability0.00e0\r\n", + "

Probability of at least one failed rotation synthesis

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Physical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Qubit namequbit_gate_ns_e3\r\n", + "

Some descriptive name for the qubit model

\n", + "\r\n", + "
\r\n", + "

You can load pre-defined qubit parameters by using the names qubit_gate_ns_e3, qubit_gate_ns_e4, qubit_gate_us_e3, qubit_gate_us_e4, qubit_maj_ns_e4, or qubit_maj_ns_e6. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).

\n", + "\r\n", + "
Instruction setGateBased\r\n", + "

Underlying qubit technology (gate-based or Majorana)

\n", + "\r\n", + "
\r\n", + "

When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either gate-based or Majorana. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.

\n", + "\r\n", + "
Single-qubit measurement time100 ns\r\n", + "

Operation time for single-qubit measurement (t_meas) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.

\n", + "\r\n", + "
Single-qubit gate time50 ns\r\n", + "

Operation time for single-qubit gate (t_gate) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.

\n", + "\r\n", + "
Two-qubit gate time50 ns\r\n", + "

Operation time for two-qubit gate in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.

\n", + "\r\n", + "
T gate time50 ns\r\n", + "

Operation time for a T gate

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to execute a T gate.

\n", + "\r\n", + "
Single-qubit measurement error rate0.001\r\n", + "

Error rate for single-qubit measurement

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit measurement in the Pauli basis may fail.

\n", + "\r\n", + "
Single-qubit error rate0.001\r\n", + "

Error rate for single-qubit Clifford gate (p)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.

\n", + "\r\n", + "
Two-qubit error rate0.001\r\n", + "

Error rate for two-qubit Clifford gate

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.

\n", + "\r\n", + "
T gate error rate0.001\r\n", + "

Error rate to prepare single-qubit T state or apply a T gate (p_T)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which executing a single T gate may fail.

\n", + "\r\n", + "
\n", + "
\r\n", + " Assumptions\r\n", + "
    \n", + "

  • More details on the following lists of assumptions can be found in the paper Accessing requirements for scaling quantum computers and their applications.

    \n", + "
    • \n", + "

  • Uniform independent physical noise. We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.

    \n", + "
    • \n", + "

  • Efficient classical computation. We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.

    \n", + "
    • \n", + "

  • Extraction circuits for planar quantum ISA. We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).

    \n", + "
    • \n", + "

  • Uniform independent logical noise. We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.

    \n", + "
    • \n", + "

  • Negligible Clifford costs for synthesis. We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.

    \n", + "
    • \n", + "

  • Smooth magic state consumption rate. We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.

    \n", + "
    • \n", + "
\n" + ], + "text/plain": [ + "{'errorBudget': {'logical': 0.0005, 'rotations': 0.0, 'tstates': 0.0005},\n", + " 'jobParams': {'errorBudget': 0.001,\n", + " 'qecScheme': {'crossingPrefactor': 0.03,\n", + " 'errorCorrectionThreshold': 0.01,\n", + " 'logicalCycleTime': '(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance',\n", + " 'name': 'surface_code',\n", + " 'physicalQubitsPerLogicalQubit': '2 * codeDistance * codeDistance'},\n", + " 'qubitParams': {'instructionSet': 'GateBased',\n", + " 'name': 'qubit_gate_ns_e3',\n", + " 'oneQubitGateErrorRate': 0.001,\n", + " 'oneQubitGateTime': '50 ns',\n", + " 'oneQubitMeasurementErrorRate': 0.001,\n", + " 'oneQubitMeasurementTime': '100 ns',\n", + " 'tGateErrorRate': 0.001,\n", + " 'tGateTime': '50 ns',\n", + " 'twoQubitGateErrorRate': 0.001,\n", + " 'twoQubitGateTime': '50 ns'}},\n", + " 'logicalCounts': {'ccixCount': 0,\n", + " 'cczCount': 1,\n", + " 'measurementCount': 0,\n", + " 'numQubits': 4,\n", + " 'rotationCount': 0,\n", + " 'rotationDepth': 0,\n", + " 'tCount': 0},\n", + " 'logicalQubit': {'codeDistance': 9,\n", + " 'logicalCycleTime': 3600.0,\n", + " 'logicalErrorRate': 3.0000000000000015e-07,\n", + " 'physicalQubits': 162},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 3,\n", + " 'algorithmicLogicalQubits': 15,\n", + " 'cliffordErrorRate': 0.001,\n", + " 'logicalDepth': 13,\n", + " 'numTfactories': 4,\n", + " 'numTfactoryRuns': 1,\n", + " 'numTsPerRotation': None,\n", + " 'numTstates': 4,\n", + " 'physicalQubitsForAlgorithm': 2430,\n", + " 'physicalQubitsForTfactories': 15680,\n", + " 'requiredLogicalQubitErrorRate': 2.564102564102564e-06,\n", + " 'requiredLogicalTstateErrorRate': 0.000125},\n", + " 'physicalQubits': 18110,\n", + " 'runtime': 46800},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '7',\n", + " 'errorBudget': '1.00e-3',\n", + " 'errorBudgetLogical': '5.00e-4',\n", + " 'errorBudgetRotations': '0.00e0',\n", + " 'errorBudgetTstates': '5.00e-4',\n", + " 'logicalCycleTime': '3us 600ns',\n", + " 'logicalErrorRate': '3.00e-7',\n", + " 'numTsPerRotation': 'No rotations in algorithm',\n", + " 'numUnitsPerRound': '2',\n", + " 'physicalQubitsForTfactoriesPercentage': '86.58 %',\n", + " 'physicalQubitsPerRound': '3920',\n", + " 'requiredLogicalQubitErrorRate': '2.56e-6',\n", + " 'requiredLogicalTstateErrorRate': '1.25e-4',\n", + " 'runtime': '46us 800ns',\n", + " 'tfactoryRuntime': '36us 400ns',\n", + " 'tfactoryRuntimePerRound': '36us 400ns',\n", + " 'tstateLogicalErrorRate': '2.13e-5',\n", + " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", + " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", + " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", + " '**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.',\n", + " '**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).',\n", + " '**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.',\n", + " '**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.',\n", + " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", + " 'groups': [{'alwaysVisible': True,\n", + " 'entries': [{'description': 'Number of physical qubits',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 2430 physical qubits to implement the algorithm logic, and 15680 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'physicalCounts/physicalQubits'},\n", + " {'description': 'Total runtime',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 3 logical cycles to run the algorithm. If however the duration of a single T factory (here: 36us 400ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/runtime'}],\n", + " 'title': 'Physical resource estimates'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 4$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 15$ logical qubits.',\n", + " 'label': 'Logical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", + " {'description': 'Number of logical cycles for the algorithm',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 0 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 1 CCZ and 0 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'label': 'Algorithmic depth',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", + " {'description': 'Number of logical cycles performed',\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 3. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'label': 'Logical depth',\n", + " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", + " {'description': 'Number of T states consumed by the algorithm',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 1 CCZ and 0 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'label': 'Number of T states',\n", + " 'path': 'physicalCounts/breakdown/numTstates'},\n", + " {'description': \"Number of T factories capable of producing the demanded 4 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 4 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{4\\\\;\\\\text{T states} \\\\cdot 36us 400ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 46us 800ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " 'label': 'Number of T factories',\n", + " 'path': 'physicalCounts/breakdown/numTfactories'},\n", + " {'description': 'Number of times all T factories are invoked',\n", + " 'explanation': 'In order to prepare the 4 T states, the 4 copies of the T factory are repeatedly invoked 1 times.',\n", + " 'label': 'Number of T factory invocations',\n", + " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", + " {'description': 'Number of physical qubits for the algorithm after layout',\n", + " 'explanation': 'The 2430 are the product of the 15 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.',\n", + " 'label': 'Physical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", + " {'description': 'Number of physical qubits for the T factories',\n", + " 'explanation': 'Each T factory requires 3920 physical qubits and we run 4 in parallel, therefore we need $15680 = 3920 \\\\cdot 4$ qubits.',\n", + " 'label': 'Physical T factory qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", + " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 15 logical qubits and the total cycle count 13.',\n", + " 'label': 'Required logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", + " {'description': 'The minimum T state error rate required for distilled T states',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 4.',\n", + " 'label': 'Required logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", + " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", + " 'explanation': 'The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.',\n", + " 'label': 'Number of T states per rotation',\n", + " 'path': 'physicalCountsFormatted/numTsPerRotation'}],\n", + " 'title': 'Resource estimates breakdown'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Name of QEC scheme',\n", + " 'explanation': 'You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.',\n", + " 'label': 'QEC scheme',\n", + " 'path': 'jobParams/qecScheme/name'},\n", + " {'description': 'Required code distance for error correction',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.000002564102564102564)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'label': 'Code distance',\n", + " 'path': 'logicalQubit/codeDistance'},\n", + " {'description': 'Number of physical qubits per logical qubit',\n", + " 'explanation': 'The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'logicalQubit/physicalQubits'},\n", + " {'description': 'Duration of a logical cycle in nanoseconds',\n", + " 'explanation': 'The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.',\n", + " 'label': 'Logical cycle time',\n", + " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", + " {'description': 'Logical qubit error rate',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{9 + 1}{2}$',\n", + " 'label': 'Logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", + " {'description': 'Crossing prefactor used in QEC scheme',\n", + " 'explanation': 'The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.',\n", + " 'label': 'Crossing prefactor',\n", + " 'path': 'jobParams/qecScheme/crossingPrefactor'},\n", + " {'description': 'Error correction threshold used in QEC scheme',\n", + " 'explanation': 'The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.',\n", + " 'label': 'Error correction threshold',\n", + " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", + " {'description': 'QEC scheme formula used to compute logical cycle time',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 3us 600ns.',\n", + " 'label': 'Logical cycle time formula',\n", + " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", + " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 162.',\n", + " 'label': 'Physical qubits formula',\n", + " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", + " 'title': 'Logical qubit parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of physical qubits for a single T factory',\n", + " 'explanation': 'This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'tfactory/physicalQubits'},\n", + " {'description': 'Runtime of a single T factory',\n", + " 'explanation': 'The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", + " {'description': 'Number of output T states produced in a single run of T factory',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.13e-5.',\n", + " 'label': 'Number of output T states per run',\n", + " 'path': 'tfactory/numTstates'},\n", + " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", + " 'explanation': 'This value includes the physical input T states of all copies of the distillation unit in the first round.',\n", + " 'label': 'Number of input T states per run',\n", + " 'path': 'tfactory/numInputTstates'},\n", + " {'description': 'The number of distillation rounds',\n", + " 'explanation': 'This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.',\n", + " 'label': 'Distillation rounds',\n", + " 'path': 'tfactory/numRounds'},\n", + " {'description': 'The number of units in each round of distillation',\n", + " 'explanation': 'This is the number of copies for the distillation units per round.',\n", + " 'label': 'Distillation units per round',\n", + " 'path': 'physicalCountsFormatted/numUnitsPerRound'},\n", + " {'description': 'The types of distillation units',\n", + " 'explanation': 'These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.',\n", + " 'label': 'Distillation units',\n", + " 'path': 'physicalCountsFormatted/unitNamePerRound'},\n", + " {'description': 'The code distance in each round of distillation',\n", + " 'explanation': 'This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.',\n", + " 'label': 'Distillation code distances',\n", + " 'path': 'physicalCountsFormatted/codeDistancePerRound'},\n", + " {'description': 'The number of physical qubits used in each round of distillation',\n", + " 'explanation': 'The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.',\n", + " 'label': 'Number of physical qubits per round',\n", + " 'path': 'physicalCountsFormatted/physicalQubitsPerRound'},\n", + " {'description': 'The runtime of each distillation round',\n", + " 'explanation': 'The runtime of the T factory is the sum of the runtimes in all rounds.',\n", + " 'label': 'Runtime per round',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", + " {'description': 'Logical T state error rate',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-4.',\n", + " 'label': 'Logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", + " 'title': 'T factory parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", + " 'explanation': 'We determine 15 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'label': 'Logical qubits (pre-layout)',\n", + " 'path': 'logicalCounts/numQubits'},\n", + " {'description': 'Number of T gates in the input quantum program',\n", + " 'explanation': 'This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.',\n", + " 'label': 'T gates',\n", + " 'path': 'logicalCounts/tCount'},\n", + " {'description': 'Number of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.',\n", + " 'label': 'Rotation gates',\n", + " 'path': 'logicalCounts/rotationCount'},\n", + " {'description': 'Depth of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.',\n", + " 'label': 'Rotation depth',\n", + " 'path': 'logicalCounts/rotationDepth'},\n", + " {'description': 'Number of CCZ-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCZ gates.',\n", + " 'label': 'CCZ gates',\n", + " 'path': 'logicalCounts/cczCount'},\n", + " {'description': 'Number of CCiX-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].',\n", + " 'label': 'CCiX gates',\n", + " 'path': 'logicalCounts/ccixCount'},\n", + " {'description': 'Number of single qubit measurements in the input quantum program',\n", + " 'explanation': 'This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.',\n", + " 'label': 'Measurement operations',\n", + " 'path': 'logicalCounts/measurementCount'}],\n", + " 'title': 'Pre-layout logical resources'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Total error budget for the algorithm',\n", + " 'explanation': \"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\n", + " 'label': 'Total error budget',\n", + " 'path': 'physicalCountsFormatted/errorBudget'},\n", + " {'description': 'Probability of at least one logical error',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'Logical error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetLogical'},\n", + " {'description': 'Probability of at least one faulty T distillation',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'T distillation error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetTstates'},\n", + " {'description': 'Probability of at least one failed rotation synthesis',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3.',\n", + " 'label': 'Rotation synthesis error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetRotations'}],\n", + " 'title': 'Assumed error budget'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Some descriptive name for the qubit model',\n", + " 'explanation': 'You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).',\n", + " 'label': 'Qubit name',\n", + " 'path': 'jobParams/qubitParams/name'},\n", + " {'description': 'Underlying qubit technology (gate-based or Majorana)',\n", + " 'explanation': 'When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.',\n", + " 'label': 'Instruction set',\n", + " 'path': 'jobParams/qubitParams/instructionSet'},\n", + " {'description': 'Operation time for single-qubit measurement (t_meas) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.',\n", + " 'label': 'Single-qubit measurement time',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementTime'},\n", + " {'description': 'Operation time for single-qubit gate (t_gate) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.',\n", + " 'label': 'Single-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateTime'},\n", + " {'description': 'Operation time for two-qubit gate in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.',\n", + " 'label': 'Two-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateTime'},\n", + " {'description': 'Operation time for a T gate',\n", + " 'explanation': 'This is the operation time in nanoseconds to execute a T gate.',\n", + " 'label': 'T gate time',\n", + " 'path': 'jobParams/qubitParams/tGateTime'},\n", + " {'description': 'Error rate for single-qubit measurement',\n", + " 'explanation': 'This is the probability in which a single-qubit measurement in the Pauli basis may fail.',\n", + " 'label': 'Single-qubit measurement error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementErrorRate'},\n", + " {'description': 'Error rate for single-qubit Clifford gate (p)',\n", + " 'explanation': 'This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.',\n", + " 'label': 'Single-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateErrorRate'},\n", + " {'description': 'Error rate for two-qubit Clifford gate',\n", + " 'explanation': 'This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.',\n", + " 'label': 'Two-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateErrorRate'},\n", + " {'description': 'Error rate to prepare single-qubit T state or apply a T gate (p_T)',\n", + " 'explanation': 'This is the probability in which executing a single T gate may fail.',\n", + " 'label': 'T gate error rate',\n", + " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", + " 'title': 'Physical qubit parameters'}]},\n", + " 'status': 'success',\n", + " 'tfactory': {'codeDistancePerRound': [7],\n", + " 'logicalErrorRate': 2.133500000000001e-05,\n", + " 'numInputTstates': 30,\n", + " 'numRounds': 1,\n", + " 'numTstates': 1,\n", + " 'numUnitsPerRound': [2],\n", + " 'physicalQubits': 3920,\n", + " 'physicalQubitsPerRound': [3920],\n", + " 'runtime': 36400.0,\n", + " 'runtimePerRound': [36400.0],\n", + " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", "# result = qsharp.azure.output(\"...\")\n", @@ -371,7 +1803,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "metadata": { "collapsed": false, "jupyter": { @@ -398,7 +1830,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, "metadata": { "collapsed": false, "jupyter": { @@ -411,10 +1843,44 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Logical algorithmic qubits = 15\n", + "Algorithmic depth = 3\n", + "Score = 45\n" + ] + }, + { + "data": { + "text/plain": [ + "45" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "evaluate_results(result)" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -422,9 +1888,9 @@ "name": "python3" }, "kernelspec": { - "display_name": "Python 3 [Default]", + "display_name": "Python 3 [Q#]", "language": "python", - "name": "python3" + "name": "python3_qsharp_b54crn" }, "language_info": { "codemirror_mode": { diff --git a/.ipynb_checkpoints/iQuHack-challenge-2023-task3-checkpoint.ipynb b/.ipynb_checkpoints/iQuHack-challenge-2023-task3-checkpoint.ipynb index 77ca776..4d5561f 100644 --- a/.ipynb_checkpoints/iQuHack-challenge-2023-task3-checkpoint.ipynb +++ b/.ipynb_checkpoints/iQuHack-challenge-2023-task3-checkpoint.ipynb @@ -67,7 +67,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": { "collapsed": false, "jupyter": { @@ -89,7 +89,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": { "collapsed": false, "jupyter": { @@ -104,14 +104,14 @@ }, "outputs": [], "source": [ - "teamname=\"msft_is_the_best\" # Update this field with your team name\n", + "teamname=\"schrodingers-duck\" # Update this field with your team name\n", "task=[\"task3\"]\n", - "slack_id=\"myslackid\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + "slack_id=\"U04L3SFUCQ2\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": { "collapsed": false, "jupyter": { @@ -148,7 +148,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 15, "metadata": { "collapsed": false, "jupyter": { @@ -169,19 +169,62 @@ "%%qsharp\n", "open Microsoft.Quantum.Canon;\n", "open Microsoft.Quantum.Diagnostics;\n", + "open Microsoft.Quantum.Arrays;\n", "\n", "// Task 3. \n", "// (input will contain 6 qubits)\n", - "operation Task3(input : Qubit[], target : Qubit) : Unit is Adj {\n", + "operation original(input : Qubit[], target : Qubit) : Unit is Adj {\n", " for i in [7, 11, 13, 14, 19, 21, 22, 25, 26, 28, 35, 37, 38, 41, 42, 44, 49, 50, 52, 56] {\n", " ControlledOnInt(i, X)(input, target);\n", " }\n", + "}\n", + "\n", + "operation CarryN(carryIn: Qubit, summand1: Qubit, summand2: Qubit, carryOut: Qubit) : Unit is Adj + Ctl {\n", + " CCNOT (summand1, summand2, carryOut);\n", + " CNOT (summand1, summand2);\n", + " CCNOT (carryIn, summand2, carryOut);\n", + " CNOT(carryIn, summand2);\n", + "}\n", + "\n", + "operation Task3(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " use sumWires = Qubit[4];\n", + " use zero = Qubit[1];\n", + " within{\n", + " //Ebene 1\n", + " CarryN(input[0], input[1], input[2], sumWires[0]);\n", + " CarryN(input[3], input[4], input[5], sumWires[1]);\n", + " //Ebene 2\n", + " CarryN(zero[0], input[2], input[5], sumWires[2]);\n", + " CarryN(sumWires[2], sumWires[0], sumWires[1], sumWires[3]);\n", + " //Outputs: input[5], sumWires[1], sumWires[3]\n", + " // == 3 --> input[5] == 1 && sumWires[1] == 1 && sumWires[3] == 0\n", + " X(sumWires[3]);\n", + " } apply{\n", + " Controlled X([input[5], sumWires[1], sumWires[3]], target);\n", + " }\n", + "}\n", + "\n", + "operation QubitArrayWrapperOperation (op : ((Qubit[], Qubit) => Unit is Adj), qs : Qubit[]) : Unit is Adj { \n", + " op(Most(qs), Tail(qs));\n", + "}\n", + "\n", + "operation TestCompoundGate () : Unit {\n", + " AssertOperationsEqualReferenced(6+1, QubitArrayWrapperOperation(Task3, _), QubitArrayWrapperOperation (original, _));\n", "}" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "TestCompoundGate();" + ] + }, + { + "cell_type": "code", + "execution_count": 17, "metadata": { "collapsed": false, "jupyter": { @@ -238,7 +281,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 18, "metadata": { "collapsed": false, "jupyter": { @@ -251,7 +294,3374 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": 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\n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + "
Qubit IDs0, 1, 2, 3, 4, 5, 6
Basis state (bitstring)AmplitudeMeas. Pr.
$\\left|0000000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0000001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0000010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0000011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0000100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0000101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0000110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0000111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0001000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0001001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0001010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0001011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0001100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0001101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0001110\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0001111\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0010000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0010001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0010010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0010011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0010100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0010101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0010110\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0010111\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0011000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0011001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0011010\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0011011\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0011100\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0011101\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0011110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0011111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0100000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0100001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0100010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0100011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0100100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0100101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0100110\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0100111\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0101000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0101001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0101010\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0101011\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0101100\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0101101\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0101110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0101111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0110000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0110001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0110010\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0110011\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0110100\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0110101\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0110110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0110111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0111000\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0111001\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0111010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0111011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0111100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0111101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0111110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|0111111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1000000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1000001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1000010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1000011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1000100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1000101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1000110\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1000111\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1001000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1001001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1001010\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1001011\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1001100\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1001101\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1001110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

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$\\left|1001111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1010000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1010001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1010010\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1010011\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1010100\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1010101\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1010110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1010111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1011000\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1011001\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1011010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1011011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1011100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1011101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1011110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1011111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1100000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1100001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1100010\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1100011\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1100100\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1100101\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1100110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1100111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1101000\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1101001\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1101010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1101011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1101100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1101101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1101110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

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$\\left|1101111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1110000\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1110001\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1110010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

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$\\left|1110011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1110100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1110101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

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$\\left|1110110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1110111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1111000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1111001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1111010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1111011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1111100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1111101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1111110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1111111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

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" + ], + "text/plain": [ + "|0000000⟩\t0.12500000000000008 + 0𝑖\n", + "|0000001⟩\t0 + 0𝑖\n", + "|0000010⟩\t0.12500000000000008 + 0𝑖\n", + "|0000011⟩\t0 + 0𝑖\n", + "|0000100⟩\t0.12500000000000008 + 0𝑖\n", + "|0000101⟩\t0 + 0𝑖\n", + "|0000110⟩\t0.12500000000000008 + 0𝑖\n", + "|0000111⟩\t0 + 0𝑖\n", + "|0001000⟩\t0.12500000000000008 + 0𝑖\n", + "|0001001⟩\t0 + 0𝑖\n", + "|0001010⟩\t0.12500000000000008 + 0𝑖\n", + "|0001011⟩\t0 + 0𝑖\n", + "|0001100⟩\t0.12500000000000008 + 0𝑖\n", + "|0001101⟩\t0 + 0𝑖\n", + "|0001110⟩\t0 + 0𝑖\n", + "|0001111⟩\t0.12500000000000008 + 0𝑖\n", + "|0010000⟩\t0.12500000000000008 + 0𝑖\n", + "|0010001⟩\t0 + 0𝑖\n", + "|0010010⟩\t0.12500000000000008 + 0𝑖\n", + "|0010011⟩\t0 + 0𝑖\n", + "|0010100⟩\t0.12500000000000008 + 0𝑖\n", + "|0010101⟩\t0 + 0𝑖\n", + "|0010110⟩\t0 + 0𝑖\n", + "|0010111⟩\t0.12500000000000008 + 0𝑖\n", + "|0011000⟩\t0.12500000000000008 + 0𝑖\n", + "|0011001⟩\t0 + 0𝑖\n", + "|0011010⟩\t0 + 0𝑖\n", + "|0011011⟩\t0.12500000000000008 + 0𝑖\n", + "|0011100⟩\t0 + 0𝑖\n", + "|0011101⟩\t0.12500000000000008 + 0𝑖\n", + "|0011110⟩\t0.12500000000000008 + 0𝑖\n", + "|0011111⟩\t0 + 0𝑖\n", + "|0100000⟩\t0.12500000000000008 + 0𝑖\n", + "|0100001⟩\t0 + 0𝑖\n", + "|0100010⟩\t0.12500000000000008 + 0𝑖\n", + "|0100011⟩\t0 + 0𝑖\n", + "|0100100⟩\t0.12500000000000008 + 0𝑖\n", + "|0100101⟩\t0 + 0𝑖\n", + "|0100110⟩\t0 + 0𝑖\n", + "|0100111⟩\t0.12500000000000008 + 0𝑖\n", + "|0101000⟩\t0.12500000000000008 + 0𝑖\n", + "|0101001⟩\t0 + 0𝑖\n", + "|0101010⟩\t0 + 0𝑖\n", + "|0101011⟩\t0.12500000000000008 + 0𝑖\n", + "|0101100⟩\t0 + 0𝑖\n", + "|0101101⟩\t0.12500000000000008 + 0𝑖\n", + "|0101110⟩\t0.12500000000000008 + 0𝑖\n", + "|0101111⟩\t0 + 0𝑖\n", + "|0110000⟩\t0.12500000000000008 + 0𝑖\n", + "|0110001⟩\t0 + 0𝑖\n", + "|0110010⟩\t0 + 0𝑖\n", + "|0110011⟩\t0.12500000000000008 + 0𝑖\n", + "|0110100⟩\t0 + 0𝑖\n", + "|0110101⟩\t0.12500000000000008 + 0𝑖\n", + "|0110110⟩\t0.12500000000000008 + 0𝑖\n", + "|0110111⟩\t0 + 0𝑖\n", + "|0111000⟩\t0 + 0𝑖\n", + "|0111001⟩\t0.12500000000000008 + 0𝑖\n", + "|0111010⟩\t0.12500000000000008 + 0𝑖\n", + "|0111011⟩\t0 + 0𝑖\n", + "|0111100⟩\t0.12500000000000008 + 0𝑖\n", + "|0111101⟩\t0 + 0𝑖\n", + "|0111110⟩\t0.12500000000000008 + 0𝑖\n", + "|0111111⟩\t0 + 0𝑖\n", + "|1000000⟩\t0.12500000000000008 + 0𝑖\n", + "|1000001⟩\t0 + 0𝑖\n", + "|1000010⟩\t0.12500000000000008 + 0𝑖\n", + "|1000011⟩\t0 + 0𝑖\n", + "|1000100⟩\t0.12500000000000008 + 0𝑖\n", + "|1000101⟩\t0 + 0𝑖\n", + "|1000110⟩\t0 + 0𝑖\n", + "|1000111⟩\t0.12500000000000008 + 0𝑖\n", + "|1001000⟩\t0.12500000000000008 + 0𝑖\n", + "|1001001⟩\t0 + 0𝑖\n", + "|1001010⟩\t0 + 0𝑖\n", + "|1001011⟩\t0.12500000000000008 + 0𝑖\n", + "|1001100⟩\t0 + 0𝑖\n", + "|1001101⟩\t0.12500000000000008 + 0𝑖\n", + "|1001110⟩\t0.12500000000000008 + 0𝑖\n", + "|1001111⟩\t0 + 0𝑖\n", + "|1010000⟩\t0.12500000000000008 + 0𝑖\n", + "|1010001⟩\t0 + 0𝑖\n", + "|1010010⟩\t0 + 0𝑖\n", + "|1010011⟩\t0.12500000000000008 + 0𝑖\n", + "|1010100⟩\t0 + 0𝑖\n", + "|1010101⟩\t0.12500000000000008 + 0𝑖\n", + "|1010110⟩\t0.12500000000000008 + 0𝑖\n", + "|1010111⟩\t0 + 0𝑖\n", + "|1011000⟩\t0 + 0𝑖\n", + "|1011001⟩\t0.12500000000000008 + 0𝑖\n", + "|1011010⟩\t0.12500000000000008 + 0𝑖\n", + "|1011011⟩\t0 + 0𝑖\n", + "|1011100⟩\t0.12500000000000008 + 0𝑖\n", + "|1011101⟩\t0 + 0𝑖\n", + "|1011110⟩\t0.12500000000000008 + 0𝑖\n", + "|1011111⟩\t0 + 0𝑖\n", + "|1100000⟩\t0.12500000000000008 + 0𝑖\n", + "|1100001⟩\t0 + 0𝑖\n", + "|1100010⟩\t0 + 0𝑖\n", + "|1100011⟩\t0.12500000000000008 + 0𝑖\n", + "|1100100⟩\t0 + 0𝑖\n", + "|1100101⟩\t0.12500000000000008 + 0𝑖\n", + "|1100110⟩\t0.12500000000000008 + 0𝑖\n", + "|1100111⟩\t0 + 0𝑖\n", + "|1101000⟩\t0 + 0𝑖\n", + "|1101001⟩\t0.12500000000000008 + 0𝑖\n", + "|1101010⟩\t0.12500000000000008 + 0𝑖\n", + "|1101011⟩\t0 + 0𝑖\n", + "|1101100⟩\t0.12500000000000008 + 0𝑖\n", + "|1101101⟩\t0 + 0𝑖\n", + "|1101110⟩\t0.12500000000000008 + 0𝑖\n", + "|1101111⟩\t0 + 0𝑖\n", + "|1110000⟩\t0 + 0𝑖\n", + "|1110001⟩\t0.12500000000000008 + 0𝑖\n", + "|1110010⟩\t0.12500000000000008 + 0𝑖\n", + "|1110011⟩\t0 + 0𝑖\n", + "|1110100⟩\t0.12500000000000008 + 0𝑖\n", + "|1110101⟩\t0 + 0𝑖\n", + "|1110110⟩\t0.12500000000000008 + 0𝑖\n", + "|1110111⟩\t0 + 0𝑖\n", + "|1111000⟩\t0.12500000000000008 + 0𝑖\n", + "|1111001⟩\t0 + 0𝑖\n", + "|1111010⟩\t0.12500000000000008 + 0𝑖\n", + "|1111011⟩\t0 + 0𝑖\n", + "|1111100⟩\t0.12500000000000008 + 0𝑖\n", + "|1111101⟩\t0 + 0𝑖\n", + "|1111110⟩\t0.12500000000000008 + 0𝑖\n", + "|1111111⟩\t0 + 0𝑖" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "()" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# Note that in the output of this cell the target qubit corresponds to the rightmost bit\n", "qsharp.config[\"dump.basisStateLabelingConvention\"]=\"Bitstring\"\n", @@ -276,7 +3686,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 19, "metadata": { "collapsed": false, "jupyter": { @@ -289,19 +3699,68 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "\"Connecting to Azure Quantum...\"", + "text/plain": [ + "Connecting to Azure Quantum..." + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Connected to Azure Quantum workspace azure-q in location uksouth.\n" + ] + }, + { + "data": { + "text/plain": [ + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 178144},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 409698},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 4},\n", + " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 168},\n", + " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 168},\n", + " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.qpu.aspen-m-2', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", "# If you're using this notebook in qBraid, keep it\n", "qsharp.azure.connect(\n", - " resourceId=\"...\",\n", - " location=\"...\",\n", + " resourceId=\"/subscriptions/7fc54e95-14cf-4a6f-b50e-d6155c241309/resourceGroups/AzureQuantum/providers/Microsoft.Quantum/Workspaces/azure-q\",\n", + " location=\"UK South\",\n", " credential=\"CLI\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 20, "metadata": { "collapsed": false, "jupyter": { @@ -314,14 +3773,33 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loading package Microsoft.Quantum.Providers.Core and dependencies...\n", + "Active target is now microsoft.estimator\n" + ] + }, + { + "data": { + "text/plain": [ + "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "qsharp.azure.target(\"microsoft.estimator\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 21, "metadata": { "collapsed": false, "jupyter": { @@ -334,7 +3812,21 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Submitting Task3_ResourceEstimationWrapper to target microsoft.estimator...\n", + "Job successfully submitted.\n", + " Job name: RE for the task 3\n", + " Job ID: 97de0812-1c25-4a9d-be97-55f936dc8c93\n", + "Waiting up to 30 seconds for Azure Quantum job to complete...\n", + "[1:13:16 PM] Current job status: Executing\n", + "[1:13:21 PM] Current job status: Succeeded\n" + ] + } + ], "source": [ "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", "result = qsharp.azure.execute(Task3_ResourceEstimationWrapper, jobName=\"RE for the task 3\")" @@ -342,7 +3834,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 22, "metadata": { "collapsed": false, "jupyter": { @@ -355,7 +3847,1051 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":80,\"cczCount\":20,\"measurementCount\":80,\"numQubits\":11,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":380,\"algorithmicLogicalQubits\":33,\"cliffordErrorRate\":0.001,\"logicalDepth\":380,\"numTfactories\":14,\"numTfactoryRuns\":29,\"numTsPerRotation\":null,\"numTstates\":400,\"physicalQubitsForAlgorithm\":7986,\"physicalQubitsForTfactories\":135520,\"requiredLogicalQubitErrorRate\":3.987240829346092E-08,\"requiredLogicalTstateErrorRate\":1.25E-06},\"physicalQubits\":143506,\"runtime\":1672000},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"11\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"94.44 %\",\"physicalQubitsPerRound\":\"9680\",\"requiredLogicalQubitErrorRate\":\"3.99e-8\",\"requiredLogicalTstateErrorRate\":\"1.25e-6\",\"runtime\":\"1ms 672us\",\"tfactoryRuntime\":\"57us 200ns\",\"tfactoryRuntimePerRound\":\"57us 200ns\",\"tstateLogicalErrorRate\":\"2.48e-7\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 7986 physical qubits to implement the algorithm logic, and 135520 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 380 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 11$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 33$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 80 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 20 CCZ and 80 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 380. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 20 CCZ and 80 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 400 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{400\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 1ms 672us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 400 T states, the 14 copies of the T factory are repeatedly invoked 29 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 7986 are the product of the 33 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 9680 physical qubits and we run 14 in parallel, therefore we need $135520 = 9680 \\\\cdot 14$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 380.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 400.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000003987240829346092)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or ¬µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[11],\"logicalErrorRate\":2.480000000000001E-07,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":9680,\"physicalQubitsPerRound\":[9680],\"runtime\":57200.0,\"runtimePerRound\":[57200.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "text/html": [ + "\r\n", + "
\r\n", + " \r\n", + " Physical resource estimates\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits143506\r\n", + "

Number of physical qubits

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\r\n", + "

This value represents the total number of physical qubits, which is the sum of 7986 physical qubits to implement the algorithm logic, and 135520 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

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Runtime1ms 672us\r\n", + "

Total runtime

\n", + "\r\n", + "
\r\n", + "

This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 380 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

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\r\n", + " \r\n", + " Resource estimates breakdown\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Logical algorithmic qubits33\r\n", + "

Number of logical qubits for the algorithm after layout

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Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 11\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 33$ logical qubits.

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Algorithmic depth380\r\n", + "

Number of logical cycles for the algorithm

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To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 80 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 20 CCZ and 80 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

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Logical depth380\r\n", + "

Number of logical cycles performed

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This number is usually equal to the logical depth of the algorithm, which is 380. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

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Number of T states400\r\n", + "

Number of T states consumed by the algorithm

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To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 20 CCZ and 80 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

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Number of T factories14\r\n", + "

Number of T factories capable of producing the demanded 400 T states during the algorithm's runtime

\n", + "\r\n", + "
\r\n", + "

The total number of T factories 14 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{400\\;\\text{T states} \\cdot 57us 200ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 1ms 672us\\;\\text{algorithm runtime}}\\right\\rceil\\)

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Number of T factory invocations29\r\n", + "

Number of times all T factories are invoked

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\r\n", + "

In order to prepare the 400 T states, the 14 copies of the T factory are repeatedly invoked 29 times.

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Physical algorithmic qubits7986\r\n", + "

Number of physical qubits for the algorithm after layout

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\r\n", + "

The 7986 are the product of the 33 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.

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Physical T factory qubits135520\r\n", + "

Number of physical qubits for the T factories

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Each T factory requires 9680 physical qubits and we run 14 in parallel, therefore we need $135520 = 9680 \\cdot 14$ qubits.

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Required logical qubit error rate3.99e-8\r\n", + "

The minimum logical qubit error rate required to run the algorithm within the error budget

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The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 380.

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Required logical T state error rate1.25e-6\r\n", + "

The minimum T state error rate required for distilled T states

\n", + "\r\n", + "
\r\n", + "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 400.

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Number of T states per rotationNo rotations in algorithm\r\n", + "

Number of T states to implement a rotation with an arbitrary angle

\n", + "\r\n", + "
\r\n", + "

The number of T states to implement a rotation with an arbitrary angle is \\(\\lceil 0.53 \\log_2(0 / 0) + 5.3\\rceil\\) [arXiv:2203.10064]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.

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\r\n", + " \r\n", + " Logical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
QEC schemesurface_code\r\n", + "

Name of QEC scheme

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\r\n", + "

You can load pre-defined QEC schemes by using the name surface_code or floquet_code. The latter only works with Majorana qubits.

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Code distance11\r\n", + "

Required code distance for error correction

\n", + "\r\n", + "
\r\n", + "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000003987240829346092)}{\\log(0.01/0.001)} - 1\\)

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Physical qubits242\r\n", + "

Number of physical qubits per logical qubit

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\r\n", + "

The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.

\n", + "\r\n", + "
Logical cycle time4us 400ns\r\n", + "

Duration of a logical cycle in nanoseconds

\n", + "\r\n", + "
\r\n", + "

The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.

\n", + "\r\n", + "
Logical qubit error rate3.00e-8\r\n", + "

Logical qubit error rate

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\r\n", + "

The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{11 + 1}{2}$

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Crossing prefactor0.03\r\n", + "

Crossing prefactor used in QEC scheme

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The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.

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Error correction threshold0.01\r\n", + "

Error correction threshold used in QEC scheme

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The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.

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Logical cycle time formula(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\r\n", + "

QEC scheme formula used to compute logical cycle time

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This is the formula that is used to compute the logical cycle time 4us 400ns.

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Physical qubits formula2 * codeDistance * codeDistance\r\n", + "

QEC scheme formula used to compute number of physical qubits per logical qubit

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This is the formula that is used to compute the number of physical qubits per logical qubits 242.

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Physical qubits9680\r\n", + "

Number of physical qubits for a single T factory

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This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.

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Runtime57us 200ns\r\n", + "

Runtime of a single T factory

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The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.

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Number of output T states per run1\r\n", + "

Number of output T states produced in a single run of T factory

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\r\n", + "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.

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Number of input T states per run30\r\n", + "

Number of physical input T states consumed in a single run of a T factory

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\r\n", + "

This value includes the physical input T states of all copies of the distillation unit in the first round.

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Distillation rounds1\r\n", + "

The number of distillation rounds

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\r\n", + "

This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.

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Distillation units per round2\r\n", + "

The number of units in each round of distillation

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\r\n", + "

This is the number of copies for the distillation units per round.

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Distillation units15-to-1 space efficient logical\r\n", + "

The types of distillation units

\n", + "\r\n", + "
\r\n", + "

These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.

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Distillation code distances11\r\n", + "

The code distance in each round of distillation

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\r\n", + "

This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.

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Number of physical qubits per round9680\r\n", + "

The number of physical qubits used in each round of distillation

\n", + "\r\n", + "
\r\n", + "

The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.

\n", + "\r\n", + "
Runtime per round57us 200ns\r\n", + "

The runtime of each distillation round

\n", + "\r\n", + "
\r\n", + "

The runtime of the T factory is the sum of the runtimes in all rounds.

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Logical T state error rate2.48e-7\r\n", + "

Logical T state error rate

\n", + "\r\n", + "
\r\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-6.

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Logical qubits (pre-layout)11\r\n", + "

Number of logical qubits in the input quantum program

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\r\n", + "

We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

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T gates0\r\n", + "

Number of T gates in the input quantum program

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\r\n", + "

This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.

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Rotation gates0\r\n", + "

Number of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.

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Rotation depth0\r\n", + "

Depth of rotation gates in the input quantum program

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\r\n", + "

This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.

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CCZ gates20\r\n", + "

Number of CCZ-gates in the input quantum program

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\r\n", + "

This is the number of CCZ gates.

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CCiX gates80\r\n", + "

Number of CCiX-gates in the input quantum program

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\r\n", + "

This is the number of CCiX gates, which applies \\(-iX\\) controlled on two control qubits [1212.5069].

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Measurement operations80\r\n", + "

Number of single qubit measurements in the input quantum program

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This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.

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\r\n", + " \r\n", + " Assumed error budget\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Total error budget1.00e-3\r\n", + "

Total error budget for the algorithm

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The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget \\(\\epsilon = \\epsilon_{\\log} + \\epsilon_{\\rm dis} + \\epsilon_{\\rm syn}\\) is uniformly distributed and applies to errors \\(\\epsilon_{\\log}\\) to implement logical qubits, an error budget \\(\\epsilon_{\\rm dis}\\) to produce T states through distillation, and an error budget \\(\\epsilon_{\\rm syn}\\) to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets \\(\\epsilon_{\\rm dis}\\) and \\(\\epsilon_{\\rm syn}\\) are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.

\n", + "\r\n", + "
Logical error probability5.00e-4\r\n", + "

Probability of at least one logical error

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This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

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T distillation error probability5.00e-4\r\n", + "

Probability of at least one faulty T distillation

\n", + "\r\n", + "
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This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
Rotation synthesis error probability0.00e0\r\n", + "

Probability of at least one failed rotation synthesis

\n", + "\r\n", + "
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This is one third of the total error budget 1.00e-3.

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\r\n", + " \r\n", + " Physical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Qubit namequbit_gate_ns_e3\r\n", + "

Some descriptive name for the qubit model

\n", + "\r\n", + "
\r\n", + "

You can load pre-defined qubit parameters by using the names qubit_gate_ns_e3, qubit_gate_ns_e4, qubit_gate_us_e3, qubit_gate_us_e4, qubit_maj_ns_e4, or qubit_maj_ns_e6. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).

\n", + "\r\n", + "
Instruction setGateBased\r\n", + "

Underlying qubit technology (gate-based or Majorana)

\n", + "\r\n", + "
\r\n", + "

When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either gate-based or Majorana. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.

\n", + "\r\n", + "
Single-qubit measurement time100 ns\r\n", + "

Operation time for single-qubit measurement (t_meas) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.

\n", + "\r\n", + "
Single-qubit gate time50 ns\r\n", + "

Operation time for single-qubit gate (t_gate) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.

\n", + "\r\n", + "
Two-qubit gate time50 ns\r\n", + "

Operation time for two-qubit gate in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.

\n", + "\r\n", + "
T gate time50 ns\r\n", + "

Operation time for a T gate

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to execute a T gate.

\n", + "\r\n", + "
Single-qubit measurement error rate0.001\r\n", + "

Error rate for single-qubit measurement

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit measurement in the Pauli basis may fail.

\n", + "\r\n", + "
Single-qubit error rate0.001\r\n", + "

Error rate for single-qubit Clifford gate (p)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.

\n", + "\r\n", + "
Two-qubit error rate0.001\r\n", + "

Error rate for two-qubit Clifford gate

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.

\n", + "\r\n", + "
T gate error rate0.001\r\n", + "

Error rate to prepare single-qubit T state or apply a T gate (p_T)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which executing a single T gate may fail.

\n", + "\r\n", + "
\n", + "
\r\n", + " Assumptions\r\n", + "
    \n", + "

  • More details on the following lists of assumptions can be found in the paper Accessing requirements for scaling quantum computers and their applications.

    \n", + "
    • \n", + "

  • Uniform independent physical noise. We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.

    \n", + "
    • \n", + "

  • Efficient classical computation. We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.

    \n", + "
    • \n", + "

  • Extraction circuits for planar quantum ISA. We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).

    \n", + "
    • \n", + "

  • Uniform independent logical noise. We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.

    \n", + "
    • \n", + "

  • Negligible Clifford costs for synthesis. We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.

    \n", + "
    • \n", + "

  • Smooth magic state consumption rate. We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.

    \n", + "
    • \n", + "
\n" + ], + "text/plain": [ + "{'errorBudget': {'logical': 0.0005, 'rotations': 0.0, 'tstates': 0.0005},\n", + " 'jobParams': {'errorBudget': 0.001,\n", + " 'qecScheme': {'crossingPrefactor': 0.03,\n", + " 'errorCorrectionThreshold': 0.01,\n", + " 'logicalCycleTime': '(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance',\n", + " 'name': 'surface_code',\n", + " 'physicalQubitsPerLogicalQubit': '2 * codeDistance * codeDistance'},\n", + " 'qubitParams': {'instructionSet': 'GateBased',\n", + " 'name': 'qubit_gate_ns_e3',\n", + " 'oneQubitGateErrorRate': 0.001,\n", + " 'oneQubitGateTime': '50 ns',\n", + " 'oneQubitMeasurementErrorRate': 0.001,\n", + " 'oneQubitMeasurementTime': '100 ns',\n", + " 'tGateErrorRate': 0.001,\n", + " 'tGateTime': '50 ns',\n", + " 'twoQubitGateErrorRate': 0.001,\n", + " 'twoQubitGateTime': '50 ns'}},\n", + " 'logicalCounts': {'ccixCount': 80,\n", + " 'cczCount': 20,\n", + " 'measurementCount': 80,\n", + " 'numQubits': 11,\n", + " 'rotationCount': 0,\n", + " 'rotationDepth': 0,\n", + " 'tCount': 0},\n", + " 'logicalQubit': {'codeDistance': 11,\n", + " 'logicalCycleTime': 4400.0,\n", + " 'logicalErrorRate': 3.000000000000002e-08,\n", + " 'physicalQubits': 242},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 380,\n", + " 'algorithmicLogicalQubits': 33,\n", + " 'cliffordErrorRate': 0.001,\n", + " 'logicalDepth': 380,\n", + " 'numTfactories': 14,\n", + " 'numTfactoryRuns': 29,\n", + " 'numTsPerRotation': None,\n", + " 'numTstates': 400,\n", + " 'physicalQubitsForAlgorithm': 7986,\n", + " 'physicalQubitsForTfactories': 135520,\n", + " 'requiredLogicalQubitErrorRate': 3.987240829346092e-08,\n", + " 'requiredLogicalTstateErrorRate': 1.25e-06},\n", + " 'physicalQubits': 143506,\n", + " 'runtime': 1672000},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '11',\n", + " 'errorBudget': '1.00e-3',\n", + " 'errorBudgetLogical': '5.00e-4',\n", + " 'errorBudgetRotations': '0.00e0',\n", + " 'errorBudgetTstates': '5.00e-4',\n", + " 'logicalCycleTime': '4us 400ns',\n", + " 'logicalErrorRate': '3.00e-8',\n", + " 'numTsPerRotation': 'No rotations in algorithm',\n", + " 'numUnitsPerRound': '2',\n", + " 'physicalQubitsForTfactoriesPercentage': '94.44 %',\n", + " 'physicalQubitsPerRound': '9680',\n", + " 'requiredLogicalQubitErrorRate': '3.99e-8',\n", + " 'requiredLogicalTstateErrorRate': '1.25e-6',\n", + " 'runtime': '1ms 672us',\n", + " 'tfactoryRuntime': '57us 200ns',\n", + " 'tfactoryRuntimePerRound': '57us 200ns',\n", + " 'tstateLogicalErrorRate': '2.48e-7',\n", + " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", + " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", + " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", + " '**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.',\n", + " '**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).',\n", + " '**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.',\n", + " '**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.',\n", + " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", + " 'groups': [{'alwaysVisible': True,\n", + " 'entries': [{'description': 'Number of physical qubits',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 7986 physical qubits to implement the algorithm logic, and 135520 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'physicalCounts/physicalQubits'},\n", + " {'description': 'Total runtime',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 380 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/runtime'}],\n", + " 'title': 'Physical resource estimates'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 11$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 33$ logical qubits.',\n", + " 'label': 'Logical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", + " {'description': 'Number of logical cycles for the algorithm',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 80 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 20 CCZ and 80 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'label': 'Algorithmic depth',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", + " {'description': 'Number of logical cycles performed',\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 380. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'label': 'Logical depth',\n", + " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", + " {'description': 'Number of T states consumed by the algorithm',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 20 CCZ and 80 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'label': 'Number of T states',\n", + " 'path': 'physicalCounts/breakdown/numTstates'},\n", + " {'description': \"Number of T factories capable of producing the demanded 400 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{400\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 1ms 672us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " 'label': 'Number of T factories',\n", + " 'path': 'physicalCounts/breakdown/numTfactories'},\n", + " {'description': 'Number of times all T factories are invoked',\n", + " 'explanation': 'In order to prepare the 400 T states, the 14 copies of the T factory are repeatedly invoked 29 times.',\n", + " 'label': 'Number of T factory invocations',\n", + " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", + " {'description': 'Number of physical qubits for the algorithm after layout',\n", + " 'explanation': 'The 7986 are the product of the 33 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.',\n", + " 'label': 'Physical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", + " {'description': 'Number of physical qubits for the T factories',\n", + " 'explanation': 'Each T factory requires 9680 physical qubits and we run 14 in parallel, therefore we need $135520 = 9680 \\\\cdot 14$ qubits.',\n", + " 'label': 'Physical T factory qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", + " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 380.',\n", + " 'label': 'Required logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", + " {'description': 'The minimum T state error rate required for distilled T states',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 400.',\n", + " 'label': 'Required logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", + " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", + " 'explanation': 'The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.',\n", + " 'label': 'Number of T states per rotation',\n", + " 'path': 'physicalCountsFormatted/numTsPerRotation'}],\n", + " 'title': 'Resource estimates breakdown'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Name of QEC scheme',\n", + " 'explanation': 'You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.',\n", + " 'label': 'QEC scheme',\n", + " 'path': 'jobParams/qecScheme/name'},\n", + " {'description': 'Required code distance for error correction',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000003987240829346092)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'label': 'Code distance',\n", + " 'path': 'logicalQubit/codeDistance'},\n", + " {'description': 'Number of physical qubits per logical qubit',\n", + " 'explanation': 'The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'logicalQubit/physicalQubits'},\n", + " {'description': 'Duration of a logical cycle in nanoseconds',\n", + " 'explanation': 'The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.',\n", + " 'label': 'Logical cycle time',\n", + " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", + " {'description': 'Logical qubit error rate',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$',\n", + " 'label': 'Logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", + " {'description': 'Crossing prefactor used in QEC scheme',\n", + " 'explanation': 'The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.',\n", + " 'label': 'Crossing prefactor',\n", + " 'path': 'jobParams/qecScheme/crossingPrefactor'},\n", + " {'description': 'Error correction threshold used in QEC scheme',\n", + " 'explanation': 'The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.',\n", + " 'label': 'Error correction threshold',\n", + " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", + " {'description': 'QEC scheme formula used to compute logical cycle time',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 4us 400ns.',\n", + " 'label': 'Logical cycle time formula',\n", + " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", + " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 242.',\n", + " 'label': 'Physical qubits formula',\n", + " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", + " 'title': 'Logical qubit parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of physical qubits for a single T factory',\n", + " 'explanation': 'This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'tfactory/physicalQubits'},\n", + " {'description': 'Runtime of a single T factory',\n", + " 'explanation': 'The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", + " {'description': 'Number of output T states produced in a single run of T factory',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.',\n", + " 'label': 'Number of output T states per run',\n", + " 'path': 'tfactory/numTstates'},\n", + " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", + " 'explanation': 'This value includes the physical input T states of all copies of the distillation unit in the first round.',\n", + " 'label': 'Number of input T states per run',\n", + " 'path': 'tfactory/numInputTstates'},\n", + " {'description': 'The number of distillation rounds',\n", + " 'explanation': 'This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.',\n", + " 'label': 'Distillation rounds',\n", + " 'path': 'tfactory/numRounds'},\n", + " {'description': 'The number of units in each round of distillation',\n", + " 'explanation': 'This is the number of copies for the distillation units per round.',\n", + " 'label': 'Distillation units per round',\n", + " 'path': 'physicalCountsFormatted/numUnitsPerRound'},\n", + " {'description': 'The types of distillation units',\n", + " 'explanation': 'These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.',\n", + " 'label': 'Distillation units',\n", + " 'path': 'physicalCountsFormatted/unitNamePerRound'},\n", + " {'description': 'The code distance in each round of distillation',\n", + " 'explanation': 'This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.',\n", + " 'label': 'Distillation code distances',\n", + " 'path': 'physicalCountsFormatted/codeDistancePerRound'},\n", + " {'description': 'The number of physical qubits used in each round of distillation',\n", + " 'explanation': 'The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.',\n", + " 'label': 'Number of physical qubits per round',\n", + " 'path': 'physicalCountsFormatted/physicalQubitsPerRound'},\n", + " {'description': 'The runtime of each distillation round',\n", + " 'explanation': 'The runtime of the T factory is the sum of the runtimes in all rounds.',\n", + " 'label': 'Runtime per round',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", + " {'description': 'Logical T state error rate',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-6.',\n", + " 'label': 'Logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", + " 'title': 'T factory parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", + " 'explanation': 'We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'label': 'Logical qubits (pre-layout)',\n", + " 'path': 'logicalCounts/numQubits'},\n", + " {'description': 'Number of T gates in the input quantum program',\n", + " 'explanation': 'This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.',\n", + " 'label': 'T gates',\n", + " 'path': 'logicalCounts/tCount'},\n", + " {'description': 'Number of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.',\n", + " 'label': 'Rotation gates',\n", + " 'path': 'logicalCounts/rotationCount'},\n", + " {'description': 'Depth of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.',\n", + " 'label': 'Rotation depth',\n", + " 'path': 'logicalCounts/rotationDepth'},\n", + " {'description': 'Number of CCZ-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCZ gates.',\n", + " 'label': 'CCZ gates',\n", + " 'path': 'logicalCounts/cczCount'},\n", + " {'description': 'Number of CCiX-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].',\n", + " 'label': 'CCiX gates',\n", + " 'path': 'logicalCounts/ccixCount'},\n", + " {'description': 'Number of single qubit measurements in the input quantum program',\n", + " 'explanation': 'This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.',\n", + " 'label': 'Measurement operations',\n", + " 'path': 'logicalCounts/measurementCount'}],\n", + " 'title': 'Pre-layout logical resources'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Total error budget for the algorithm',\n", + " 'explanation': \"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\n", + " 'label': 'Total error budget',\n", + " 'path': 'physicalCountsFormatted/errorBudget'},\n", + " {'description': 'Probability of at least one logical error',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'Logical error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetLogical'},\n", + " {'description': 'Probability of at least one faulty T distillation',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'T distillation error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetTstates'},\n", + " {'description': 'Probability of at least one failed rotation synthesis',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3.',\n", + " 'label': 'Rotation synthesis error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetRotations'}],\n", + " 'title': 'Assumed error budget'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Some descriptive name for the qubit model',\n", + " 'explanation': 'You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).',\n", + " 'label': 'Qubit name',\n", + " 'path': 'jobParams/qubitParams/name'},\n", + " {'description': 'Underlying qubit technology (gate-based or Majorana)',\n", + " 'explanation': 'When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.',\n", + " 'label': 'Instruction set',\n", + " 'path': 'jobParams/qubitParams/instructionSet'},\n", + " {'description': 'Operation time for single-qubit measurement (t_meas) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.',\n", + " 'label': 'Single-qubit measurement time',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementTime'},\n", + " {'description': 'Operation time for single-qubit gate (t_gate) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.',\n", + " 'label': 'Single-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateTime'},\n", + " {'description': 'Operation time for two-qubit gate in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.',\n", + " 'label': 'Two-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateTime'},\n", + " {'description': 'Operation time for a T gate',\n", + " 'explanation': 'This is the operation time in nanoseconds to execute a T gate.',\n", + " 'label': 'T gate time',\n", + " 'path': 'jobParams/qubitParams/tGateTime'},\n", + " {'description': 'Error rate for single-qubit measurement',\n", + " 'explanation': 'This is the probability in which a single-qubit measurement in the Pauli basis may fail.',\n", + " 'label': 'Single-qubit measurement error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementErrorRate'},\n", + " {'description': 'Error rate for single-qubit Clifford gate (p)',\n", + " 'explanation': 'This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.',\n", + " 'label': 'Single-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateErrorRate'},\n", + " {'description': 'Error rate for two-qubit Clifford gate',\n", + " 'explanation': 'This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.',\n", + " 'label': 'Two-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateErrorRate'},\n", + " {'description': 'Error rate to prepare single-qubit T state or apply a T gate (p_T)',\n", + " 'explanation': 'This is the probability in which executing a single T gate may fail.',\n", + " 'label': 'T gate error rate',\n", + " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", + " 'title': 'Physical qubit parameters'}]},\n", + " 'status': 'success',\n", + " 'tfactory': {'codeDistancePerRound': [11],\n", + " 'logicalErrorRate': 2.480000000000001e-07,\n", + " 'numInputTstates': 30,\n", + " 'numRounds': 1,\n", + " 'numTstates': 1,\n", + " 'numUnitsPerRound': [2],\n", + " 'physicalQubits': 9680,\n", + " 'physicalQubitsPerRound': [9680],\n", + " 'runtime': 57200.0,\n", + " 'runtimePerRound': [57200.0],\n", + " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", "# result = qsharp.azure.output(\"...\")\n", @@ -364,7 +4900,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 23, "metadata": { "collapsed": false, "jupyter": { @@ -391,7 +4927,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 24, "metadata": { "collapsed": false, "jupyter": { @@ -404,10 +4940,44 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Logical algorithmic qubits = 33\n", + "Algorithmic depth = 380\n", + "Score = 12540\n" + ] + }, + { + "data": { + "text/plain": [ + "12540" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "evaluate_results(result)" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -415,9 +4985,9 @@ "name": "python3" }, "kernelspec": { - "display_name": "Python 3 [Default]", + "display_name": "Python 3 [Q#]", "language": "python", - "name": "python3" + "name": "python3_qsharp_b54crn" }, "language_info": { "codemirror_mode": { diff --git a/.ipynb_checkpoints/iQuHack-challenge-2023-task6-checkpoint.ipynb b/.ipynb_checkpoints/iQuHack-challenge-2023-task6-checkpoint.ipynb index 7babc33..330ddb9 100644 --- a/.ipynb_checkpoints/iQuHack-challenge-2023-task6-checkpoint.ipynb +++ b/.ipynb_checkpoints/iQuHack-challenge-2023-task6-checkpoint.ipynb @@ -67,7 +67,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 14, "metadata": { "collapsed": false, "jupyter": { @@ -89,7 +89,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 15, "metadata": { "collapsed": false, "jupyter": { @@ -111,7 +111,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 16, "metadata": { "collapsed": false, "jupyter": { @@ -148,7 +148,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 27, "metadata": { "collapsed": false, "jupyter": { @@ -196,7 +196,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 28, "metadata": {}, "outputs": [], "source": [ @@ -205,7 +205,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 29, "metadata": { "collapsed": false, "jupyter": { @@ -262,7 +262,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 30, "metadata": { "collapsed": false, "jupyter": { @@ -307,12 +307,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -332,12 +332,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -357,12 +357,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -382,12 +382,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -407,12 +407,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -432,12 +432,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -457,12 +457,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -482,12 +482,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -507,12 +507,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -532,12 +532,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -557,12 +557,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -582,12 +582,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -607,12 +607,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -632,12 +632,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -657,12 +657,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -682,12 +682,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -707,12 +707,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -732,12 +732,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -757,12 +757,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -782,12 +782,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -807,12 +807,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", "

\r\n", " \r\n", " \r\n", @@ -832,12 +832,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -857,12 +857,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -882,12 +882,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -907,12 +907,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -932,12 +932,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", "

\r\n", " \r\n", " \r\n", @@ -957,12 +957,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -982,12 +982,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1007,12 +1007,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1032,12 +1032,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

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\r\n", " \r\n", " \r\n", @@ -1057,12 +1057,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1107,12 +1107,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1157,12 +1157,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1182,12 +1182,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1207,12 +1207,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -1232,12 +1232,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -1257,12 +1257,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -1282,12 +1282,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -1457,12 +1457,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -1557,12 +1557,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", "

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\r\n", " \r\n", " \r\n", @@ -1882,12 +1882,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1907,12 +1907,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1932,12 +1932,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1957,12 +1957,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1982,12 +1982,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2007,12 +2007,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2032,12 +2032,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2057,12 +2057,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2082,12 +2082,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2107,12 +2107,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2132,12 +2132,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2157,12 +2157,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2182,12 +2182,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2207,12 +2207,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2232,12 +2232,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2257,12 +2257,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2282,12 +2282,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2307,12 +2307,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2332,12 +2332,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2357,12 +2357,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2382,12 +2382,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2407,12 +2407,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2432,12 +2432,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2457,12 +2457,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2482,12 +2482,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2507,12 +2507,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2532,12 +2532,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2557,12 +2557,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2582,12 +2582,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2607,12 +2607,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2632,12 +2632,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2657,12 +2657,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2682,12 +2682,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2707,12 +2707,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2732,12 +2732,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2757,12 +2757,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2782,12 +2782,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2807,12 +2807,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2832,12 +2832,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2857,12 +2857,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2882,12 +2882,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2907,12 +2907,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2932,12 +2932,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2957,12 +2957,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2982,12 +2982,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3007,12 +3007,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3032,12 +3032,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3057,12 +3057,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3082,12 +3082,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3107,12 +3107,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3132,12 +3132,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3157,12 +3157,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3182,12 +3182,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3207,12 +3207,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3232,12 +3232,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3257,12 +3257,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3282,12 +3282,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3307,12 +3307,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3332,12 +3332,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3357,12 +3357,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3382,12 +3382,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3407,12 +3407,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3432,12 +3432,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3457,12 +3457,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3482,12 +3482,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3507,12 +3507,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3532,12 +3532,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3557,12 +3557,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3582,12 +3582,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3607,12 +3607,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3632,12 +3632,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3657,12 +3657,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3682,12 +3682,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3707,12 +3707,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3732,12 +3732,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3757,12 +3757,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3782,12 +3782,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3807,12 +3807,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3832,12 +3832,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3857,12 +3857,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3882,12 +3882,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3907,12 +3907,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3932,12 +3932,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3957,12 +3957,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3982,12 +3982,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4007,12 +4007,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4032,12 +4032,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4057,12 +4057,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4082,12 +4082,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4107,12 +4107,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4132,12 +4132,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4157,12 +4157,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4182,12 +4182,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4207,12 +4207,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4232,12 +4232,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4257,12 +4257,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4282,12 +4282,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4307,12 +4307,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4332,12 +4332,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4357,12 +4357,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4382,12 +4382,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4407,12 +4407,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4432,12 +4432,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4457,12 +4457,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4482,12 +4482,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4507,12 +4507,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4532,12 +4532,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4557,12 +4557,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4582,12 +4582,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4607,12 +4607,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4632,12 +4632,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4657,12 +4657,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4682,12 +4682,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4707,12 +4707,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4732,12 +4732,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4757,12 +4757,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4782,12 +4782,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4807,12 +4807,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4832,12 +4832,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4857,12 +4857,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4882,12 +4882,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4907,12 +4907,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4932,12 +4932,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4957,12 +4957,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4982,12 +4982,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5007,12 +5007,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5032,12 +5032,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5057,12 +5057,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5082,12 +5082,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5107,12 +5107,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5132,12 +5132,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5157,12 +5157,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5182,12 +5182,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5207,12 +5207,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5232,12 +5232,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5257,12 +5257,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5282,12 +5282,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5307,12 +5307,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5332,12 +5332,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5357,12 +5357,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5382,12 +5382,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5407,12 +5407,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5432,12 +5432,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5457,12 +5457,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5482,12 +5482,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5507,12 +5507,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5532,12 +5532,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5557,12 +5557,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5582,12 +5582,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5607,12 +5607,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5632,12 +5632,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5657,12 +5657,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5682,12 +5682,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5707,12 +5707,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5732,12 +5732,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5757,12 +5757,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5782,12 +5782,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5807,12 +5807,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5832,12 +5832,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5857,12 +5857,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5882,12 +5882,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5907,12 +5907,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5932,12 +5932,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5957,12 +5957,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5982,12 +5982,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6007,12 +6007,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6032,12 +6032,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6057,12 +6057,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6082,12 +6082,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6107,12 +6107,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6132,12 +6132,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6157,12 +6157,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6182,12 +6182,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6207,12 +6207,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6232,12 +6232,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6257,12 +6257,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6282,12 +6282,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6307,12 +6307,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6332,12 +6332,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6357,12 +6357,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6382,12 +6382,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6407,12 +6407,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6432,12 +6432,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6457,12 +6457,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6482,12 +6482,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6507,12 +6507,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6532,12 +6532,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6557,12 +6557,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6582,12 +6582,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6607,12 +6607,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6632,12 +6632,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6657,12 +6657,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6682,12 +6682,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6966,7 +6966,7 @@ "()" ] }, - "execution_count": 7, + "execution_count": 30, "metadata": {}, "output_type": "execute_result" } @@ -6995,7 +6995,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 31, "metadata": { "collapsed": false, "jupyter": { @@ -7029,8 +7029,8 @@ { "data": { "text/plain": [ - "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 177740},\n", - " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 321366},\n", + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 178621},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 409767},\n", " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 4},\n", " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", @@ -7038,14 +7038,14 @@ " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", - " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 166},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 168},\n", " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", - " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 166},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 168},\n", " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", @@ -7053,7 +7053,7 @@ " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" ] }, - "execution_count": 8, + "execution_count": 31, "metadata": {}, "output_type": "execute_result" } @@ -7069,7 +7069,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 32, "metadata": { "collapsed": false, "jupyter": { @@ -7097,7 +7097,7 @@ "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" ] }, - "execution_count": 9, + "execution_count": 32, "metadata": {}, "output_type": "execute_result" } @@ -7108,7 +7108,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 33, "metadata": { "collapsed": false, "jupyter": { @@ -7129,9 +7129,10 @@ "Submitting Task6_ResourceEstimationWrapper to target microsoft.estimator...\n", "Job successfully submitted.\n", " Job name: RE for the task 6\n", - " Job ID: 1678631d-016c-4332-ba1f-61fcb3b081b9\n", + " Job ID: 51c97eab-212e-45b6-9f03-7489fad62c36\n", "Waiting up to 30 seconds for Azure Quantum job to complete...\n", - "[12:40:10 PM] Current job status: Succeeded\n" + "[1:15:38 PM] Current job status: Executing\n", + "[1:15:43 PM] Current job status: Succeeded\n" ] } ], @@ -7142,7 +7143,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 34, "metadata": { "collapsed": false, "jupyter": { @@ -7158,7 +7159,7 @@ "outputs": [ { "data": { - "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":6,\"cczCount\":2,\"measurementCount\":6,\"numQubits\":12,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":9,\"logicalCycleTime\":3600.0,\"logicalErrorRate\":3.0000000000000015E-07,\"physicalQubits\":162},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":30,\"algorithmicLogicalQubits\":35,\"cliffordErrorRate\":0.001,\"logicalDepth\":30,\"numTfactories\":14,\"numTfactoryRuns\":3,\"numTsPerRotation\":null,\"numTstates\":32,\"physicalQubitsForAlgorithm\":5670,\"physicalQubitsForTfactories\":90720,\"requiredLogicalQubitErrorRate\":4.761904761904762E-07,\"requiredLogicalTstateErrorRate\":1.5625E-05},\"physicalQubits\":96390,\"runtime\":108000},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"3us 600ns\",\"logicalErrorRate\":\"3.00e-7\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"94.12 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"4.76e-7\",\"requiredLogicalTstateErrorRate\":\"1.56e-5\",\"runtime\":\"108us\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 5670 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 30 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 12$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 35$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 6 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 2 CCZ and 6 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 30. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 2 CCZ and 6 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 32 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{32\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 108us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 32 T states, the 14 copies of the T factory are repeatedly invoked 3 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 5670 are the product of the 35 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\\\cdot 14$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 35 logical qubits and the total cycle count 30.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 32.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. 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This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 3us 600ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 162.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.56e-5.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 35 from this number by assuming to align them in a 2D grid. 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Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. 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"{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":96,\"cczCount\":16,\"measurementCount\":96,\"numQubits\":15,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":13,\"logicalCycleTime\":5200.0,\"logicalErrorRate\":3.000000000000002E-09,\"physicalQubits\":338},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":432,\"algorithmicLogicalQubits\":42,\"cliffordErrorRate\":0.001,\"logicalDepth\":432,\"numTfactories\":12,\"numTfactoryRuns\":38,\"numTsPerRotation\":null,\"numTstates\":448,\"physicalQubitsForAlgorithm\":14196,\"physicalQubitsForTfactories\":116160,\"requiredLogicalQubitErrorRate\":2.755731922398589E-08,\"requiredLogicalTstateErrorRate\":1.1160714285714287E-06},\"physicalQubits\":130356,\"runtime\":2246400},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"11\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"5us 200ns\",\"logicalErrorRate\":\"3.00e-9\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"89.11 %\",\"physicalQubitsPerRound\":\"9680\",\"requiredLogicalQubitErrorRate\":\"2.76e-8\",\"requiredLogicalTstateErrorRate\":\"1.12e-6\",\"runtime\":\"2ms 246us 400ns\",\"tfactoryRuntime\":\"57us 200ns\",\"tfactoryRuntimePerRound\":\"57us 200ns\",\"tstateLogicalErrorRate\":\"2.48e-7\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 14196 physical qubits to implement the algorithm logic, and 116160 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (5us 200ns) multiplied by the 432 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 15$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 42$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 96 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 16 CCZ and 96 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 432. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 16 CCZ and 96 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 448 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{448\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 2ms 246us 400ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 448 T states, the 12 copies of the T factory are repeatedly invoked 38 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 14196 are the product of the 42 logical qubits after layout and the 338 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 9680 physical qubits and we run 12 in parallel, therefore we need $116160 = 9680 \\\\cdot 12$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 42 logical qubits and the total cycle count 432.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 448.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000002755731922398589)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{13 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 5us 200ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 338.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.12e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 42 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[11],\"logicalErrorRate\":2.480000000000001E-07,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":9680,\"physicalQubitsPerRound\":[9680],\"runtime\":57200.0,\"runtimePerRound\":[57200.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", "text/html": [ "\r\n", "
\r\n", @@ -7170,24 +7171,24 @@ "\r\n", " \r\n", " Physical qubits\r\n", - " 96390\r\n", + " 130356\r\n", " \r\n", "

Number of physical qubits

\n", "\r\n", "
\r\n", - "

This value represents the total number of physical qubits, which is the sum of 5670 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

\n", + "

This value represents the total number of physical qubits, which is the sum of 14196 physical qubits to implement the algorithm logic, and 116160 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Runtime\r\n", - " 108us\r\n", + " 2ms 246us 400ns\r\n", " \r\n", "

Total runtime

\n", "\r\n", "
\r\n", - "

This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 30 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

\n", + "

This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (5us 200ns) multiplied by the 432 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

\n", "\r\n", " \r\n", " \n", @@ -7202,120 +7203,120 @@ "\r\n", " \r\n", " Logical algorithmic qubits\r\n", - " 35\r\n", + " 42\r\n", " \r\n", "

Number of logical qubits for the algorithm after layout

\n", "\r\n", "
\r\n", - "

Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 12\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 35$ logical qubits.

\n", + "

Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 15\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 42$ logical qubits.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Algorithmic depth\r\n", - " 30\r\n", + " 432\r\n", " \r\n", "

Number of logical cycles for the algorithm

\n", "\r\n", "
\r\n", - "

To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 6 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 2 CCZ and 6 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

\n", + "

To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 96 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 16 CCZ and 96 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Logical depth\r\n", - " 30\r\n", + " 432\r\n", " \r\n", "

Number of logical cycles performed

\n", "\r\n", "
\r\n", - "

This number is usually equal to the logical depth of the algorithm, which is 30. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", + "

This number is usually equal to the logical depth of the algorithm, which is 432. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Number of T states\r\n", - " 32\r\n", + " 448\r\n", " \r\n", "

Number of T states consumed by the algorithm

\n", "\r\n", "
\r\n", - "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 2 CCZ and 6 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", + "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 16 CCZ and 96 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Number of T factories\r\n", - " 14\r\n", + " 12\r\n", " \r\n", - "

Number of T factories capable of producing the demanded 32 T states during the algorithm's runtime

\n", + "

Number of T factories capable of producing the demanded 448 T states during the algorithm's runtime

\n", "\r\n", "
\r\n", - "

The total number of T factories 14 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{32\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 108us\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", + "

The total number of T factories 12 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{448\\;\\text{T states} \\cdot 57us 200ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 2ms 246us 400ns\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Number of T factory invocations\r\n", - " 3\r\n", + " 38\r\n", " \r\n", "

Number of times all T factories are invoked

\n", "\r\n", "
\r\n", - "

In order to prepare the 32 T states, the 14 copies of the T factory are repeatedly invoked 3 times.

\n", + "

In order to prepare the 448 T states, the 12 copies of the T factory are repeatedly invoked 38 times.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Physical algorithmic qubits\r\n", - " 5670\r\n", + " 14196\r\n", " \r\n", "

Number of physical qubits for the algorithm after layout

\n", "\r\n", "
\r\n", - "

The 5670 are the product of the 35 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.

\n", + "

The 14196 are the product of the 42 logical qubits after layout and the 338 physical qubits that encode a single logical qubit.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Physical T factory qubits\r\n", - " 90720\r\n", + " 116160\r\n", " \r\n", "

Number of physical qubits for the T factories

\n", "\r\n", "
\r\n", - "

Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\cdot 14$ qubits.

\n", + "

Each T factory requires 9680 physical qubits and we run 12 in parallel, therefore we need $116160 = 9680 \\cdot 12$ qubits.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Required logical qubit error rate\r\n", - " 4.76e-7\r\n", + " 2.76e-8\r\n", " \r\n", "

The minimum logical qubit error rate required to run the algorithm within the error budget

\n", "\r\n", "
\r\n", - "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 35 logical qubits and the total cycle count 30.

\n", + "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 42 logical qubits and the total cycle count 432.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Required logical T state error rate\r\n", - " 1.56e-5\r\n", + " 1.12e-6\r\n", " \r\n", "

The minimum T state error rate required for distilled T states

\n", "\r\n", "
\r\n", - "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 32.

\n", + "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 448.

\n", "\r\n", " \r\n", " \n", @@ -7354,19 +7355,19 @@ "\r\n", " \r\n", " Code distance\r\n", - " 9\r\n", + " 13\r\n", " \r\n", "

Required code distance for error correction

\n", "\r\n", "
\r\n", - "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.0000004761904761904762)}{\\log(0.01/0.001)} - 1\\)

\n", + "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000002755731922398589)}{\\log(0.01/0.001)} - 1\\)

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Physical qubits\r\n", - " 162\r\n", + " 338\r\n", " \r\n", "

Number of physical qubits per logical qubit

\n", "\r\n", @@ -7378,7 +7379,7 @@ "\r\n", " \r\n", " Logical cycle time\r\n", - " 3us 600ns\r\n", + " 5us 200ns\r\n", " \r\n", "

Duration of a logical cycle in nanoseconds

\n", "\r\n", @@ -7390,12 +7391,12 @@ "\r\n", " \r\n", " Logical qubit error rate\r\n", - " 3.00e-7\r\n", + " 3.00e-9\r\n", " \r\n", "

Logical qubit error rate

\n", "\r\n", "
\r\n", - "

The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{9 + 1}{2}$

\n", + "

The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{13 + 1}{2}$

\n", "\r\n", " \r\n", " \n", @@ -7431,7 +7432,7 @@ "

QEC scheme formula used to compute logical cycle time

\n", "\r\n", "
\r\n", - "

This is the formula that is used to compute the logical cycle time 3us 600ns.

\n", + "

This is the formula that is used to compute the logical cycle time 5us 200ns.

\n", "\r\n", " \r\n", " \n", @@ -7443,7 +7444,7 @@ "

QEC scheme formula used to compute number of physical qubits per logical qubit

\n", "\r\n", "
\r\n", - "

This is the formula that is used to compute the number of physical qubits per logical qubits 162.

\n", + "

This is the formula that is used to compute the number of physical qubits per logical qubits 338.

\n", "\r\n", " \r\n", " \n", @@ -7458,7 +7459,7 @@ "\r\n", " \r\n", " Physical qubits\r\n", - " 6480\r\n", + " 9680\r\n", " \r\n", "

Number of physical qubits for a single T factory

\n", "\r\n", @@ -7470,7 +7471,7 @@ "\r\n", " \r\n", " Runtime\r\n", - " 46us 800ns\r\n", + " 57us 200ns\r\n", " \r\n", "

Runtime of a single T factory

\n", "\r\n", @@ -7487,7 +7488,7 @@ "

Number of output T states produced in a single run of T factory

\n", "\r\n", "
\r\n", - "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.

\n", + "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.

\n", "\r\n", " \r\n", " \n", @@ -7542,7 +7543,7 @@ "\r\n", " \r\n", " Distillation code distances\r\n", - " 9\r\n", + " 11\r\n", " \r\n", "

The code distance in each round of distillation

\n", "\r\n", @@ -7554,7 +7555,7 @@ "\r\n", " \r\n", " Number of physical qubits per round\r\n", - " 6480\r\n", + " 9680\r\n", " \r\n", "

The number of physical qubits used in each round of distillation

\n", "\r\n", @@ -7566,7 +7567,7 @@ "\r\n", " \r\n", " Runtime per round\r\n", - " 46us 800ns\r\n", + " 57us 200ns\r\n", " \r\n", "

The runtime of each distillation round

\n", "\r\n", @@ -7578,12 +7579,12 @@ "\r\n", " \r\n", " Logical T state error rate\r\n", - " 2.17e-6\r\n", + " 2.48e-7\r\n", " \r\n", "

Logical T state error rate

\n", "\r\n", "
\r\n", - "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.56e-5.

\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.12e-6.

\n", "\r\n", " \r\n", " \n", @@ -7598,12 +7599,12 @@ "\r\n", " \r\n", " Logical qubits (pre-layout)\r\n", - " 12\r\n", + " 15\r\n", " \r\n", "

Number of logical qubits in the input quantum program

\n", "\r\n", "
\r\n", - "

We determine 35 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", + "

We determine 42 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", "\r\n", " \r\n", " \n", @@ -7646,7 +7647,7 @@ "\r\n", " \r\n", " CCZ gates\r\n", - " 2\r\n", + " 16\r\n", " \r\n", "

Number of CCZ-gates in the input quantum program

\n", "\r\n", @@ -7658,7 +7659,7 @@ "\r\n", " \r\n", " CCiX gates\r\n", - " 6\r\n", + " 96\r\n", " \r\n", "

Number of CCiX-gates in the input quantum program

\n", "\r\n", @@ -7670,7 +7671,7 @@ "\r\n", " \r\n", " Measurement operations\r\n", - " 6\r\n", + " 96\r\n", " \r\n", "

Number of single qubit measurements in the input quantum program

\n", "\r\n", @@ -7901,48 +7902,48 @@ " 'tGateTime': '50 ns',\n", " 'twoQubitGateErrorRate': 0.001,\n", " 'twoQubitGateTime': '50 ns'}},\n", - " 'logicalCounts': {'ccixCount': 6,\n", - " 'cczCount': 2,\n", - " 'measurementCount': 6,\n", - " 'numQubits': 12,\n", + " 'logicalCounts': {'ccixCount': 96,\n", + " 'cczCount': 16,\n", + " 'measurementCount': 96,\n", + " 'numQubits': 15,\n", " 'rotationCount': 0,\n", " 'rotationDepth': 0,\n", " 'tCount': 0},\n", - " 'logicalQubit': {'codeDistance': 9,\n", - " 'logicalCycleTime': 3600.0,\n", - " 'logicalErrorRate': 3.0000000000000015e-07,\n", - " 'physicalQubits': 162},\n", - " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 30,\n", - " 'algorithmicLogicalQubits': 35,\n", + " 'logicalQubit': {'codeDistance': 13,\n", + " 'logicalCycleTime': 5200.0,\n", + " 'logicalErrorRate': 3.000000000000002e-09,\n", + " 'physicalQubits': 338},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 432,\n", + " 'algorithmicLogicalQubits': 42,\n", " 'cliffordErrorRate': 0.001,\n", - " 'logicalDepth': 30,\n", - " 'numTfactories': 14,\n", - " 'numTfactoryRuns': 3,\n", + " 'logicalDepth': 432,\n", + " 'numTfactories': 12,\n", + " 'numTfactoryRuns': 38,\n", " 'numTsPerRotation': None,\n", - " 'numTstates': 32,\n", - " 'physicalQubitsForAlgorithm': 5670,\n", - " 'physicalQubitsForTfactories': 90720,\n", - " 'requiredLogicalQubitErrorRate': 4.761904761904762e-07,\n", - " 'requiredLogicalTstateErrorRate': 1.5625e-05},\n", - " 'physicalQubits': 96390,\n", - " 'runtime': 108000},\n", - " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", + " 'numTstates': 448,\n", + " 'physicalQubitsForAlgorithm': 14196,\n", + " 'physicalQubitsForTfactories': 116160,\n", + " 'requiredLogicalQubitErrorRate': 2.755731922398589e-08,\n", + " 'requiredLogicalTstateErrorRate': 1.1160714285714287e-06},\n", + " 'physicalQubits': 130356,\n", + " 'runtime': 2246400},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '11',\n", " 'errorBudget': '1.00e-3',\n", " 'errorBudgetLogical': '5.00e-4',\n", " 'errorBudgetRotations': '0.00e0',\n", " 'errorBudgetTstates': '5.00e-4',\n", - " 'logicalCycleTime': '3us 600ns',\n", - " 'logicalErrorRate': '3.00e-7',\n", + " 'logicalCycleTime': '5us 200ns',\n", + " 'logicalErrorRate': '3.00e-9',\n", " 'numTsPerRotation': 'No rotations in algorithm',\n", " 'numUnitsPerRound': '2',\n", - " 'physicalQubitsForTfactoriesPercentage': '94.12 %',\n", - " 'physicalQubitsPerRound': '6480',\n", - " 'requiredLogicalQubitErrorRate': '4.76e-7',\n", - " 'requiredLogicalTstateErrorRate': '1.56e-5',\n", - " 'runtime': '108us',\n", - " 'tfactoryRuntime': '46us 800ns',\n", - " 'tfactoryRuntimePerRound': '46us 800ns',\n", - " 'tstateLogicalErrorRate': '2.17e-6',\n", + " 'physicalQubitsForTfactoriesPercentage': '89.11 %',\n", + " 'physicalQubitsPerRound': '9680',\n", + " 'requiredLogicalQubitErrorRate': '2.76e-8',\n", + " 'requiredLogicalTstateErrorRate': '1.12e-6',\n", + " 'runtime': '2ms 246us 400ns',\n", + " 'tfactoryRuntime': '57us 200ns',\n", + " 'tfactoryRuntimePerRound': '57us 200ns',\n", + " 'tstateLogicalErrorRate': '2.48e-7',\n", " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", @@ -7953,53 +7954,53 @@ " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", " 'groups': [{'alwaysVisible': True,\n", " 'entries': [{'description': 'Number of physical qubits',\n", - " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 5670 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 14196 physical qubits to implement the algorithm logic, and 116160 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", " 'label': 'Physical qubits',\n", " 'path': 'physicalCounts/physicalQubits'},\n", " {'description': 'Total runtime',\n", - " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 30 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (5us 200ns) multiplied by the 432 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", " 'label': 'Runtime',\n", " 'path': 'physicalCountsFormatted/runtime'}],\n", " 'title': 'Physical resource estimates'},\n", " {'alwaysVisible': False,\n", " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", - " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 12$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 35$ logical qubits.',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 15$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 42$ logical qubits.',\n", " 'label': 'Logical algorithmic qubits',\n", " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", " {'description': 'Number of logical cycles for the algorithm',\n", - " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 6 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 2 CCZ and 6 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 96 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 16 CCZ and 96 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", " 'label': 'Algorithmic depth',\n", " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", " {'description': 'Number of logical cycles performed',\n", - " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 30. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 432. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", " 'label': 'Logical depth',\n", " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", " {'description': 'Number of T states consumed by the algorithm',\n", - " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 2 CCZ and 6 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 16 CCZ and 96 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", " 'label': 'Number of T states',\n", " 'path': 'physicalCounts/breakdown/numTstates'},\n", - " {'description': \"Number of T factories capable of producing the demanded 32 T states during the algorithm's runtime\",\n", - " 'explanation': 'The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{32\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 108us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " {'description': \"Number of T factories capable of producing the demanded 448 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{448\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 2ms 246us 400ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", " 'label': 'Number of T factories',\n", " 'path': 'physicalCounts/breakdown/numTfactories'},\n", " {'description': 'Number of times all T factories are invoked',\n", - " 'explanation': 'In order to prepare the 32 T states, the 14 copies of the T factory are repeatedly invoked 3 times.',\n", + " 'explanation': 'In order to prepare the 448 T states, the 12 copies of the T factory are repeatedly invoked 38 times.',\n", " 'label': 'Number of T factory invocations',\n", " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", " {'description': 'Number of physical qubits for the algorithm after layout',\n", - " 'explanation': 'The 5670 are the product of the 35 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.',\n", + " 'explanation': 'The 14196 are the product of the 42 logical qubits after layout and the 338 physical qubits that encode a single logical qubit.',\n", " 'label': 'Physical algorithmic qubits',\n", " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", " {'description': 'Number of physical qubits for the T factories',\n", - " 'explanation': 'Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\\\cdot 14$ qubits.',\n", + " 'explanation': 'Each T factory requires 9680 physical qubits and we run 12 in parallel, therefore we need $116160 = 9680 \\\\cdot 12$ qubits.',\n", " 'label': 'Physical T factory qubits',\n", " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", - " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 35 logical qubits and the total cycle count 30.',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 42 logical qubits and the total cycle count 432.',\n", " 'label': 'Required logical qubit error rate',\n", " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", " {'description': 'The minimum T state error rate required for distilled T states',\n", - " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 32.',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 448.',\n", " 'label': 'Required logical T state error rate',\n", " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", @@ -8013,7 +8014,7 @@ " 'label': 'QEC scheme',\n", " 'path': 'jobParams/qecScheme/name'},\n", " {'description': 'Required code distance for error correction',\n", - " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.0000004761904761904762)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000002755731922398589)}{\\\\log(0.01/0.001)} - 1$',\n", " 'label': 'Code distance',\n", " 'path': 'logicalQubit/codeDistance'},\n", " {'description': 'Number of physical qubits per logical qubit',\n", @@ -8025,7 +8026,7 @@ " 'label': 'Logical cycle time',\n", " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", " {'description': 'Logical qubit error rate',\n", - " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{9 + 1}{2}$',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{13 + 1}{2}$',\n", " 'label': 'Logical qubit error rate',\n", " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", " {'description': 'Crossing prefactor used in QEC scheme',\n", @@ -8037,11 +8038,11 @@ " 'label': 'Error correction threshold',\n", " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", " {'description': 'QEC scheme formula used to compute logical cycle time',\n", - " 'explanation': 'This is the formula that is used to compute the logical cycle time 3us 600ns.',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 5us 200ns.',\n", " 'label': 'Logical cycle time formula',\n", " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", - " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 162.',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 338.',\n", " 'label': 'Physical qubits formula',\n", " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", " 'title': 'Logical qubit parameters'},\n", @@ -8055,7 +8056,7 @@ " 'label': 'Runtime',\n", " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", " {'description': 'Number of output T states produced in a single run of T factory',\n", - " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.',\n", " 'label': 'Number of output T states per run',\n", " 'path': 'tfactory/numTstates'},\n", " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", @@ -8087,13 +8088,13 @@ " 'label': 'Runtime per round',\n", " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", " {'description': 'Logical T state error rate',\n", - " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.56e-5.',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.12e-6.',\n", " 'label': 'Logical T state error rate',\n", " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", " 'title': 'T factory parameters'},\n", " {'alwaysVisible': False,\n", " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", - " 'explanation': 'We determine 35 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'explanation': 'We determine 42 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", " 'label': 'Logical qubits (pre-layout)',\n", " 'path': 'logicalCounts/numQubits'},\n", " {'description': 'Number of T gates in the input quantum program',\n", @@ -8182,20 +8183,20 @@ " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", " 'title': 'Physical qubit parameters'}]},\n", " 'status': 'success',\n", - " 'tfactory': {'codeDistancePerRound': [9],\n", - " 'logicalErrorRate': 2.165000000000001e-06,\n", + " 'tfactory': {'codeDistancePerRound': [11],\n", + " 'logicalErrorRate': 2.480000000000001e-07,\n", " 'numInputTstates': 30,\n", " 'numRounds': 1,\n", " 'numTstates': 1,\n", " 'numUnitsPerRound': [2],\n", - " 'physicalQubits': 6480,\n", - " 'physicalQubitsPerRound': [6480],\n", - " 'runtime': 46800.0,\n", - " 'runtimePerRound': [46800.0],\n", + " 'physicalQubits': 9680,\n", + " 'physicalQubitsPerRound': [9680],\n", + " 'runtime': 57200.0,\n", + " 'runtimePerRound': [57200.0],\n", " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" ] }, - "execution_count": 11, + "execution_count": 34, "metadata": {}, "output_type": "execute_result" } @@ -8208,7 +8209,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 35, "metadata": { "collapsed": false, "jupyter": { @@ -8235,7 +8236,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 36, "metadata": { "collapsed": false, "jupyter": { @@ -8253,18 +8254,18 @@ "name": "stdout", "output_type": "stream", "text": [ - "Logical algorithmic qubits = 35\n", - "Algorithmic depth = 30\n", - "Score = 1050\n" + "Logical algorithmic qubits = 42\n", + "Algorithmic depth = 432\n", + "Score = 18144\n" ] }, { "data": { "text/plain": [ - "1050" + "18144" ] }, - "execution_count": 13, + "execution_count": 36, "metadata": {}, "output_type": "execute_result" } diff --git a/iQuHack-challenge-2023-task1.ipynb b/iQuHack-challenge-2023-task1.ipynb index 6899603..cb5da8d 100644 --- a/iQuHack-challenge-2023-task1.ipynb +++ b/iQuHack-challenge-2023-task1.ipynb @@ -121,13 +121,6 @@ "from qsharp import azure" ] }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, { "cell_type": "code", "execution_count": 2, @@ -146,7 +139,7 @@ "outputs": [], "source": [ "teamname=\"schrodingers-duck\" # Update this field with your team name\n", - "task=[\"task6\"]\n", + "task=[\"task1\"]\n", "slack_id=\"U04L3SFUCQ2\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" ] }, @@ -189,7 +182,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 4, "metadata": { "collapsed": false, "jupyter": { @@ -246,7 +239,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ @@ -255,7 +248,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 6, "metadata": { "collapsed": false, "jupyter": { @@ -312,7 +305,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 7, "metadata": { "collapsed": false, "jupyter": { @@ -357,12 +350,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -382,12 +375,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -407,12 +400,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -432,12 +425,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -457,12 +450,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -482,12 +475,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -507,12 +500,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -532,12 +525,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -568,7 +561,7 @@ "()" ] }, - "execution_count": 22, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } @@ -597,7 +590,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 8, "metadata": { "collapsed": false, "jupyter": { @@ -631,23 +624,23 @@ { "data": { "text/plain": [ - "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 165633},\n", - " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 398028},\n", - " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 2},\n", + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 177969},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 303174},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 4},\n", " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", - " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 180},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 166},\n", " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", - " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 180},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 166},\n", " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", @@ -655,7 +648,7 @@ " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" ] }, - "execution_count": 23, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -671,7 +664,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 9, "metadata": { "collapsed": false, "jupyter": { @@ -699,7 +692,7 @@ "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" ] }, - "execution_count": 24, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } @@ -710,7 +703,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 10, "metadata": { "collapsed": false, "jupyter": { @@ -731,10 +724,9 @@ "Submitting Task1_ResourceEstimationWrapper to target microsoft.estimator...\n", "Job successfully submitted.\n", " Job name: RE for the task 1\n", - " Job ID: 8dfa4a14-f799-49f9-98b5-d62cd808a86f\n", + " Job ID: e139e938-3193-4d04-8a64-e5451930285f\n", "Waiting up to 30 seconds for Azure Quantum job to complete...\n", - "[9:45:41 AM] Current job status: Executing\n", - "[9:45:46 AM] Current job status: Succeeded\n" + "[12:49:16 PM] Current job status: Succeeded\n" ] } ], @@ -745,7 +737,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 11, "metadata": { "collapsed": false, "jupyter": { @@ -1798,7 +1790,7 @@ " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" ] }, - "execution_count": 26, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" } @@ -1811,7 +1803,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 12, "metadata": { "collapsed": false, "jupyter": { @@ -1838,7 +1830,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 13, "metadata": { "collapsed": false, "jupyter": { @@ -1867,7 +1859,7 @@ "45" ] }, - "execution_count": 28, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" } diff --git a/iQuHack-challenge-2023-task2.ipynb b/iQuHack-challenge-2023-task2.ipynb index 267e958..c41a4bc 100644 --- a/iQuHack-challenge-2023-task2.ipynb +++ b/iQuHack-challenge-2023-task2.ipynb @@ -101,7 +101,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 25, "metadata": { "collapsed": false, "jupyter": { @@ -123,7 +123,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 26, "metadata": { "collapsed": false, "jupyter": { @@ -145,7 +145,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 27, "metadata": { "collapsed": false, "jupyter": { @@ -182,7 +182,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 38, "metadata": { "collapsed": false, "jupyter": { @@ -243,7 +243,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 39, "metadata": {}, "outputs": [], "source": [ @@ -252,7 +252,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 40, "metadata": { "collapsed": false, "jupyter": { @@ -309,7 +309,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 41, "metadata": { "collapsed": false, "jupyter": { @@ -354,12 +354,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -379,12 +379,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -404,12 +404,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -429,12 +429,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -454,12 +454,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -479,12 +479,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -504,12 +504,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -529,12 +529,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -554,12 +554,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -579,12 +579,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -604,12 +604,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -629,12 +629,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -654,12 +654,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -679,12 +679,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -704,12 +704,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -729,12 +729,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -754,12 +754,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -779,12 +779,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -804,12 +804,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -829,12 +829,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -854,12 +854,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -879,12 +879,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -904,12 +904,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -929,12 +929,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -954,12 +954,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -979,12 +979,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1004,12 +1004,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1029,12 +1029,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1054,12 +1054,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1079,12 +1079,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1104,12 +1104,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1129,12 +1129,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1154,12 +1154,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1179,12 +1179,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1204,12 +1204,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1229,12 +1229,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1254,12 +1254,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1279,12 +1279,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1304,12 +1304,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1329,12 +1329,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1354,12 +1354,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1379,12 +1379,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1404,12 +1404,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1429,12 +1429,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1454,12 +1454,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1479,12 +1479,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1504,12 +1504,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1529,12 +1529,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1554,12 +1554,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1579,12 +1579,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1604,12 +1604,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1629,12 +1629,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1654,12 +1654,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1679,12 +1679,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1704,12 +1704,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1729,12 +1729,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1754,12 +1754,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -1779,12 +1779,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -1804,12 +1804,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -1829,12 +1829,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -1854,12 +1854,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -1879,12 +1879,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -1904,12 +1904,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -1929,12 +1929,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -2021,7 +2021,7 @@ "()" ] }, - "execution_count": 18, + "execution_count": 41, "metadata": {}, "output_type": "execute_result" } @@ -2050,7 +2050,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 42, "metadata": { "collapsed": false, "jupyter": { @@ -2084,23 +2084,23 @@ { "data": { "text/plain": [ - "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 175517},\n", - " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 438370},\n", - " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 2},\n", + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 178071},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 409594},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 4},\n", " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", - " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 169},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 167},\n", " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", - " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 169},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 167},\n", " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", @@ -2108,7 +2108,7 @@ " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" ] }, - "execution_count": 19, + "execution_count": 42, "metadata": {}, "output_type": "execute_result" } @@ -2124,7 +2124,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 43, "metadata": { "collapsed": false, "jupyter": { @@ -2152,7 +2152,7 @@ "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" ] }, - "execution_count": 20, + "execution_count": 43, "metadata": {}, "output_type": "execute_result" } @@ -2163,7 +2163,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 44, "metadata": { "collapsed": false, "jupyter": { @@ -2184,9 +2184,10 @@ "Submitting Task2_ResourceEstimationWrapper to target microsoft.estimator...\n", "Job successfully submitted.\n", " Job name: RE for the task 2\n", - " Job ID: f8a7b04a-cd5c-4fea-aec9-ec6f246a8c34\n", + " Job ID: 4e3f0c4e-e8f0-49d5-99bf-d4d7d51bc4f7\n", "Waiting up to 30 seconds for Azure Quantum job to complete...\n", - "[11:51:48 AM] Current job status: Succeeded\n" + "[1:12:00 PM] Current job status: Executing\n", + "[1:12:06 PM] Current job status: Succeeded\n" ] } ], @@ -2197,7 +2198,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 45, "metadata": { "collapsed": false, "jupyter": { @@ -2213,7 +2214,7 @@ "outputs": [ { "data": { - "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":16,\"cczCount\":6,\"measurementCount\":16,\"numQubits\":9,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":82,\"algorithmicLogicalQubits\":28,\"cliffordErrorRate\":0.001,\"logicalDepth\":82,\"numTfactories\":12,\"numTfactoryRuns\":8,\"numTsPerRotation\":null,\"numTstates\":88,\"physicalQubitsForAlgorithm\":6776,\"physicalQubitsForTfactories\":77760,\"requiredLogicalQubitErrorRate\":2.177700348432056E-07,\"requiredLogicalTstateErrorRate\":5.681818181818182E-06},\"physicalQubits\":84536,\"runtime\":360800},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"91.98 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"2.18e-7\",\"requiredLogicalTstateErrorRate\":\"5.68e-6\",\"runtime\":\"360us 800ns\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 6776 physical qubits to implement the algorithm logic, and 77760 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 82 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 9$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 28$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 16 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 6 CCZ and 16 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 82. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 6 CCZ and 16 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 88 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{88\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 360us 800ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 88 T states, the 12 copies of the T factory are repeatedly invoked 8 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 6776 are the product of the 28 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 12 in parallel, therefore we need $77760 = 6480 \\\\cdot 12$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 28 logical qubits and the total cycle count 82.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 88.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.0000002177700348432056)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 5.68e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 28 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":30,\"cczCount\":10,\"measurementCount\":30,\"numQubits\":9,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":150,\"algorithmicLogicalQubits\":28,\"cliffordErrorRate\":0.001,\"logicalDepth\":150,\"numTfactories\":12,\"numTfactoryRuns\":14,\"numTsPerRotation\":null,\"numTstates\":160,\"physicalQubitsForAlgorithm\":6776,\"physicalQubitsForTfactories\":77760,\"requiredLogicalQubitErrorRate\":1.1904761904761904E-07,\"requiredLogicalTstateErrorRate\":3.125E-06},\"physicalQubits\":84536,\"runtime\":660000},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"91.98 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"1.19e-7\",\"requiredLogicalTstateErrorRate\":\"3.13e-6\",\"runtime\":\"660us\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 6776 physical qubits to implement the algorithm logic, and 77760 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 150 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 9$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 28$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 30 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 10 CCZ and 30 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 150. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 10 CCZ and 30 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 160 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{160\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 660us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 160 T states, the 12 copies of the T factory are repeatedly invoked 14 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 6776 are the product of the 28 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 12 in parallel, therefore we need $77760 = 6480 \\\\cdot 12$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 28 logical qubits and the total cycle count 150.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 160.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000011904761904761904)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 3.13e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 28 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", "text/html": [ "\r\n", "
\r\n", @@ -2237,12 +2238,12 @@ "\r\n", " \r\n", " Runtime\r\n", - " 360us 800ns\r\n", + " 660us\r\n", " \r\n", "

Total runtime

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This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 82 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

\n", + "

This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 150 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

\n", "\r\n", " \r\n", " \n", @@ -2269,36 +2270,36 @@ "\r\n", " \r\n", " Algorithmic depth\r\n", - " 82\r\n", + " 150\r\n", " \r\n", "

Number of logical cycles for the algorithm

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\r\n", - "

To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 16 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 6 CCZ and 16 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

\n", + "

To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 30 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 10 CCZ and 30 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Logical depth\r\n", - " 82\r\n", + " 150\r\n", " \r\n", "

Number of logical cycles performed

\n", "\r\n", "
\r\n", - "

This number is usually equal to the logical depth of the algorithm, which is 82. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", + "

This number is usually equal to the logical depth of the algorithm, which is 150. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Number of T states\r\n", - " 88\r\n", + " 160\r\n", " \r\n", "

Number of T states consumed by the algorithm

\n", "\r\n", "
\r\n", - "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 6 CCZ and 16 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", + "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 10 CCZ and 30 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", "\r\n", " \r\n", " \n", @@ -2307,22 +2308,22 @@ " Number of T factories\r\n", " 12\r\n", " \r\n", - "

Number of T factories capable of producing the demanded 88 T states during the algorithm's runtime

\n", + "

Number of T factories capable of producing the demanded 160 T states during the algorithm's runtime

\n", "\r\n", "
\r\n", - "

The total number of T factories 12 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{88\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 360us 800ns\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", + "

The total number of T factories 12 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{160\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 660us\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Number of T factory invocations\r\n", - " 8\r\n", + " 14\r\n", " \r\n", "

Number of times all T factories are invoked

\n", "\r\n", "
\r\n", - "

In order to prepare the 88 T states, the 12 copies of the T factory are repeatedly invoked 8 times.

\n", + "

In order to prepare the 160 T states, the 12 copies of the T factory are repeatedly invoked 14 times.

\n", "\r\n", " \r\n", " \n", @@ -2353,24 +2354,24 @@ "\r\n", " \r\n", " Required logical qubit error rate\r\n", - " 2.18e-7\r\n", + " 1.19e-7\r\n", " \r\n", "

The minimum logical qubit error rate required to run the algorithm within the error budget

\n", "\r\n", "
\r\n", - "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 28 logical qubits and the total cycle count 82.

\n", + "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 28 logical qubits and the total cycle count 150.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Required logical T state error rate\r\n", - " 5.68e-6\r\n", + " 3.13e-6\r\n", " \r\n", "

The minimum T state error rate required for distilled T states

\n", "\r\n", "
\r\n", - "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 88.

\n", + "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 160.

\n", "\r\n", " \r\n", " \n", @@ -2414,7 +2415,7 @@ "

Required code distance for error correction

\n", "\r\n", "
\r\n", - "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.0000002177700348432056)}{\\log(0.01/0.001)} - 1\\)

\n", + "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000011904761904761904)}{\\log(0.01/0.001)} - 1\\)

\n", "\r\n", " \r\n", " \n", @@ -2638,7 +2639,7 @@ "

Logical T state error rate

\n", "\r\n", "
\r\n", - "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 5.68e-6.

\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 3.13e-6.

\n", "\r\n", " \r\n", " \n", @@ -2701,7 +2702,7 @@ "\r\n", " \r\n", " CCZ gates\r\n", - " 6\r\n", + " 10\r\n", " \r\n", "

Number of CCZ-gates in the input quantum program

\n", "\r\n", @@ -2713,7 +2714,7 @@ "\r\n", " \r\n", " CCiX gates\r\n", - " 16\r\n", + " 30\r\n", " \r\n", "

Number of CCiX-gates in the input quantum program

\n", "\r\n", @@ -2725,7 +2726,7 @@ "\r\n", " \r\n", " Measurement operations\r\n", - " 16\r\n", + " 30\r\n", " \r\n", "

Number of single qubit measurements in the input quantum program

\n", "\r\n", @@ -2956,9 +2957,9 @@ " 'tGateTime': '50 ns',\n", " 'twoQubitGateErrorRate': 0.001,\n", " 'twoQubitGateTime': '50 ns'}},\n", - " 'logicalCounts': {'ccixCount': 16,\n", - " 'cczCount': 6,\n", - " 'measurementCount': 16,\n", + " 'logicalCounts': {'ccixCount': 30,\n", + " 'cczCount': 10,\n", + " 'measurementCount': 30,\n", " 'numQubits': 9,\n", " 'rotationCount': 0,\n", " 'rotationDepth': 0,\n", @@ -2967,20 +2968,20 @@ " 'logicalCycleTime': 4400.0,\n", " 'logicalErrorRate': 3.000000000000002e-08,\n", " 'physicalQubits': 242},\n", - " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 82,\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 150,\n", " 'algorithmicLogicalQubits': 28,\n", " 'cliffordErrorRate': 0.001,\n", - " 'logicalDepth': 82,\n", + " 'logicalDepth': 150,\n", " 'numTfactories': 12,\n", - " 'numTfactoryRuns': 8,\n", + " 'numTfactoryRuns': 14,\n", " 'numTsPerRotation': None,\n", - " 'numTstates': 88,\n", + " 'numTstates': 160,\n", " 'physicalQubitsForAlgorithm': 6776,\n", " 'physicalQubitsForTfactories': 77760,\n", - " 'requiredLogicalQubitErrorRate': 2.177700348432056e-07,\n", - " 'requiredLogicalTstateErrorRate': 5.681818181818182e-06},\n", + " 'requiredLogicalQubitErrorRate': 1.1904761904761904e-07,\n", + " 'requiredLogicalTstateErrorRate': 3.125e-06},\n", " 'physicalQubits': 84536,\n", - " 'runtime': 360800},\n", + " 'runtime': 660000},\n", " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", " 'errorBudget': '1.00e-3',\n", " 'errorBudgetLogical': '5.00e-4',\n", @@ -2992,9 +2993,9 @@ " 'numUnitsPerRound': '2',\n", " 'physicalQubitsForTfactoriesPercentage': '91.98 %',\n", " 'physicalQubitsPerRound': '6480',\n", - " 'requiredLogicalQubitErrorRate': '2.18e-7',\n", - " 'requiredLogicalTstateErrorRate': '5.68e-6',\n", - " 'runtime': '360us 800ns',\n", + " 'requiredLogicalQubitErrorRate': '1.19e-7',\n", + " 'requiredLogicalTstateErrorRate': '3.13e-6',\n", + " 'runtime': '660us',\n", " 'tfactoryRuntime': '46us 800ns',\n", " 'tfactoryRuntimePerRound': '46us 800ns',\n", " 'tstateLogicalErrorRate': '2.17e-6',\n", @@ -3012,7 +3013,7 @@ " 'label': 'Physical qubits',\n", " 'path': 'physicalCounts/physicalQubits'},\n", " {'description': 'Total runtime',\n", - " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 82 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 150 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", " 'label': 'Runtime',\n", " 'path': 'physicalCountsFormatted/runtime'}],\n", " 'title': 'Physical resource estimates'},\n", @@ -3022,23 +3023,23 @@ " 'label': 'Logical algorithmic qubits',\n", " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", " {'description': 'Number of logical cycles for the algorithm',\n", - " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 16 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 6 CCZ and 16 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 30 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 10 CCZ and 30 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", " 'label': 'Algorithmic depth',\n", " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", " {'description': 'Number of logical cycles performed',\n", - " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 82. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 150. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", " 'label': 'Logical depth',\n", " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", " {'description': 'Number of T states consumed by the algorithm',\n", - " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 6 CCZ and 16 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 10 CCZ and 30 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", " 'label': 'Number of T states',\n", " 'path': 'physicalCounts/breakdown/numTstates'},\n", - " {'description': \"Number of T factories capable of producing the demanded 88 T states during the algorithm's runtime\",\n", - " 'explanation': 'The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{88\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 360us 800ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " {'description': \"Number of T factories capable of producing the demanded 160 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{160\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 660us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", " 'label': 'Number of T factories',\n", " 'path': 'physicalCounts/breakdown/numTfactories'},\n", " {'description': 'Number of times all T factories are invoked',\n", - " 'explanation': 'In order to prepare the 88 T states, the 12 copies of the T factory are repeatedly invoked 8 times.',\n", + " 'explanation': 'In order to prepare the 160 T states, the 12 copies of the T factory are repeatedly invoked 14 times.',\n", " 'label': 'Number of T factory invocations',\n", " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", " {'description': 'Number of physical qubits for the algorithm after layout',\n", @@ -3050,11 +3051,11 @@ " 'label': 'Physical T factory qubits',\n", " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", - " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 28 logical qubits and the total cycle count 82.',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 28 logical qubits and the total cycle count 150.',\n", " 'label': 'Required logical qubit error rate',\n", " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", " {'description': 'The minimum T state error rate required for distilled T states',\n", - " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 88.',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 160.',\n", " 'label': 'Required logical T state error rate',\n", " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", @@ -3068,7 +3069,7 @@ " 'label': 'QEC scheme',\n", " 'path': 'jobParams/qecScheme/name'},\n", " {'description': 'Required code distance for error correction',\n", - " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.0000002177700348432056)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000011904761904761904)}{\\\\log(0.01/0.001)} - 1$',\n", " 'label': 'Code distance',\n", " 'path': 'logicalQubit/codeDistance'},\n", " {'description': 'Number of physical qubits per logical qubit',\n", @@ -3142,7 +3143,7 @@ " 'label': 'Runtime per round',\n", " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", " {'description': 'Logical T state error rate',\n", - " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 5.68e-6.',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 3.13e-6.',\n", " 'label': 'Logical T state error rate',\n", " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", " 'title': 'T factory parameters'},\n", @@ -3250,7 +3251,7 @@ " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" ] }, - "execution_count": 22, + "execution_count": 45, "metadata": {}, "output_type": "execute_result" } @@ -3263,7 +3264,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 46, "metadata": { "collapsed": false, "jupyter": { @@ -3290,7 +3291,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 47, "metadata": { "collapsed": false, "jupyter": { @@ -3309,17 +3310,17 @@ "output_type": "stream", "text": [ "Logical algorithmic qubits = 28\n", - "Algorithmic depth = 82\n", - "Score = 2296\n" + "Algorithmic depth = 150\n", + "Score = 4200\n" ] }, { "data": { "text/plain": [ - "2296" + "4200" ] }, - "execution_count": 24, + "execution_count": 47, "metadata": {}, "output_type": "execute_result" } @@ -3328,6 +3329,13 @@ "evaluate_results(result)" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, { "cell_type": "code", "execution_count": null, diff --git a/iQuHack-challenge-2023-task3.ipynb b/iQuHack-challenge-2023-task3.ipynb index 8133476..4d5561f 100644 --- a/iQuHack-challenge-2023-task3.ipynb +++ b/iQuHack-challenge-2023-task3.ipynb @@ -67,7 +67,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": { "collapsed": false, "jupyter": { @@ -89,7 +89,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "metadata": { "collapsed": false, "jupyter": { @@ -104,14 +104,14 @@ }, "outputs": [], "source": [ - "teamname=\"msft_is_the_best\" # Update this field with your team name\n", + "teamname=\"schrodingers-duck\" # Update this field with your team name\n", "task=[\"task3\"]\n", - "slack_id=\"myslackid\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + "slack_id=\"U04L3SFUCQ2\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": { "collapsed": false, "jupyter": { @@ -148,7 +148,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 15, "metadata": { "collapsed": false, "jupyter": { @@ -215,7 +215,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 16, "metadata": {}, "outputs": [], "source": [ @@ -224,7 +224,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 17, "metadata": { "collapsed": false, "jupyter": { @@ -281,7 +281,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 18, "metadata": { "collapsed": false, "jupyter": { @@ -326,12 +326,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -351,12 +351,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -376,12 +376,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -401,12 +401,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -451,12 +451,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -476,12 +476,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -501,12 +501,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -526,12 +526,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -551,12 +551,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -576,12 +576,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -601,12 +601,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -626,12 +626,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -651,12 +651,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -676,12 +676,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -701,12 +701,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -726,12 +726,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1051,12 +1051,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1076,12 +1076,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1101,12 +1101,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1126,12 +1126,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1151,12 +1151,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1176,12 +1176,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1201,12 +1201,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1226,12 +1226,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1251,12 +1251,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1276,12 +1276,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1301,12 +1301,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1326,12 +1326,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1351,12 +1351,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1376,12 +1376,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1401,12 +1401,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1426,12 +1426,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1451,12 +1451,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1476,12 +1476,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1501,12 +1501,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1526,12 +1526,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1551,12 +1551,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1576,12 +1576,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1601,12 +1601,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1626,12 +1626,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1651,12 +1651,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1676,12 +1676,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1701,12 +1701,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1726,12 +1726,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1751,12 +1751,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1776,12 +1776,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1801,12 +1801,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1826,12 +1826,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1851,12 +1851,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1876,12 +1876,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1901,12 +1901,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1926,12 +1926,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1951,12 +1951,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1976,12 +1976,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2001,12 +2001,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2026,12 +2026,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2051,12 +2051,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2076,12 +2076,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2101,12 +2101,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2126,12 +2126,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2151,12 +2151,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2176,12 +2176,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2201,12 +2201,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2226,12 +2226,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2251,12 +2251,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2276,12 +2276,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2301,12 +2301,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2326,12 +2326,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2351,12 +2351,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2376,12 +2376,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2401,12 +2401,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2426,12 +2426,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2451,12 +2451,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2476,12 +2476,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2501,12 +2501,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2526,12 +2526,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2551,12 +2551,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2576,12 +2576,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2601,12 +2601,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2626,12 +2626,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2651,12 +2651,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2676,12 +2676,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2701,12 +2701,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2726,12 +2726,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2751,12 +2751,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2776,12 +2776,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2801,12 +2801,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2826,12 +2826,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2851,12 +2851,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2876,12 +2876,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2901,12 +2901,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2926,12 +2926,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2951,12 +2951,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2976,12 +2976,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3001,12 +3001,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3026,12 +3026,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3051,12 +3051,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3076,12 +3076,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3101,12 +3101,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3126,12 +3126,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3151,12 +3151,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3176,12 +3176,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3201,12 +3201,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3226,12 +3226,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3251,12 +3251,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3276,12 +3276,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3301,12 +3301,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3326,12 +3326,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3351,12 +3351,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3376,12 +3376,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3401,12 +3401,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3426,12 +3426,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3451,12 +3451,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3476,12 +3476,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3501,12 +3501,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3657,7 +3657,7 @@ "()" ] }, - "execution_count": 7, + "execution_count": 18, "metadata": {}, "output_type": "execute_result" } @@ -3686,7 +3686,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 19, "metadata": { "collapsed": false, "jupyter": { @@ -3720,23 +3720,23 @@ { "data": { "text/plain": [ - "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 171513},\n", - " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 434582},\n", - " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 2},\n", + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 178144},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 409698},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 4},\n", " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", - " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 175},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 168},\n", " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", - " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 175},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 168},\n", " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", @@ -3744,7 +3744,7 @@ " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" ] }, - "execution_count": 8, + "execution_count": 19, "metadata": {}, "output_type": "execute_result" } @@ -3760,7 +3760,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 20, "metadata": { "collapsed": false, "jupyter": { @@ -3788,7 +3788,7 @@ "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" ] }, - "execution_count": 9, + "execution_count": 20, "metadata": {}, "output_type": "execute_result" } @@ -3799,7 +3799,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 21, "metadata": { "collapsed": false, "jupyter": { @@ -3820,9 +3820,10 @@ "Submitting Task3_ResourceEstimationWrapper to target microsoft.estimator...\n", "Job successfully submitted.\n", " Job name: RE for the task 3\n", - " Job ID: 5e58d190-e0a8-4e7c-8a6a-3ffb25f39cd5\n", + " Job ID: 97de0812-1c25-4a9d-be97-55f936dc8c93\n", "Waiting up to 30 seconds for Azure Quantum job to complete...\n", - "[10:42:27 AM] Current job status: Succeeded\n" + "[1:13:16 PM] Current job status: Executing\n", + "[1:13:21 PM] Current job status: Succeeded\n" ] } ], @@ -3833,7 +3834,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 22, "metadata": { "collapsed": false, "jupyter": { @@ -3849,7 +3850,7 @@ "outputs": [ { "data": { - "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":1,\"cczCount\":17,\"measurementCount\":1,\"numQubits\":13,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":55,\"algorithmicLogicalQubits\":38,\"cliffordErrorRate\":0.001,\"logicalDepth\":55,\"numTfactories\":14,\"numTfactoryRuns\":6,\"numTsPerRotation\":null,\"numTstates\":72,\"physicalQubitsForAlgorithm\":9196,\"physicalQubitsForTfactories\":90720,\"requiredLogicalQubitErrorRate\":2.3923444976076555E-07,\"requiredLogicalTstateErrorRate\":6.944444444444445E-06},\"physicalQubits\":99916,\"runtime\":242000},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"90.80 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"2.39e-7\",\"requiredLogicalTstateErrorRate\":\"6.94e-6\",\"runtime\":\"242us\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 9196 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 55 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 13$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 38$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 1 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 17 CCZ and 1 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 55. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 17 CCZ and 1 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 72 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{72\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 242us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 72 T states, the 14 copies of the T factory are repeatedly invoked 6 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 9196 are the product of the 38 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\\\cdot 14$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 55.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 72.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000023923444976076555)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.94e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":80,\"cczCount\":20,\"measurementCount\":80,\"numQubits\":11,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":380,\"algorithmicLogicalQubits\":33,\"cliffordErrorRate\":0.001,\"logicalDepth\":380,\"numTfactories\":14,\"numTfactoryRuns\":29,\"numTsPerRotation\":null,\"numTstates\":400,\"physicalQubitsForAlgorithm\":7986,\"physicalQubitsForTfactories\":135520,\"requiredLogicalQubitErrorRate\":3.987240829346092E-08,\"requiredLogicalTstateErrorRate\":1.25E-06},\"physicalQubits\":143506,\"runtime\":1672000},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"11\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"94.44 %\",\"physicalQubitsPerRound\":\"9680\",\"requiredLogicalQubitErrorRate\":\"3.99e-8\",\"requiredLogicalTstateErrorRate\":\"1.25e-6\",\"runtime\":\"1ms 672us\",\"tfactoryRuntime\":\"57us 200ns\",\"tfactoryRuntimePerRound\":\"57us 200ns\",\"tstateLogicalErrorRate\":\"2.48e-7\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 7986 physical qubits to implement the algorithm logic, and 135520 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 380 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 11$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 33$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 80 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 20 CCZ and 80 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 380. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 20 CCZ and 80 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 400 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{400\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 1ms 672us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 400 T states, the 14 copies of the T factory are repeatedly invoked 29 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 7986 are the product of the 33 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 9680 physical qubits and we run 14 in parallel, therefore we need $135520 = 9680 \\\\cdot 14$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 380.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 400.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000003987240829346092)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[11],\"logicalErrorRate\":2.480000000000001E-07,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":9680,\"physicalQubitsPerRound\":[9680],\"runtime\":57200.0,\"runtimePerRound\":[57200.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", "text/html": [ "\r\n", "
\r\n", @@ -3861,24 +3862,24 @@ "\r\n", " \r\n", " Physical qubits\r\n", - " 99916\r\n", + " 143506\r\n", " \r\n", "

Number of physical qubits

\n", "\r\n", "
\r\n", - "

This value represents the total number of physical qubits, which is the sum of 9196 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

\n", + "

This value represents the total number of physical qubits, which is the sum of 7986 physical qubits to implement the algorithm logic, and 135520 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Runtime\r\n", - " 242us\r\n", + " 1ms 672us\r\n", " \r\n", "

Total runtime

\n", "\r\n", "
\r\n", - "

This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 55 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

\n", + "

This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 380 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

\n", "\r\n", " \r\n", " \n", @@ -3893,48 +3894,48 @@ "\r\n", " \r\n", " Logical algorithmic qubits\r\n", - " 38\r\n", + " 33\r\n", " \r\n", "

Number of logical qubits for the algorithm after layout

\n", "\r\n", "
\r\n", - "

Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 13\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 38$ logical qubits.

\n", + "

Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 11\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 33$ logical qubits.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Algorithmic depth\r\n", - " 55\r\n", + " 380\r\n", " \r\n", "

Number of logical cycles for the algorithm

\n", "\r\n", "
\r\n", - "

To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 1 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 17 CCZ and 1 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

\n", + "

To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 80 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 20 CCZ and 80 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Logical depth\r\n", - " 55\r\n", + " 380\r\n", " \r\n", "

Number of logical cycles performed

\n", "\r\n", "
\r\n", - "

This number is usually equal to the logical depth of the algorithm, which is 55. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", + "

This number is usually equal to the logical depth of the algorithm, which is 380. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Number of T states\r\n", - " 72\r\n", + " 400\r\n", " \r\n", "

Number of T states consumed by the algorithm

\n", "\r\n", "
\r\n", - "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 17 CCZ and 1 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", + "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 20 CCZ and 80 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", "\r\n", " \r\n", " \n", @@ -3943,70 +3944,70 @@ " Number of T factories\r\n", " 14\r\n", " \r\n", - "

Number of T factories capable of producing the demanded 72 T states during the algorithm's runtime

\n", + "

Number of T factories capable of producing the demanded 400 T states during the algorithm's runtime

\n", "\r\n", "
\r\n", - "

The total number of T factories 14 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{72\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 242us\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", + "

The total number of T factories 14 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{400\\;\\text{T states} \\cdot 57us 200ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 1ms 672us\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Number of T factory invocations\r\n", - " 6\r\n", + " 29\r\n", " \r\n", "

Number of times all T factories are invoked

\n", "\r\n", "
\r\n", - "

In order to prepare the 72 T states, the 14 copies of the T factory are repeatedly invoked 6 times.

\n", + "

In order to prepare the 400 T states, the 14 copies of the T factory are repeatedly invoked 29 times.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Physical algorithmic qubits\r\n", - " 9196\r\n", + " 7986\r\n", " \r\n", "

Number of physical qubits for the algorithm after layout

\n", "\r\n", "
\r\n", - "

The 9196 are the product of the 38 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.

\n", + "

The 7986 are the product of the 33 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Physical T factory qubits\r\n", - " 90720\r\n", + " 135520\r\n", " \r\n", "

Number of physical qubits for the T factories

\n", "\r\n", "
\r\n", - "

Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\cdot 14$ qubits.

\n", + "

Each T factory requires 9680 physical qubits and we run 14 in parallel, therefore we need $135520 = 9680 \\cdot 14$ qubits.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Required logical qubit error rate\r\n", - " 2.39e-7\r\n", + " 3.99e-8\r\n", " \r\n", "

The minimum logical qubit error rate required to run the algorithm within the error budget

\n", "\r\n", "
\r\n", - "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 55.

\n", + "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 380.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Required logical T state error rate\r\n", - " 6.94e-6\r\n", + " 1.25e-6\r\n", " \r\n", "

The minimum T state error rate required for distilled T states

\n", "\r\n", "
\r\n", - "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 72.

\n", + "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 400.

\n", "\r\n", " \r\n", " \n", @@ -4050,7 +4051,7 @@ "

Required code distance for error correction

\n", "\r\n", "
\r\n", - "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000023923444976076555)}{\\log(0.01/0.001)} - 1\\)

\n", + "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000003987240829346092)}{\\log(0.01/0.001)} - 1\\)

\n", "\r\n", " \r\n", " \n", @@ -4149,7 +4150,7 @@ "\r\n", " \r\n", " Physical qubits\r\n", - " 6480\r\n", + " 9680\r\n", " \r\n", "

Number of physical qubits for a single T factory

\n", "\r\n", @@ -4161,7 +4162,7 @@ "\r\n", " \r\n", " Runtime\r\n", - " 46us 800ns\r\n", + " 57us 200ns\r\n", " \r\n", "

Runtime of a single T factory

\n", "\r\n", @@ -4178,7 +4179,7 @@ "

Number of output T states produced in a single run of T factory

\n", "\r\n", "
\r\n", - "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.

\n", + "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.

\n", "\r\n", " \r\n", " \n", @@ -4233,7 +4234,7 @@ "\r\n", " \r\n", " Distillation code distances\r\n", - " 9\r\n", + " 11\r\n", " \r\n", "

The code distance in each round of distillation

\n", "\r\n", @@ -4245,7 +4246,7 @@ "\r\n", " \r\n", " Number of physical qubits per round\r\n", - " 6480\r\n", + " 9680\r\n", " \r\n", "

The number of physical qubits used in each round of distillation

\n", "\r\n", @@ -4257,7 +4258,7 @@ "\r\n", " \r\n", " Runtime per round\r\n", - " 46us 800ns\r\n", + " 57us 200ns\r\n", " \r\n", "

The runtime of each distillation round

\n", "\r\n", @@ -4269,12 +4270,12 @@ "\r\n", " \r\n", " Logical T state error rate\r\n", - " 2.17e-6\r\n", + " 2.48e-7\r\n", " \r\n", "

Logical T state error rate

\n", "\r\n", "
\r\n", - "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.94e-6.

\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-6.

\n", "\r\n", " \r\n", " \n", @@ -4289,12 +4290,12 @@ "\r\n", " \r\n", " Logical qubits (pre-layout)\r\n", - " 13\r\n", + " 11\r\n", " \r\n", "

Number of logical qubits in the input quantum program

\n", "\r\n", "
\r\n", - "

We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", + "

We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", "\r\n", " \r\n", " \n", @@ -4337,7 +4338,7 @@ "\r\n", " \r\n", " CCZ gates\r\n", - " 17\r\n", + " 20\r\n", " \r\n", "

Number of CCZ-gates in the input quantum program

\n", "\r\n", @@ -4349,7 +4350,7 @@ "\r\n", " \r\n", " CCiX gates\r\n", - " 1\r\n", + " 80\r\n", " \r\n", "

Number of CCiX-gates in the input quantum program

\n", "\r\n", @@ -4361,7 +4362,7 @@ "\r\n", " \r\n", " Measurement operations\r\n", - " 1\r\n", + " 80\r\n", " \r\n", "

Number of single qubit measurements in the input quantum program

\n", "\r\n", @@ -4592,10 +4593,10 @@ " 'tGateTime': '50 ns',\n", " 'twoQubitGateErrorRate': 0.001,\n", " 'twoQubitGateTime': '50 ns'}},\n", - " 'logicalCounts': {'ccixCount': 1,\n", - " 'cczCount': 17,\n", - " 'measurementCount': 1,\n", - " 'numQubits': 13,\n", + " 'logicalCounts': {'ccixCount': 80,\n", + " 'cczCount': 20,\n", + " 'measurementCount': 80,\n", + " 'numQubits': 11,\n", " 'rotationCount': 0,\n", " 'rotationDepth': 0,\n", " 'tCount': 0},\n", @@ -4603,21 +4604,21 @@ " 'logicalCycleTime': 4400.0,\n", " 'logicalErrorRate': 3.000000000000002e-08,\n", " 'physicalQubits': 242},\n", - " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 55,\n", - " 'algorithmicLogicalQubits': 38,\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 380,\n", + " 'algorithmicLogicalQubits': 33,\n", " 'cliffordErrorRate': 0.001,\n", - " 'logicalDepth': 55,\n", + " 'logicalDepth': 380,\n", " 'numTfactories': 14,\n", - " 'numTfactoryRuns': 6,\n", + " 'numTfactoryRuns': 29,\n", " 'numTsPerRotation': None,\n", - " 'numTstates': 72,\n", - " 'physicalQubitsForAlgorithm': 9196,\n", - " 'physicalQubitsForTfactories': 90720,\n", - " 'requiredLogicalQubitErrorRate': 2.3923444976076555e-07,\n", - " 'requiredLogicalTstateErrorRate': 6.944444444444445e-06},\n", - " 'physicalQubits': 99916,\n", - " 'runtime': 242000},\n", - " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", + " 'numTstates': 400,\n", + " 'physicalQubitsForAlgorithm': 7986,\n", + " 'physicalQubitsForTfactories': 135520,\n", + " 'requiredLogicalQubitErrorRate': 3.987240829346092e-08,\n", + " 'requiredLogicalTstateErrorRate': 1.25e-06},\n", + " 'physicalQubits': 143506,\n", + " 'runtime': 1672000},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '11',\n", " 'errorBudget': '1.00e-3',\n", " 'errorBudgetLogical': '5.00e-4',\n", " 'errorBudgetRotations': '0.00e0',\n", @@ -4626,14 +4627,14 @@ " 'logicalErrorRate': '3.00e-8',\n", " 'numTsPerRotation': 'No rotations in algorithm',\n", " 'numUnitsPerRound': '2',\n", - " 'physicalQubitsForTfactoriesPercentage': '90.80 %',\n", - " 'physicalQubitsPerRound': '6480',\n", - " 'requiredLogicalQubitErrorRate': '2.39e-7',\n", - " 'requiredLogicalTstateErrorRate': '6.94e-6',\n", - " 'runtime': '242us',\n", - " 'tfactoryRuntime': '46us 800ns',\n", - " 'tfactoryRuntimePerRound': '46us 800ns',\n", - " 'tstateLogicalErrorRate': '2.17e-6',\n", + " 'physicalQubitsForTfactoriesPercentage': '94.44 %',\n", + " 'physicalQubitsPerRound': '9680',\n", + " 'requiredLogicalQubitErrorRate': '3.99e-8',\n", + " 'requiredLogicalTstateErrorRate': '1.25e-6',\n", + " 'runtime': '1ms 672us',\n", + " 'tfactoryRuntime': '57us 200ns',\n", + " 'tfactoryRuntimePerRound': '57us 200ns',\n", + " 'tstateLogicalErrorRate': '2.48e-7',\n", " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", @@ -4644,53 +4645,53 @@ " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", " 'groups': [{'alwaysVisible': True,\n", " 'entries': [{'description': 'Number of physical qubits',\n", - " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 9196 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 7986 physical qubits to implement the algorithm logic, and 135520 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", " 'label': 'Physical qubits',\n", " 'path': 'physicalCounts/physicalQubits'},\n", " {'description': 'Total runtime',\n", - " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 55 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 380 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", " 'label': 'Runtime',\n", " 'path': 'physicalCountsFormatted/runtime'}],\n", " 'title': 'Physical resource estimates'},\n", " {'alwaysVisible': False,\n", " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", - " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 13$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 38$ logical qubits.',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 11$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 33$ logical qubits.',\n", " 'label': 'Logical algorithmic qubits',\n", " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", " {'description': 'Number of logical cycles for the algorithm',\n", - " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 1 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 17 CCZ and 1 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 80 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 20 CCZ and 80 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", " 'label': 'Algorithmic depth',\n", " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", " {'description': 'Number of logical cycles performed',\n", - " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 55. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 380. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", " 'label': 'Logical depth',\n", " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", " {'description': 'Number of T states consumed by the algorithm',\n", - " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 17 CCZ and 1 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 20 CCZ and 80 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", " 'label': 'Number of T states',\n", " 'path': 'physicalCounts/breakdown/numTstates'},\n", - " {'description': \"Number of T factories capable of producing the demanded 72 T states during the algorithm's runtime\",\n", - " 'explanation': 'The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{72\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 242us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " {'description': \"Number of T factories capable of producing the demanded 400 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{400\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 1ms 672us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", " 'label': 'Number of T factories',\n", " 'path': 'physicalCounts/breakdown/numTfactories'},\n", " {'description': 'Number of times all T factories are invoked',\n", - " 'explanation': 'In order to prepare the 72 T states, the 14 copies of the T factory are repeatedly invoked 6 times.',\n", + " 'explanation': 'In order to prepare the 400 T states, the 14 copies of the T factory are repeatedly invoked 29 times.',\n", " 'label': 'Number of T factory invocations',\n", " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", " {'description': 'Number of physical qubits for the algorithm after layout',\n", - " 'explanation': 'The 9196 are the product of the 38 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.',\n", + " 'explanation': 'The 7986 are the product of the 33 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.',\n", " 'label': 'Physical algorithmic qubits',\n", " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", " {'description': 'Number of physical qubits for the T factories',\n", - " 'explanation': 'Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\\\cdot 14$ qubits.',\n", + " 'explanation': 'Each T factory requires 9680 physical qubits and we run 14 in parallel, therefore we need $135520 = 9680 \\\\cdot 14$ qubits.',\n", " 'label': 'Physical T factory qubits',\n", " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", - " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 55.',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 380.',\n", " 'label': 'Required logical qubit error rate',\n", " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", " {'description': 'The minimum T state error rate required for distilled T states',\n", - " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 72.',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 400.',\n", " 'label': 'Required logical T state error rate',\n", " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", @@ -4704,7 +4705,7 @@ " 'label': 'QEC scheme',\n", " 'path': 'jobParams/qecScheme/name'},\n", " {'description': 'Required code distance for error correction',\n", - " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000023923444976076555)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000003987240829346092)}{\\\\log(0.01/0.001)} - 1$',\n", " 'label': 'Code distance',\n", " 'path': 'logicalQubit/codeDistance'},\n", " {'description': 'Number of physical qubits per logical qubit',\n", @@ -4746,7 +4747,7 @@ " 'label': 'Runtime',\n", " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", " {'description': 'Number of output T states produced in a single run of T factory',\n", - " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.',\n", " 'label': 'Number of output T states per run',\n", " 'path': 'tfactory/numTstates'},\n", " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", @@ -4778,13 +4779,13 @@ " 'label': 'Runtime per round',\n", " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", " {'description': 'Logical T state error rate',\n", - " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.94e-6.',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-6.',\n", " 'label': 'Logical T state error rate',\n", " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", " 'title': 'T factory parameters'},\n", " {'alwaysVisible': False,\n", " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", - " 'explanation': 'We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'explanation': 'We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", " 'label': 'Logical qubits (pre-layout)',\n", " 'path': 'logicalCounts/numQubits'},\n", " {'description': 'Number of T gates in the input quantum program',\n", @@ -4873,20 +4874,20 @@ " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", " 'title': 'Physical qubit parameters'}]},\n", " 'status': 'success',\n", - " 'tfactory': {'codeDistancePerRound': [9],\n", - " 'logicalErrorRate': 2.165000000000001e-06,\n", + " 'tfactory': {'codeDistancePerRound': [11],\n", + " 'logicalErrorRate': 2.480000000000001e-07,\n", " 'numInputTstates': 30,\n", " 'numRounds': 1,\n", " 'numTstates': 1,\n", " 'numUnitsPerRound': [2],\n", - " 'physicalQubits': 6480,\n", - " 'physicalQubitsPerRound': [6480],\n", - " 'runtime': 46800.0,\n", - " 'runtimePerRound': [46800.0],\n", + " 'physicalQubits': 9680,\n", + " 'physicalQubitsPerRound': [9680],\n", + " 'runtime': 57200.0,\n", + " 'runtimePerRound': [57200.0],\n", " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" ] }, - "execution_count": 11, + "execution_count": 22, "metadata": {}, "output_type": "execute_result" } @@ -4899,7 +4900,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 23, "metadata": { "collapsed": false, "jupyter": { @@ -4926,7 +4927,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 24, "metadata": { "collapsed": false, "jupyter": { @@ -4944,18 +4945,18 @@ "name": "stdout", "output_type": "stream", "text": [ - "Logical algorithmic qubits = 38\n", - "Algorithmic depth = 55\n", - "Score = 2090\n" + "Logical algorithmic qubits = 33\n", + "Algorithmic depth = 380\n", + "Score = 12540\n" ] }, { "data": { "text/plain": [ - "2090" + "12540" ] }, - "execution_count": 13, + "execution_count": 24, "metadata": {}, "output_type": "execute_result" } diff --git a/iQuHack-challenge-2023-task6.ipynb b/iQuHack-challenge-2023-task6.ipynb index 7babc33..330ddb9 100644 --- a/iQuHack-challenge-2023-task6.ipynb +++ b/iQuHack-challenge-2023-task6.ipynb @@ -67,7 +67,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 14, "metadata": { "collapsed": false, "jupyter": { @@ -89,7 +89,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 15, "metadata": { "collapsed": false, "jupyter": { @@ -111,7 +111,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 16, "metadata": { "collapsed": false, "jupyter": { @@ -148,7 +148,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 27, "metadata": { "collapsed": false, "jupyter": { @@ -196,7 +196,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 28, "metadata": {}, "outputs": [], "source": [ @@ -205,7 +205,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 29, "metadata": { "collapsed": false, "jupyter": { @@ -262,7 +262,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 30, "metadata": { "collapsed": false, "jupyter": { @@ -307,12 +307,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -332,12 +332,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -357,12 +357,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -382,12 +382,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -407,12 +407,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -432,12 +432,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -457,12 +457,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -482,12 +482,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -507,12 +507,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -532,12 +532,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -557,12 +557,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -582,12 +582,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -607,12 +607,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -632,12 +632,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -657,12 +657,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -682,12 +682,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -707,12 +707,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -732,12 +732,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -757,12 +757,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -782,12 +782,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -807,12 +807,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -832,12 +832,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -857,12 +857,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -882,12 +882,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -907,12 +907,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -932,12 +932,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -957,12 +957,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -982,12 +982,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1007,12 +1007,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1032,12 +1032,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1057,12 +1057,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1082,12 +1082,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1107,12 +1107,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1132,12 +1132,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1157,12 +1157,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1182,12 +1182,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1207,12 +1207,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1232,12 +1232,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1257,12 +1257,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1282,12 +1282,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1307,12 +1307,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1332,12 +1332,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1357,12 +1357,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1382,12 +1382,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1407,12 +1407,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1432,12 +1432,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1457,12 +1457,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1482,12 +1482,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1507,12 +1507,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1532,12 +1532,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1557,12 +1557,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1582,12 +1582,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1607,12 +1607,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1632,12 +1632,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1657,12 +1657,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1682,12 +1682,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1707,12 +1707,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1732,12 +1732,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1757,12 +1757,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1782,12 +1782,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1807,12 +1807,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1832,12 +1832,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1857,12 +1857,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1882,12 +1882,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1907,12 +1907,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1932,12 +1932,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1957,12 +1957,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1982,12 +1982,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2007,12 +2007,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2032,12 +2032,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2057,12 +2057,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2082,12 +2082,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2107,12 +2107,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2132,12 +2132,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2157,12 +2157,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2182,12 +2182,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2207,12 +2207,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2232,12 +2232,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2257,12 +2257,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2282,12 +2282,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2307,12 +2307,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2332,12 +2332,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2357,12 +2357,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2382,12 +2382,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2407,12 +2407,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2432,12 +2432,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2457,12 +2457,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2482,12 +2482,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2507,12 +2507,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2532,12 +2532,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2557,12 +2557,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2582,12 +2582,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2607,12 +2607,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2632,12 +2632,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2657,12 +2657,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2682,12 +2682,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2707,12 +2707,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2732,12 +2732,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2757,12 +2757,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2782,12 +2782,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2807,12 +2807,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2832,12 +2832,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2857,12 +2857,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2882,12 +2882,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2907,12 +2907,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2932,12 +2932,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2957,12 +2957,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2982,12 +2982,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3007,12 +3007,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3032,12 +3032,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3057,12 +3057,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3082,12 +3082,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3107,12 +3107,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3132,12 +3132,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3157,12 +3157,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3182,12 +3182,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3207,12 +3207,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3232,12 +3232,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3257,12 +3257,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3282,12 +3282,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3307,12 +3307,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3332,12 +3332,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3357,12 +3357,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3382,12 +3382,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3407,12 +3407,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3432,12 +3432,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3457,12 +3457,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3482,12 +3482,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3507,12 +3507,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3532,12 +3532,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3557,12 +3557,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3582,12 +3582,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3607,12 +3607,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3632,12 +3632,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3657,12 +3657,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3682,12 +3682,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3707,12 +3707,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3732,12 +3732,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3757,12 +3757,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3782,12 +3782,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3807,12 +3807,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3832,12 +3832,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3857,12 +3857,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3882,12 +3882,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3907,12 +3907,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3932,12 +3932,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3957,12 +3957,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3982,12 +3982,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4007,12 +4007,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4032,12 +4032,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4057,12 +4057,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4082,12 +4082,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4107,12 +4107,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4132,12 +4132,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4157,12 +4157,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4182,12 +4182,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4207,12 +4207,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4232,12 +4232,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4257,12 +4257,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4282,12 +4282,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4307,12 +4307,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4332,12 +4332,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4357,12 +4357,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4382,12 +4382,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4407,12 +4407,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4432,12 +4432,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4457,12 +4457,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4482,12 +4482,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4507,12 +4507,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4532,12 +4532,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4557,12 +4557,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4582,12 +4582,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4607,12 +4607,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4632,12 +4632,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4657,12 +4657,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4682,12 +4682,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4707,12 +4707,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4732,12 +4732,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4757,12 +4757,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4782,12 +4782,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4807,12 +4807,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4832,12 +4832,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4857,12 +4857,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4882,12 +4882,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4907,12 +4907,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4932,12 +4932,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4957,12 +4957,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4982,12 +4982,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5007,12 +5007,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5032,12 +5032,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5057,12 +5057,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5082,12 +5082,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5107,12 +5107,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5132,12 +5132,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5157,12 +5157,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5182,12 +5182,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5207,12 +5207,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5232,12 +5232,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5257,12 +5257,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5282,12 +5282,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5307,12 +5307,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5332,12 +5332,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5357,12 +5357,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5382,12 +5382,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5407,12 +5407,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5432,12 +5432,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5457,12 +5457,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5482,12 +5482,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5507,12 +5507,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5532,12 +5532,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5557,12 +5557,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5582,12 +5582,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5607,12 +5607,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5632,12 +5632,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5657,12 +5657,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5682,12 +5682,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5707,12 +5707,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5732,12 +5732,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5757,12 +5757,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5782,12 +5782,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5807,12 +5807,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5832,12 +5832,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5857,12 +5857,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5882,12 +5882,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5907,12 +5907,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5932,12 +5932,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5957,12 +5957,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5982,12 +5982,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6007,12 +6007,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6032,12 +6032,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6057,12 +6057,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6082,12 +6082,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6107,12 +6107,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6132,12 +6132,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6157,12 +6157,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6182,12 +6182,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6207,12 +6207,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6232,12 +6232,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6257,12 +6257,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6282,12 +6282,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6307,12 +6307,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6332,12 +6332,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6357,12 +6357,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6382,12 +6382,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6407,12 +6407,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6432,12 +6432,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6457,12 +6457,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6482,12 +6482,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6507,12 +6507,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6532,12 +6532,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6557,12 +6557,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6582,12 +6582,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6607,12 +6607,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6632,12 +6632,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6657,12 +6657,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6682,12 +6682,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6966,7 +6966,7 @@ "()" ] }, - "execution_count": 7, + "execution_count": 30, "metadata": {}, "output_type": "execute_result" } @@ -6995,7 +6995,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 31, "metadata": { "collapsed": false, "jupyter": { @@ -7029,8 +7029,8 @@ { "data": { "text/plain": [ - "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 177740},\n", - " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 321366},\n", + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 178621},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 409767},\n", " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 4},\n", " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", @@ -7038,14 +7038,14 @@ " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", - " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 166},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 168},\n", " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", - " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 166},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 168},\n", " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", @@ -7053,7 +7053,7 @@ " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" ] }, - "execution_count": 8, + "execution_count": 31, "metadata": {}, "output_type": "execute_result" } @@ -7069,7 +7069,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 32, "metadata": { "collapsed": false, "jupyter": { @@ -7097,7 +7097,7 @@ "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" ] }, - "execution_count": 9, + "execution_count": 32, "metadata": {}, "output_type": "execute_result" } @@ -7108,7 +7108,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 33, "metadata": { "collapsed": false, "jupyter": { @@ -7129,9 +7129,10 @@ "Submitting Task6_ResourceEstimationWrapper to target microsoft.estimator...\n", "Job successfully submitted.\n", " Job name: RE for the task 6\n", - " Job ID: 1678631d-016c-4332-ba1f-61fcb3b081b9\n", + " Job ID: 51c97eab-212e-45b6-9f03-7489fad62c36\n", "Waiting up to 30 seconds for Azure Quantum job to complete...\n", - "[12:40:10 PM] Current job status: Succeeded\n" + "[1:15:38 PM] Current job status: Executing\n", + "[1:15:43 PM] Current job status: Succeeded\n" ] } ], @@ -7142,7 +7143,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 34, "metadata": { "collapsed": false, "jupyter": { @@ -7158,7 +7159,7 @@ "outputs": [ { "data": { - "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":6,\"cczCount\":2,\"measurementCount\":6,\"numQubits\":12,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":9,\"logicalCycleTime\":3600.0,\"logicalErrorRate\":3.0000000000000015E-07,\"physicalQubits\":162},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":30,\"algorithmicLogicalQubits\":35,\"cliffordErrorRate\":0.001,\"logicalDepth\":30,\"numTfactories\":14,\"numTfactoryRuns\":3,\"numTsPerRotation\":null,\"numTstates\":32,\"physicalQubitsForAlgorithm\":5670,\"physicalQubitsForTfactories\":90720,\"requiredLogicalQubitErrorRate\":4.761904761904762E-07,\"requiredLogicalTstateErrorRate\":1.5625E-05},\"physicalQubits\":96390,\"runtime\":108000},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"3us 600ns\",\"logicalErrorRate\":\"3.00e-7\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"94.12 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"4.76e-7\",\"requiredLogicalTstateErrorRate\":\"1.56e-5\",\"runtime\":\"108us\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 5670 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 30 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 12$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 35$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 6 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 2 CCZ and 6 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 30. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 2 CCZ and 6 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 32 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{32\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 108us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 32 T states, the 14 copies of the T factory are repeatedly invoked 3 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 5670 are the product of the 35 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\\\cdot 14$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 35 logical qubits and the total cycle count 30.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 32.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.0000004761904761904762)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{9 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 3us 600ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 162.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.56e-5.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 35 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":96,\"cczCount\":16,\"measurementCount\":96,\"numQubits\":15,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":13,\"logicalCycleTime\":5200.0,\"logicalErrorRate\":3.000000000000002E-09,\"physicalQubits\":338},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":432,\"algorithmicLogicalQubits\":42,\"cliffordErrorRate\":0.001,\"logicalDepth\":432,\"numTfactories\":12,\"numTfactoryRuns\":38,\"numTsPerRotation\":null,\"numTstates\":448,\"physicalQubitsForAlgorithm\":14196,\"physicalQubitsForTfactories\":116160,\"requiredLogicalQubitErrorRate\":2.755731922398589E-08,\"requiredLogicalTstateErrorRate\":1.1160714285714287E-06},\"physicalQubits\":130356,\"runtime\":2246400},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"11\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"5us 200ns\",\"logicalErrorRate\":\"3.00e-9\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"89.11 %\",\"physicalQubitsPerRound\":\"9680\",\"requiredLogicalQubitErrorRate\":\"2.76e-8\",\"requiredLogicalTstateErrorRate\":\"1.12e-6\",\"runtime\":\"2ms 246us 400ns\",\"tfactoryRuntime\":\"57us 200ns\",\"tfactoryRuntimePerRound\":\"57us 200ns\",\"tstateLogicalErrorRate\":\"2.48e-7\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 14196 physical qubits to implement the algorithm logic, and 116160 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (5us 200ns) multiplied by the 432 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 15$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 42$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 96 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 16 CCZ and 96 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 432. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 16 CCZ and 96 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 448 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{448\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 2ms 246us 400ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 448 T states, the 12 copies of the T factory are repeatedly invoked 38 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 14196 are the product of the 42 logical qubits after layout and the 338 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 9680 physical qubits and we run 12 in parallel, therefore we need $116160 = 9680 \\\\cdot 12$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 42 logical qubits and the total cycle count 432.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 448.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000002755731922398589)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{13 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 5us 200ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 338.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.12e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 42 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[11],\"logicalErrorRate\":2.480000000000001E-07,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":9680,\"physicalQubitsPerRound\":[9680],\"runtime\":57200.0,\"runtimePerRound\":[57200.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", "text/html": [ "\r\n", "
\r\n", @@ -7170,24 +7171,24 @@ "\r\n", " \r\n", " Physical qubits\r\n", - " 96390\r\n", + " 130356\r\n", " \r\n", "

Number of physical qubits

\n", "\r\n", "
\r\n", - "

This value represents the total number of physical qubits, which is the sum of 5670 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

\n", + "

This value represents the total number of physical qubits, which is the sum of 14196 physical qubits to implement the algorithm logic, and 116160 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Runtime\r\n", - " 108us\r\n", + " 2ms 246us 400ns\r\n", " \r\n", "

Total runtime

\n", "\r\n", "
\r\n", - "

This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 30 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

\n", + "

This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (5us 200ns) multiplied by the 432 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

\n", "\r\n", " \r\n", " \n", @@ -7202,120 +7203,120 @@ "\r\n", " \r\n", " Logical algorithmic qubits\r\n", - " 35\r\n", + " 42\r\n", " \r\n", "

Number of logical qubits for the algorithm after layout

\n", "\r\n", "
\r\n", - "

Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 12\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 35$ logical qubits.

\n", + "

Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 15\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 42$ logical qubits.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Algorithmic depth\r\n", - " 30\r\n", + " 432\r\n", " \r\n", "

Number of logical cycles for the algorithm

\n", "\r\n", "
\r\n", - "

To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 6 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 2 CCZ and 6 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

\n", + "

To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 96 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 16 CCZ and 96 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Logical depth\r\n", - " 30\r\n", + " 432\r\n", " \r\n", "

Number of logical cycles performed

\n", "\r\n", "
\r\n", - "

This number is usually equal to the logical depth of the algorithm, which is 30. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", + "

This number is usually equal to the logical depth of the algorithm, which is 432. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Number of T states\r\n", - " 32\r\n", + " 448\r\n", " \r\n", "

Number of T states consumed by the algorithm

\n", "\r\n", "
\r\n", - "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 2 CCZ and 6 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", + "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 16 CCZ and 96 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Number of T factories\r\n", - " 14\r\n", + " 12\r\n", " \r\n", - "

Number of T factories capable of producing the demanded 32 T states during the algorithm's runtime

\n", + "

Number of T factories capable of producing the demanded 448 T states during the algorithm's runtime

\n", "\r\n", "
\r\n", - "

The total number of T factories 14 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{32\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 108us\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", + "

The total number of T factories 12 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{448\\;\\text{T states} \\cdot 57us 200ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 2ms 246us 400ns\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Number of T factory invocations\r\n", - " 3\r\n", + " 38\r\n", " \r\n", "

Number of times all T factories are invoked

\n", "\r\n", "
\r\n", - "

In order to prepare the 32 T states, the 14 copies of the T factory are repeatedly invoked 3 times.

\n", + "

In order to prepare the 448 T states, the 12 copies of the T factory are repeatedly invoked 38 times.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Physical algorithmic qubits\r\n", - " 5670\r\n", + " 14196\r\n", " \r\n", "

Number of physical qubits for the algorithm after layout

\n", "\r\n", "
\r\n", - "

The 5670 are the product of the 35 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.

\n", + "

The 14196 are the product of the 42 logical qubits after layout and the 338 physical qubits that encode a single logical qubit.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Physical T factory qubits\r\n", - " 90720\r\n", + " 116160\r\n", " \r\n", "

Number of physical qubits for the T factories

\n", "\r\n", "
\r\n", - "

Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\cdot 14$ qubits.

\n", + "

Each T factory requires 9680 physical qubits and we run 12 in parallel, therefore we need $116160 = 9680 \\cdot 12$ qubits.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Required logical qubit error rate\r\n", - " 4.76e-7\r\n", + " 2.76e-8\r\n", " \r\n", "

The minimum logical qubit error rate required to run the algorithm within the error budget

\n", "\r\n", "
\r\n", - "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 35 logical qubits and the total cycle count 30.

\n", + "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 42 logical qubits and the total cycle count 432.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Required logical T state error rate\r\n", - " 1.56e-5\r\n", + " 1.12e-6\r\n", " \r\n", "

The minimum T state error rate required for distilled T states

\n", "\r\n", "
\r\n", - "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 32.

\n", + "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 448.

\n", "\r\n", " \r\n", " \n", @@ -7354,19 +7355,19 @@ "\r\n", " \r\n", " Code distance\r\n", - " 9\r\n", + " 13\r\n", " \r\n", "

Required code distance for error correction

\n", "\r\n", "
\r\n", - "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.0000004761904761904762)}{\\log(0.01/0.001)} - 1\\)

\n", + "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000002755731922398589)}{\\log(0.01/0.001)} - 1\\)

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Physical qubits\r\n", - " 162\r\n", + " 338\r\n", " \r\n", "

Number of physical qubits per logical qubit

\n", "\r\n", @@ -7378,7 +7379,7 @@ "\r\n", " \r\n", " Logical cycle time\r\n", - " 3us 600ns\r\n", + " 5us 200ns\r\n", " \r\n", "

Duration of a logical cycle in nanoseconds

\n", "\r\n", @@ -7390,12 +7391,12 @@ "\r\n", " \r\n", " Logical qubit error rate\r\n", - " 3.00e-7\r\n", + " 3.00e-9\r\n", " \r\n", "

Logical qubit error rate

\n", "\r\n", "
\r\n", - "

The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{9 + 1}{2}$

\n", + "

The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{13 + 1}{2}$

\n", "\r\n", " \r\n", " \n", @@ -7431,7 +7432,7 @@ "

QEC scheme formula used to compute logical cycle time

\n", "\r\n", "
\r\n", - "

This is the formula that is used to compute the logical cycle time 3us 600ns.

\n", + "

This is the formula that is used to compute the logical cycle time 5us 200ns.

\n", "\r\n", " \r\n", " \n", @@ -7443,7 +7444,7 @@ "

QEC scheme formula used to compute number of physical qubits per logical qubit

\n", "\r\n", "
\r\n", - "

This is the formula that is used to compute the number of physical qubits per logical qubits 162.

\n", + "

This is the formula that is used to compute the number of physical qubits per logical qubits 338.

\n", "\r\n", " \r\n", " \n", @@ -7458,7 +7459,7 @@ "\r\n", " \r\n", " Physical qubits\r\n", - " 6480\r\n", + " 9680\r\n", " \r\n", "

Number of physical qubits for a single T factory

\n", "\r\n", @@ -7470,7 +7471,7 @@ "\r\n", " \r\n", " Runtime\r\n", - " 46us 800ns\r\n", + " 57us 200ns\r\n", " \r\n", "

Runtime of a single T factory

\n", "\r\n", @@ -7487,7 +7488,7 @@ "

Number of output T states produced in a single run of T factory

\n", "\r\n", "
\r\n", - "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.

\n", + "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.

\n", "\r\n", " \r\n", " \n", @@ -7542,7 +7543,7 @@ "\r\n", " \r\n", " Distillation code distances\r\n", - " 9\r\n", + " 11\r\n", " \r\n", "

The code distance in each round of distillation

\n", "\r\n", @@ -7554,7 +7555,7 @@ "\r\n", " \r\n", " Number of physical qubits per round\r\n", - " 6480\r\n", + " 9680\r\n", " \r\n", "

The number of physical qubits used in each round of distillation

\n", "\r\n", @@ -7566,7 +7567,7 @@ "\r\n", " \r\n", " Runtime per round\r\n", - " 46us 800ns\r\n", + " 57us 200ns\r\n", " \r\n", "

The runtime of each distillation round

\n", "\r\n", @@ -7578,12 +7579,12 @@ "\r\n", " \r\n", " Logical T state error rate\r\n", - " 2.17e-6\r\n", + " 2.48e-7\r\n", " \r\n", "

Logical T state error rate

\n", "\r\n", "
\r\n", - "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.56e-5.

\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.12e-6.

\n", "\r\n", " \r\n", " \n", @@ -7598,12 +7599,12 @@ "\r\n", " \r\n", " Logical qubits (pre-layout)\r\n", - " 12\r\n", + " 15\r\n", " \r\n", "

Number of logical qubits in the input quantum program

\n", "\r\n", "
\r\n", - "

We determine 35 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", + "

We determine 42 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", "\r\n", " \r\n", " \n", @@ -7646,7 +7647,7 @@ "\r\n", " \r\n", " CCZ gates\r\n", - " 2\r\n", + " 16\r\n", " \r\n", "

Number of CCZ-gates in the input quantum program

\n", "\r\n", @@ -7658,7 +7659,7 @@ "\r\n", " \r\n", " CCiX gates\r\n", - " 6\r\n", + " 96\r\n", " \r\n", "

Number of CCiX-gates in the input quantum program

\n", "\r\n", @@ -7670,7 +7671,7 @@ "\r\n", " \r\n", " Measurement operations\r\n", - " 6\r\n", + " 96\r\n", " \r\n", "

Number of single qubit measurements in the input quantum program

\n", "\r\n", @@ -7901,48 +7902,48 @@ " 'tGateTime': '50 ns',\n", " 'twoQubitGateErrorRate': 0.001,\n", " 'twoQubitGateTime': '50 ns'}},\n", - " 'logicalCounts': {'ccixCount': 6,\n", - " 'cczCount': 2,\n", - " 'measurementCount': 6,\n", - " 'numQubits': 12,\n", + " 'logicalCounts': {'ccixCount': 96,\n", + " 'cczCount': 16,\n", + " 'measurementCount': 96,\n", + " 'numQubits': 15,\n", " 'rotationCount': 0,\n", " 'rotationDepth': 0,\n", " 'tCount': 0},\n", - " 'logicalQubit': {'codeDistance': 9,\n", - " 'logicalCycleTime': 3600.0,\n", - " 'logicalErrorRate': 3.0000000000000015e-07,\n", - " 'physicalQubits': 162},\n", - " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 30,\n", - " 'algorithmicLogicalQubits': 35,\n", + " 'logicalQubit': {'codeDistance': 13,\n", + " 'logicalCycleTime': 5200.0,\n", + " 'logicalErrorRate': 3.000000000000002e-09,\n", + " 'physicalQubits': 338},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 432,\n", + " 'algorithmicLogicalQubits': 42,\n", " 'cliffordErrorRate': 0.001,\n", - " 'logicalDepth': 30,\n", - " 'numTfactories': 14,\n", - " 'numTfactoryRuns': 3,\n", + " 'logicalDepth': 432,\n", + " 'numTfactories': 12,\n", + " 'numTfactoryRuns': 38,\n", " 'numTsPerRotation': None,\n", - " 'numTstates': 32,\n", - " 'physicalQubitsForAlgorithm': 5670,\n", - " 'physicalQubitsForTfactories': 90720,\n", - " 'requiredLogicalQubitErrorRate': 4.761904761904762e-07,\n", - " 'requiredLogicalTstateErrorRate': 1.5625e-05},\n", - " 'physicalQubits': 96390,\n", - " 'runtime': 108000},\n", - " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", + " 'numTstates': 448,\n", + " 'physicalQubitsForAlgorithm': 14196,\n", + " 'physicalQubitsForTfactories': 116160,\n", + " 'requiredLogicalQubitErrorRate': 2.755731922398589e-08,\n", + " 'requiredLogicalTstateErrorRate': 1.1160714285714287e-06},\n", + " 'physicalQubits': 130356,\n", + " 'runtime': 2246400},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '11',\n", " 'errorBudget': '1.00e-3',\n", " 'errorBudgetLogical': '5.00e-4',\n", " 'errorBudgetRotations': '0.00e0',\n", " 'errorBudgetTstates': '5.00e-4',\n", - " 'logicalCycleTime': '3us 600ns',\n", - " 'logicalErrorRate': '3.00e-7',\n", + " 'logicalCycleTime': '5us 200ns',\n", + " 'logicalErrorRate': '3.00e-9',\n", " 'numTsPerRotation': 'No rotations in algorithm',\n", " 'numUnitsPerRound': '2',\n", - " 'physicalQubitsForTfactoriesPercentage': '94.12 %',\n", - " 'physicalQubitsPerRound': '6480',\n", - " 'requiredLogicalQubitErrorRate': '4.76e-7',\n", - " 'requiredLogicalTstateErrorRate': '1.56e-5',\n", - " 'runtime': '108us',\n", - " 'tfactoryRuntime': '46us 800ns',\n", - " 'tfactoryRuntimePerRound': '46us 800ns',\n", - " 'tstateLogicalErrorRate': '2.17e-6',\n", + " 'physicalQubitsForTfactoriesPercentage': '89.11 %',\n", + " 'physicalQubitsPerRound': '9680',\n", + " 'requiredLogicalQubitErrorRate': '2.76e-8',\n", + " 'requiredLogicalTstateErrorRate': '1.12e-6',\n", + " 'runtime': '2ms 246us 400ns',\n", + " 'tfactoryRuntime': '57us 200ns',\n", + " 'tfactoryRuntimePerRound': '57us 200ns',\n", + " 'tstateLogicalErrorRate': '2.48e-7',\n", " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", @@ -7953,53 +7954,53 @@ " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", " 'groups': [{'alwaysVisible': True,\n", " 'entries': [{'description': 'Number of physical qubits',\n", - " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 5670 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 14196 physical qubits to implement the algorithm logic, and 116160 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", " 'label': 'Physical qubits',\n", " 'path': 'physicalCounts/physicalQubits'},\n", " {'description': 'Total runtime',\n", - " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 30 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (5us 200ns) multiplied by the 432 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", " 'label': 'Runtime',\n", " 'path': 'physicalCountsFormatted/runtime'}],\n", " 'title': 'Physical resource estimates'},\n", " {'alwaysVisible': False,\n", " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", - " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 12$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 35$ logical qubits.',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 15$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 42$ logical qubits.',\n", " 'label': 'Logical algorithmic qubits',\n", " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", " {'description': 'Number of logical cycles for the algorithm',\n", - " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 6 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 2 CCZ and 6 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 96 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 16 CCZ and 96 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", " 'label': 'Algorithmic depth',\n", " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", " {'description': 'Number of logical cycles performed',\n", - " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 30. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 432. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", " 'label': 'Logical depth',\n", " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", " {'description': 'Number of T states consumed by the algorithm',\n", - " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 2 CCZ and 6 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 16 CCZ and 96 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", " 'label': 'Number of T states',\n", " 'path': 'physicalCounts/breakdown/numTstates'},\n", - " {'description': \"Number of T factories capable of producing the demanded 32 T states during the algorithm's runtime\",\n", - " 'explanation': 'The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{32\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 108us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " {'description': \"Number of T factories capable of producing the demanded 448 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{448\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 2ms 246us 400ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", " 'label': 'Number of T factories',\n", " 'path': 'physicalCounts/breakdown/numTfactories'},\n", " {'description': 'Number of times all T factories are invoked',\n", - " 'explanation': 'In order to prepare the 32 T states, the 14 copies of the T factory are repeatedly invoked 3 times.',\n", + " 'explanation': 'In order to prepare the 448 T states, the 12 copies of the T factory are repeatedly invoked 38 times.',\n", " 'label': 'Number of T factory invocations',\n", " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", " {'description': 'Number of physical qubits for the algorithm after layout',\n", - " 'explanation': 'The 5670 are the product of the 35 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.',\n", + " 'explanation': 'The 14196 are the product of the 42 logical qubits after layout and the 338 physical qubits that encode a single logical qubit.',\n", " 'label': 'Physical algorithmic qubits',\n", " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", " {'description': 'Number of physical qubits for the T factories',\n", - " 'explanation': 'Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\\\cdot 14$ qubits.',\n", + " 'explanation': 'Each T factory requires 9680 physical qubits and we run 12 in parallel, therefore we need $116160 = 9680 \\\\cdot 12$ qubits.',\n", " 'label': 'Physical T factory qubits',\n", " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", - " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 35 logical qubits and the total cycle count 30.',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 42 logical qubits and the total cycle count 432.',\n", " 'label': 'Required logical qubit error rate',\n", " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", " {'description': 'The minimum T state error rate required for distilled T states',\n", - " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 32.',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 448.',\n", " 'label': 'Required logical T state error rate',\n", " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", @@ -8013,7 +8014,7 @@ " 'label': 'QEC scheme',\n", " 'path': 'jobParams/qecScheme/name'},\n", " {'description': 'Required code distance for error correction',\n", - " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.0000004761904761904762)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000002755731922398589)}{\\\\log(0.01/0.001)} - 1$',\n", " 'label': 'Code distance',\n", " 'path': 'logicalQubit/codeDistance'},\n", " {'description': 'Number of physical qubits per logical qubit',\n", @@ -8025,7 +8026,7 @@ " 'label': 'Logical cycle time',\n", " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", " {'description': 'Logical qubit error rate',\n", - " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{9 + 1}{2}$',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{13 + 1}{2}$',\n", " 'label': 'Logical qubit error rate',\n", " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", " {'description': 'Crossing prefactor used in QEC scheme',\n", @@ -8037,11 +8038,11 @@ " 'label': 'Error correction threshold',\n", " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", " {'description': 'QEC scheme formula used to compute logical cycle time',\n", - " 'explanation': 'This is the formula that is used to compute the logical cycle time 3us 600ns.',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 5us 200ns.',\n", " 'label': 'Logical cycle time formula',\n", " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", - " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 162.',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 338.',\n", " 'label': 'Physical qubits formula',\n", " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", " 'title': 'Logical qubit parameters'},\n", @@ -8055,7 +8056,7 @@ " 'label': 'Runtime',\n", " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", " {'description': 'Number of output T states produced in a single run of T factory',\n", - " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.',\n", " 'label': 'Number of output T states per run',\n", " 'path': 'tfactory/numTstates'},\n", " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", @@ -8087,13 +8088,13 @@ " 'label': 'Runtime per round',\n", " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", " {'description': 'Logical T state error rate',\n", - " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.56e-5.',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.12e-6.',\n", " 'label': 'Logical T state error rate',\n", " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", " 'title': 'T factory parameters'},\n", " {'alwaysVisible': False,\n", " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", - " 'explanation': 'We determine 35 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'explanation': 'We determine 42 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", " 'label': 'Logical qubits (pre-layout)',\n", " 'path': 'logicalCounts/numQubits'},\n", " {'description': 'Number of T gates in the input quantum program',\n", @@ -8182,20 +8183,20 @@ " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", " 'title': 'Physical qubit parameters'}]},\n", " 'status': 'success',\n", - " 'tfactory': {'codeDistancePerRound': [9],\n", - " 'logicalErrorRate': 2.165000000000001e-06,\n", + " 'tfactory': {'codeDistancePerRound': [11],\n", + " 'logicalErrorRate': 2.480000000000001e-07,\n", " 'numInputTstates': 30,\n", " 'numRounds': 1,\n", " 'numTstates': 1,\n", " 'numUnitsPerRound': [2],\n", - " 'physicalQubits': 6480,\n", - " 'physicalQubitsPerRound': [6480],\n", - " 'runtime': 46800.0,\n", - " 'runtimePerRound': [46800.0],\n", + " 'physicalQubits': 9680,\n", + " 'physicalQubitsPerRound': [9680],\n", + " 'runtime': 57200.0,\n", + " 'runtimePerRound': [57200.0],\n", " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" ] }, - "execution_count": 11, + "execution_count": 34, "metadata": {}, "output_type": "execute_result" } @@ -8208,7 +8209,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 35, "metadata": { "collapsed": false, "jupyter": { @@ -8235,7 +8236,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 36, "metadata": { "collapsed": false, "jupyter": { @@ -8253,18 +8254,18 @@ "name": "stdout", "output_type": "stream", "text": [ - "Logical algorithmic qubits = 35\n", - "Algorithmic depth = 30\n", - "Score = 1050\n" + "Logical algorithmic qubits = 42\n", + "Algorithmic depth = 432\n", + "Score = 18144\n" ] }, { "data": { "text/plain": [ - "1050" + "18144" ] }, - "execution_count": 13, + "execution_count": 36, "metadata": {}, "output_type": "execute_result" } diff --git a/iQuHack-challenge-2023-task7.ipynb b/iQuHack-challenge-2023-task7.ipynb index 84be853..89a785e 100644 --- a/iQuHack-challenge-2023-task7.ipynb +++ b/iQuHack-challenge-2023-task7.ipynb @@ -67,7 +67,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 14, "metadata": { "collapsed": false, "jupyter": { @@ -80,15 +80,7 @@ } } }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Preparing Q# environment...\n" - ] - } - ], + "outputs": [], "source": [ "# Run this code cell to import the modules required to work with Q# and Azure\n", "import qsharp\n", @@ -97,7 +89,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 15, "metadata": { "collapsed": false, "jupyter": { @@ -119,7 +111,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 16, "metadata": { "collapsed": false, "jupyter": { @@ -156,7 +148,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 27, "metadata": { "collapsed": false, "jupyter": { @@ -206,7 +198,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 28, "metadata": {}, "outputs": [], "source": [ @@ -215,7 +207,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 29, "metadata": { "collapsed": false, "jupyter": { @@ -272,7 +264,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 30, "metadata": { "collapsed": false, "jupyter": { @@ -317,12 +309,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -342,12 +334,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -367,12 +359,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -392,12 +384,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -417,12 +409,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -442,12 +434,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -467,12 +459,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -492,12 +484,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -517,12 +509,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -542,12 +534,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -567,12 +559,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -592,12 +584,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -617,12 +609,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -642,12 +634,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -667,12 +659,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -692,12 +684,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -717,12 +709,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -742,12 +734,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -767,12 +759,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -792,12 +784,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -817,12 +809,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -842,12 +834,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -867,12 +859,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -892,12 +884,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -917,12 +909,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -942,12 +934,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -967,12 +959,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -992,12 +984,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1017,12 +1009,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1042,12 +1034,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1067,12 +1059,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1092,12 +1084,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1117,12 +1109,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1142,12 +1134,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1167,12 +1159,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1192,12 +1184,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1217,12 +1209,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1242,12 +1234,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1267,12 +1259,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1292,12 +1284,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1317,12 +1309,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1342,12 +1334,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1367,12 +1359,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1392,12 +1384,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1417,12 +1409,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1442,12 +1434,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1467,12 +1459,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1492,12 +1484,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1517,12 +1509,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1542,12 +1534,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1567,12 +1559,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1592,12 +1584,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1617,12 +1609,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1642,12 +1634,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1667,12 +1659,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1692,12 +1684,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1717,12 +1709,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1742,12 +1734,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1767,12 +1759,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1792,12 +1784,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1817,12 +1809,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1842,12 +1834,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1867,12 +1859,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1892,12 +1884,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1917,12 +1909,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1942,12 +1934,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1967,12 +1959,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1992,12 +1984,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2017,12 +2009,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2042,12 +2034,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2067,12 +2059,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2092,12 +2084,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2117,12 +2109,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2142,12 +2134,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2167,12 +2159,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2192,12 +2184,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2217,12 +2209,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2242,12 +2234,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2267,12 +2259,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2292,12 +2284,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2317,12 +2309,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2342,12 +2334,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2367,12 +2359,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2392,12 +2384,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2417,12 +2409,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2442,12 +2434,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2467,12 +2459,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2492,12 +2484,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2517,12 +2509,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2542,12 +2534,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2567,12 +2559,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2592,12 +2584,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2617,12 +2609,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2642,12 +2634,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2667,12 +2659,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2692,12 +2684,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2717,12 +2709,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2742,12 +2734,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2767,12 +2759,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2792,12 +2784,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2817,12 +2809,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2842,12 +2834,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2867,12 +2859,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2892,12 +2884,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2917,12 +2909,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2942,12 +2934,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2967,12 +2959,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2992,12 +2984,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3017,12 +3009,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3042,12 +3034,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3067,12 +3059,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3092,12 +3084,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3117,12 +3109,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3142,12 +3134,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3167,12 +3159,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3192,12 +3184,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3217,12 +3209,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3242,12 +3234,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3267,12 +3259,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3292,12 +3284,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3317,12 +3309,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3342,12 +3334,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3367,12 +3359,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3392,12 +3384,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3417,12 +3409,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3442,12 +3434,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3467,12 +3459,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3492,12 +3484,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3648,7 +3640,7 @@ "()" ] }, - "execution_count": 7, + "execution_count": 30, "metadata": {}, "output_type": "execute_result" } @@ -3677,7 +3669,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 31, "metadata": { "collapsed": false, "jupyter": { @@ -3711,23 +3703,23 @@ { "data": { "text/plain": [ - "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 176914},\n", - " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 423509},\n", + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 178643},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 426101},\n", " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 4},\n", " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", - " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", - " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 166},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 69},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 168},\n", " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", - " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", - " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 166},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 69},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 168},\n", " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", @@ -3735,7 +3727,7 @@ " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" ] }, - "execution_count": 8, + "execution_count": 31, "metadata": {}, "output_type": "execute_result" } @@ -3751,7 +3743,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 32, "metadata": { "collapsed": false, "jupyter": { @@ -3779,7 +3771,7 @@ "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" ] }, - "execution_count": 9, + "execution_count": 32, "metadata": {}, "output_type": "execute_result" } @@ -3790,7 +3782,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 33, "metadata": { "collapsed": false, "jupyter": { @@ -3811,10 +3803,10 @@ "Submitting Task7_ResourceEstimationWrapper to target microsoft.estimator...\n", "Job successfully submitted.\n", " Job name: RE for the task 7\n", - " Job ID: fd0504b4-d2d0-4bfc-a151-f6708f20d5ce\n", + " Job ID: a7d42efd-1393-44bf-bf4d-7e90bcc2df62\n", "Waiting up to 30 seconds for Azure Quantum job to complete...\n", - "[12:35:59 PM] Current job status: Waiting\n", - "[12:36:04 PM] Current job status: Succeeded\n" + "[1:17:00 PM] Current job status: Executing\n", + "[1:17:05 PM] Current job status: Succeeded\n" ] } ], @@ -3825,7 +3817,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 34, "metadata": { "collapsed": false, "jupyter": { @@ -4878,7 +4870,7 @@ " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" ] }, - "execution_count": 11, + "execution_count": 34, "metadata": {}, "output_type": "execute_result" } @@ -4891,7 +4883,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 35, "metadata": { "collapsed": false, "jupyter": { @@ -4918,7 +4910,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 36, "metadata": { "collapsed": false, "jupyter": { @@ -4947,7 +4939,7 @@ "2546" ] }, - "execution_count": 13, + "execution_count": 36, "metadata": {}, "output_type": "execute_result" } diff --git a/iQuHack-challenge-2023-task9.ipynb b/iQuHack-challenge-2023-task9.ipynb index eea076e..2f3bf93 100644 --- a/iQuHack-challenge-2023-task9.ipynb +++ b/iQuHack-challenge-2023-task9.ipynb @@ -67,7 +67,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "collapsed": false, "jupyter": { @@ -89,7 +89,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": { "collapsed": false, "jupyter": { @@ -104,14 +104,14 @@ }, "outputs": [], "source": [ - "teamname=\"msft_is_the_best\" # Update this field with your team name\n", - "task=[\"task9\"]\n", - "slack_id=\"myslackid\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + "teamname=\"schrodingers-duck\" # Update this field with your team name\n", + "task=[\"task8\"]\n", + "slack_id=\"U04L3SFUCQ2\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": { "collapsed": false, "jupyter": { @@ -148,7 +148,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": { "collapsed": false, "jupyter": { @@ -172,6 +172,12 @@ "\n", "// Task 9. \n", "// (input will contain 8 qubits)\n", + "operation original(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " for i in [31,46,61,76,91,106,121,136,151,166,181,196,211,226,241] {\n", + " ControlledOnInt(i, X)(input, target);\n", + " }\n", + "}\n", + "\n", "operation Task9(input : Qubit[], target : Qubit) : Unit is Adj {\n", " for i in [31,46,61,76,91,106,121,136,151,166,181,196,211,226,241] {\n", " ControlledOnInt(i, X)(input, target);\n", @@ -181,7 +187,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": { "collapsed": false, "jupyter": { @@ -238,7 +244,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": { "collapsed": false, "jupyter": { @@ -251,7 +257,6702 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": 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Qubit IDs0, 1, 2, 3, 4, 5, 6, 7, 8
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$\\left|001000110100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001001000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001001010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001001100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001001110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001010000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001010010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001010100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001010110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001011000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001011010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001011100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001011110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001100000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001100010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001100100100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001100110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001101000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001101010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001101100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001101110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001110000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001110010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001110100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001110110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001111000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001111010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001111100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001111110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
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\r\n", + "

\r\n", + "
$\\left|010000010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010000100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010000110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010001000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010001010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010001100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010001110100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010010000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|010010010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010010100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|010010110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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\r\n", + "
$\\left|010011010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|010011100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|010011110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|010100000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010100010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010100100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010100110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010101000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010101010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010101100100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010101110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010110010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010111010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|011000100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|011000110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|011001100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|011010010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|011010100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|011010110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|011011010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|011110110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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\r\n", + "
$\\left|011111010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011111110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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\r\n", + "
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\r\n", + "
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\r\n", + "
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\r\n", + "
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\r\n", + "
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\r\n", + "
$\\left|100011010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|100100110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100101010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|100101110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|100110110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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$\\left|100111110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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$\\left|101000010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|101000110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|101001000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101001010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101010000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101010100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101010110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101011000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101011100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101011110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101100000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101100010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101100100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101101010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101101110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101111010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101111100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101111110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110000010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110000100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110000110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110001000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110001100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110001110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110010000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110010010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110010100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110010110100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110011000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110011010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110011100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110011110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110100000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110100010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

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$\\left|110100100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110100110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|110101000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110101010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

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$\\left|110101100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|110101110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|110110000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110110010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110110100100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110110110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110111000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110111010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110111100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110111110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111000010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111000100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111000110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111001000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111001010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111001100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111001110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111010000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111010010100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111010110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111011000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111011010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111011100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111011110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111100010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111100110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111101000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111101010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111101100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111101110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111110000100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111110010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111110100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111110110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111111000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111111010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111111100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111111110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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"metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# Note that in the output of this cell the target qubit corresponds to the rightmost bit\n", "qsharp.config[\"dump.basisStateLabelingConvention\"]=\"Bitstring\"\n", @@ -276,7 +6977,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "metadata": { "collapsed": false, "jupyter": { @@ -289,19 +6990,68 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "\"Connecting to Azure Quantum...\"", + "text/plain": [ + "Connecting to Azure Quantum..." + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Connected to Azure Quantum workspace azure-q in location uksouth.\n" + ] + }, + { + "data": { + "text/plain": [ + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 178414},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 303167},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 4},\n", + " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 166},\n", + " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 166},\n", + " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.qpu.aspen-m-2', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", "# If you're using this notebook in qBraid, keep it\n", "qsharp.azure.connect(\n", - " resourceId=\"...\",\n", - " location=\"...\",\n", + " resourceId=\"/subscriptions/7fc54e95-14cf-4a6f-b50e-d6155c241309/resourceGroups/AzureQuantum/providers/Microsoft.Quantum/Workspaces/azure-q\",\n", + " location=\"UK South\",\n", " credential=\"CLI\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, "metadata": { "collapsed": false, "jupyter": { @@ -314,14 +7064,33 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loading package Microsoft.Quantum.Providers.Core and dependencies...\n", + "Active target is now microsoft.estimator\n" + ] + }, + { + "data": { + "text/plain": [ + "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "qsharp.azure.target(\"microsoft.estimator\")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "metadata": { "collapsed": false, "jupyter": { @@ -334,7 +7103,20 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Submitting Task9_ResourceEstimationWrapper to target microsoft.estimator...\n", + "Job successfully submitted.\n", + " Job name: RE for the task 9\n", + " Job ID: ae3e32d3-3d41-40d0-8170-61957fdfc5ca\n", + "Waiting up to 30 seconds for Azure Quantum job to complete...\n", + "[12:43:18 PM] Current job status: Succeeded\n" + ] + } + ], "source": [ "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", "result = qsharp.azure.execute(Task9_ResourceEstimationWrapper, jobName=\"RE for the task 9\")" @@ -342,7 +7124,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "metadata": { "collapsed": false, "jupyter": { @@ -355,7 +7137,1051 @@ } } }, - "outputs": [], + "outputs": [ + { + "data": { + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":90,\"cczCount\":15,\"measurementCount\":90,\"numQubits\":15,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":13,\"logicalCycleTime\":5200.0,\"logicalErrorRate\":3.000000000000002E-09,\"physicalQubits\":338},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":405,\"algorithmicLogicalQubits\":42,\"cliffordErrorRate\":0.001,\"logicalDepth\":405,\"numTfactories\":12,\"numTfactoryRuns\":35,\"numTsPerRotation\":null,\"numTstates\":420,\"physicalQubitsForAlgorithm\":14196,\"physicalQubitsForTfactories\":116160,\"requiredLogicalQubitErrorRate\":2.9394473838918283E-08,\"requiredLogicalTstateErrorRate\":1.1904761904761906E-06},\"physicalQubits\":130356,\"runtime\":2106000},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"11\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"5us 200ns\",\"logicalErrorRate\":\"3.00e-9\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"89.11 %\",\"physicalQubitsPerRound\":\"9680\",\"requiredLogicalQubitErrorRate\":\"2.94e-8\",\"requiredLogicalTstateErrorRate\":\"1.19e-6\",\"runtime\":\"2ms 106us\",\"tfactoryRuntime\":\"57us 200ns\",\"tfactoryRuntimePerRound\":\"57us 200ns\",\"tstateLogicalErrorRate\":\"2.48e-7\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 14196 physical qubits to implement the algorithm logic, and 116160 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (5us 200ns) multiplied by the 405 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 15$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 42$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 90 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 15 CCZ and 90 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 405. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 15 CCZ and 90 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 420 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{420\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 2ms 106us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 420 T states, the 12 copies of the T factory are repeatedly invoked 35 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 14196 are the product of the 42 logical qubits after layout and the 338 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 9680 physical qubits and we run 12 in parallel, therefore we need $116160 = 9680 \\\\cdot 12$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 42 logical qubits and the total cycle count 405.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 420.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.000000029394473838918283)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{13 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 5us 200ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 338.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.19e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 42 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or ¬µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[11],\"logicalErrorRate\":2.480000000000001E-07,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":9680,\"physicalQubitsPerRound\":[9680],\"runtime\":57200.0,\"runtimePerRound\":[57200.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "text/html": [ + "\r\n", + "
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Physical qubits130356\r\n", + "

Number of physical qubits

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This value represents the total number of physical qubits, which is the sum of 14196 physical qubits to implement the algorithm logic, and 116160 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

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Runtime2ms 106us\r\n", + "

Total runtime

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This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (5us 200ns) multiplied by the 405 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

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Logical algorithmic qubits42\r\n", + "

Number of logical qubits for the algorithm after layout

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Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 15\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 42$ logical qubits.

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Algorithmic depth405\r\n", + "

Number of logical cycles for the algorithm

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To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 90 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 15 CCZ and 90 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

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Logical depth405\r\n", + "

Number of logical cycles performed

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This number is usually equal to the logical depth of the algorithm, which is 405. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", + "\r\n", + "
Number of T states420\r\n", + "

Number of T states consumed by the algorithm

\n", + "\r\n", + "
\r\n", + "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 15 CCZ and 90 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", + "\r\n", + "
Number of T factories12\r\n", + "

Number of T factories capable of producing the demanded 420 T states during the algorithm's runtime

\n", + "\r\n", + "
\r\n", + "

The total number of T factories 12 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{420\\;\\text{T states} \\cdot 57us 200ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 2ms 106us\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", + "\r\n", + "
Number of T factory invocations35\r\n", + "

Number of times all T factories are invoked

\n", + "\r\n", + "
\r\n", + "

In order to prepare the 420 T states, the 12 copies of the T factory are repeatedly invoked 35 times.

\n", + "\r\n", + "
Physical algorithmic qubits14196\r\n", + "

Number of physical qubits for the algorithm after layout

\n", + "\r\n", + "
\r\n", + "

The 14196 are the product of the 42 logical qubits after layout and the 338 physical qubits that encode a single logical qubit.

\n", + "\r\n", + "
Physical T factory qubits116160\r\n", + "

Number of physical qubits for the T factories

\n", + "\r\n", + "
\r\n", + "

Each T factory requires 9680 physical qubits and we run 12 in parallel, therefore we need $116160 = 9680 \\cdot 12$ qubits.

\n", + "\r\n", + "
Required logical qubit error rate2.94e-8\r\n", + "

The minimum logical qubit error rate required to run the algorithm within the error budget

\n", + "\r\n", + "
\r\n", + "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 42 logical qubits and the total cycle count 405.

\n", + "\r\n", + "
Required logical T state error rate1.19e-6\r\n", + "

The minimum T state error rate required for distilled T states

\n", + "\r\n", + "
\r\n", + "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 420.

\n", + "\r\n", + "
Number of T states per rotationNo rotations in algorithm\r\n", + "

Number of T states to implement a rotation with an arbitrary angle

\n", + "\r\n", + "
\r\n", + "

The number of T states to implement a rotation with an arbitrary angle is \\(\\lceil 0.53 \\log_2(0 / 0) + 5.3\\rceil\\) [arXiv:2203.10064]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Logical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
QEC schemesurface_code\r\n", + "

Name of QEC scheme

\n", + "\r\n", + "
\r\n", + "

You can load pre-defined QEC schemes by using the name surface_code or floquet_code. The latter only works with Majorana qubits.

\n", + "\r\n", + "
Code distance13\r\n", + "

Required code distance for error correction

\n", + "\r\n", + "
\r\n", + "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.000000029394473838918283)}{\\log(0.01/0.001)} - 1\\)

\n", + "\r\n", + "
Physical qubits338\r\n", + "

Number of physical qubits per logical qubit

\n", + "\r\n", + "
\r\n", + "

The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.

\n", + "\r\n", + "
Logical cycle time5us 200ns\r\n", + "

Duration of a logical cycle in nanoseconds

\n", + "\r\n", + "
\r\n", + "

The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.

\n", + "\r\n", + "
Logical qubit error rate3.00e-9\r\n", + "

Logical qubit error rate

\n", + "\r\n", + "
\r\n", + "

The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{13 + 1}{2}$

\n", + "\r\n", + "
Crossing prefactor0.03\r\n", + "

Crossing prefactor used in QEC scheme

\n", + "\r\n", + "
\r\n", + "

The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.

\n", + "\r\n", + "
Error correction threshold0.01\r\n", + "

Error correction threshold used in QEC scheme

\n", + "\r\n", + "
\r\n", + "

The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.

\n", + "\r\n", + "
Logical cycle time formula(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\r\n", + "

QEC scheme formula used to compute logical cycle time

\n", + "\r\n", + "
\r\n", + "

This is the formula that is used to compute the logical cycle time 5us 200ns.

\n", + "\r\n", + "
Physical qubits formula2 * codeDistance * codeDistance\r\n", + "

QEC scheme formula used to compute number of physical qubits per logical qubit

\n", + "\r\n", + "
\r\n", + "

This is the formula that is used to compute the number of physical qubits per logical qubits 338.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " T factory parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits9680\r\n", + "

Number of physical qubits for a single T factory

\n", + "\r\n", + "
\r\n", + "

This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.

\n", + "\r\n", + "
Runtime57us 200ns\r\n", + "

Runtime of a single T factory

\n", + "\r\n", + "
\r\n", + "

The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.

\n", + "\r\n", + "
Number of output T states per run1\r\n", + "

Number of output T states produced in a single run of T factory

\n", + "\r\n", + "
\r\n", + "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.

\n", + "\r\n", + "
Number of input T states per run30\r\n", + "

Number of physical input T states consumed in a single run of a T factory

\n", + "\r\n", + "
\r\n", + "

This value includes the physical input T states of all copies of the distillation unit in the first round.

\n", + "\r\n", + "
Distillation rounds1\r\n", + "

The number of distillation rounds

\n", + "\r\n", + "
\r\n", + "

This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.

\n", + "\r\n", + "
Distillation units per round2\r\n", + "

The number of units in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the number of copies for the distillation units per round.

\n", + "\r\n", + "
Distillation units15-to-1 space efficient logical\r\n", + "

The types of distillation units

\n", + "\r\n", + "
\r\n", + "

These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.

\n", + "\r\n", + "
Distillation code distances11\r\n", + "

The code distance in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.

\n", + "\r\n", + "
Number of physical qubits per round9680\r\n", + "

The number of physical qubits used in each round of distillation

\n", + "\r\n", + "
\r\n", + "

The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.

\n", + "\r\n", + "
Runtime per round57us 200ns\r\n", + "

The runtime of each distillation round

\n", + "\r\n", + "
\r\n", + "

The runtime of the T factory is the sum of the runtimes in all rounds.

\n", + "\r\n", + "
Logical T state error rate2.48e-7\r\n", + "

Logical T state error rate

\n", + "\r\n", + "
\r\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.19e-6.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Pre-layout logical resources\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Logical qubits (pre-layout)15\r\n", + "

Number of logical qubits in the input quantum program

\n", + "\r\n", + "
\r\n", + "

We determine 42 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", + "\r\n", + "
T gates0\r\n", + "

Number of T gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.

\n", + "\r\n", + "
Rotation gates0\r\n", + "

Number of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.

\n", + "\r\n", + "
Rotation depth0\r\n", + "

Depth of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.

\n", + "\r\n", + "
CCZ gates15\r\n", + "

Number of CCZ-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCZ gates.

\n", + "\r\n", + "
CCiX gates90\r\n", + "

Number of CCiX-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCiX gates, which applies \\(-iX\\) controlled on two control qubits [1212.5069].

\n", + "\r\n", + "
Measurement operations90\r\n", + "

Number of single qubit measurements in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Assumed error budget\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Total error budget1.00e-3\r\n", + "

Total error budget for the algorithm

\n", + "\r\n", + "
\r\n", + "

The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget \\(\\epsilon = \\epsilon_{\\log} + \\epsilon_{\\rm dis} + \\epsilon_{\\rm syn}\\) is uniformly distributed and applies to errors \\(\\epsilon_{\\log}\\) to implement logical qubits, an error budget \\(\\epsilon_{\\rm dis}\\) to produce T states through distillation, and an error budget \\(\\epsilon_{\\rm syn}\\) to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets \\(\\epsilon_{\\rm dis}\\) and \\(\\epsilon_{\\rm syn}\\) are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.

\n", + "\r\n", + "
Logical error probability5.00e-4\r\n", + "

Probability of at least one logical error

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
T distillation error probability5.00e-4\r\n", + "

Probability of at least one faulty T distillation

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
Rotation synthesis error probability0.00e0\r\n", + "

Probability of at least one failed rotation synthesis

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Physical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Qubit namequbit_gate_ns_e3\r\n", + "

Some descriptive name for the qubit model

\n", + "\r\n", + "
\r\n", + "

You can load pre-defined qubit parameters by using the names qubit_gate_ns_e3, qubit_gate_ns_e4, qubit_gate_us_e3, qubit_gate_us_e4, qubit_maj_ns_e4, or qubit_maj_ns_e6. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).

\n", + "\r\n", + "
Instruction setGateBased\r\n", + "

Underlying qubit technology (gate-based or Majorana)

\n", + "\r\n", + "
\r\n", + "

When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either gate-based or Majorana. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.

\n", + "\r\n", + "
Single-qubit measurement time100 ns\r\n", + "

Operation time for single-qubit measurement (t_meas) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.

\n", + "\r\n", + "
Single-qubit gate time50 ns\r\n", + "

Operation time for single-qubit gate (t_gate) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.

\n", + "\r\n", + "
Two-qubit gate time50 ns\r\n", + "

Operation time for two-qubit gate in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.

\n", + "\r\n", + "
T gate time50 ns\r\n", + "

Operation time for a T gate

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to execute a T gate.

\n", + "\r\n", + "
Single-qubit measurement error rate0.001\r\n", + "

Error rate for single-qubit measurement

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit measurement in the Pauli basis may fail.

\n", + "\r\n", + "
Single-qubit error rate0.001\r\n", + "

Error rate for single-qubit Clifford gate (p)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.

\n", + "\r\n", + "
Two-qubit error rate0.001\r\n", + "

Error rate for two-qubit Clifford gate

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.

\n", + "\r\n", + "
T gate error rate0.001\r\n", + "

Error rate to prepare single-qubit T state or apply a T gate (p_T)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which executing a single T gate may fail.

\n", + "\r\n", + "
\n", + "
\r\n", + " Assumptions\r\n", + "
    \n", + "

  • More details on the following lists of assumptions can be found in the paper Accessing requirements for scaling quantum computers and their applications.

    \n", + "
    • \n", + "

  • Uniform independent physical noise. We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.

    \n", + "
    • \n", + "

  • Efficient classical computation. We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.

    \n", + "
    • \n", + "

  • Extraction circuits for planar quantum ISA. We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).

    \n", + "
    • \n", + "

  • Uniform independent logical noise. We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.

    \n", + "
    • \n", + "

  • Negligible Clifford costs for synthesis. We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.

    \n", + "
    • \n", + "

  • Smooth magic state consumption rate. We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.

    \n", + "
    • \n", + "
\n" + ], + "text/plain": [ + "{'errorBudget': {'logical': 0.0005, 'rotations': 0.0, 'tstates': 0.0005},\n", + " 'jobParams': {'errorBudget': 0.001,\n", + " 'qecScheme': {'crossingPrefactor': 0.03,\n", + " 'errorCorrectionThreshold': 0.01,\n", + " 'logicalCycleTime': '(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance',\n", + " 'name': 'surface_code',\n", + " 'physicalQubitsPerLogicalQubit': '2 * codeDistance * codeDistance'},\n", + " 'qubitParams': {'instructionSet': 'GateBased',\n", + " 'name': 'qubit_gate_ns_e3',\n", + " 'oneQubitGateErrorRate': 0.001,\n", + " 'oneQubitGateTime': '50 ns',\n", + " 'oneQubitMeasurementErrorRate': 0.001,\n", + " 'oneQubitMeasurementTime': '100 ns',\n", + " 'tGateErrorRate': 0.001,\n", + " 'tGateTime': '50 ns',\n", + " 'twoQubitGateErrorRate': 0.001,\n", + " 'twoQubitGateTime': '50 ns'}},\n", + " 'logicalCounts': {'ccixCount': 90,\n", + " 'cczCount': 15,\n", + " 'measurementCount': 90,\n", + " 'numQubits': 15,\n", + " 'rotationCount': 0,\n", + " 'rotationDepth': 0,\n", + " 'tCount': 0},\n", + " 'logicalQubit': {'codeDistance': 13,\n", + " 'logicalCycleTime': 5200.0,\n", + " 'logicalErrorRate': 3.000000000000002e-09,\n", + " 'physicalQubits': 338},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 405,\n", + " 'algorithmicLogicalQubits': 42,\n", + " 'cliffordErrorRate': 0.001,\n", + " 'logicalDepth': 405,\n", + " 'numTfactories': 12,\n", + " 'numTfactoryRuns': 35,\n", + " 'numTsPerRotation': None,\n", + " 'numTstates': 420,\n", + " 'physicalQubitsForAlgorithm': 14196,\n", + " 'physicalQubitsForTfactories': 116160,\n", + " 'requiredLogicalQubitErrorRate': 2.9394473838918283e-08,\n", + " 'requiredLogicalTstateErrorRate': 1.1904761904761906e-06},\n", + " 'physicalQubits': 130356,\n", + " 'runtime': 2106000},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '11',\n", + " 'errorBudget': '1.00e-3',\n", + " 'errorBudgetLogical': '5.00e-4',\n", + " 'errorBudgetRotations': '0.00e0',\n", + " 'errorBudgetTstates': '5.00e-4',\n", + " 'logicalCycleTime': '5us 200ns',\n", + " 'logicalErrorRate': '3.00e-9',\n", + " 'numTsPerRotation': 'No rotations in algorithm',\n", + " 'numUnitsPerRound': '2',\n", + " 'physicalQubitsForTfactoriesPercentage': '89.11 %',\n", + " 'physicalQubitsPerRound': '9680',\n", + " 'requiredLogicalQubitErrorRate': '2.94e-8',\n", + " 'requiredLogicalTstateErrorRate': '1.19e-6',\n", + " 'runtime': '2ms 106us',\n", + " 'tfactoryRuntime': '57us 200ns',\n", + " 'tfactoryRuntimePerRound': '57us 200ns',\n", + " 'tstateLogicalErrorRate': '2.48e-7',\n", + " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", + " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", + " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", + " '**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.',\n", + " '**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).',\n", + " '**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.',\n", + " '**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.',\n", + " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", + " 'groups': [{'alwaysVisible': True,\n", + " 'entries': [{'description': 'Number of physical qubits',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 14196 physical qubits to implement the algorithm logic, and 116160 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'physicalCounts/physicalQubits'},\n", + " {'description': 'Total runtime',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (5us 200ns) multiplied by the 405 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/runtime'}],\n", + " 'title': 'Physical resource estimates'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 15$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 42$ logical qubits.',\n", + " 'label': 'Logical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", + " {'description': 'Number of logical cycles for the algorithm',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 90 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 15 CCZ and 90 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'label': 'Algorithmic depth',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", + " {'description': 'Number of logical cycles performed',\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 405. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'label': 'Logical depth',\n", + " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", + " {'description': 'Number of T states consumed by the algorithm',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 15 CCZ and 90 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'label': 'Number of T states',\n", + " 'path': 'physicalCounts/breakdown/numTstates'},\n", + " {'description': \"Number of T factories capable of producing the demanded 420 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{420\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 2ms 106us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " 'label': 'Number of T factories',\n", + " 'path': 'physicalCounts/breakdown/numTfactories'},\n", + " {'description': 'Number of times all T factories are invoked',\n", + " 'explanation': 'In order to prepare the 420 T states, the 12 copies of the T factory are repeatedly invoked 35 times.',\n", + " 'label': 'Number of T factory invocations',\n", + " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", + " {'description': 'Number of physical qubits for the algorithm after layout',\n", + " 'explanation': 'The 14196 are the product of the 42 logical qubits after layout and the 338 physical qubits that encode a single logical qubit.',\n", + " 'label': 'Physical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", + " {'description': 'Number of physical qubits for the T factories',\n", + " 'explanation': 'Each T factory requires 9680 physical qubits and we run 12 in parallel, therefore we need $116160 = 9680 \\\\cdot 12$ qubits.',\n", + " 'label': 'Physical T factory qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", + " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 42 logical qubits and the total cycle count 405.',\n", + " 'label': 'Required logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", + " {'description': 'The minimum T state error rate required for distilled T states',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 420.',\n", + " 'label': 'Required logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", + " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", + " 'explanation': 'The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.',\n", + " 'label': 'Number of T states per rotation',\n", + " 'path': 'physicalCountsFormatted/numTsPerRotation'}],\n", + " 'title': 'Resource estimates breakdown'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Name of QEC scheme',\n", + " 'explanation': 'You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.',\n", + " 'label': 'QEC scheme',\n", + " 'path': 'jobParams/qecScheme/name'},\n", + " {'description': 'Required code distance for error correction',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.000000029394473838918283)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'label': 'Code distance',\n", + " 'path': 'logicalQubit/codeDistance'},\n", + " {'description': 'Number of physical qubits per logical qubit',\n", + " 'explanation': 'The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'logicalQubit/physicalQubits'},\n", + " {'description': 'Duration of a logical cycle in nanoseconds',\n", + " 'explanation': 'The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.',\n", + " 'label': 'Logical cycle time',\n", + " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", + " {'description': 'Logical qubit error rate',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{13 + 1}{2}$',\n", + " 'label': 'Logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", + " {'description': 'Crossing prefactor used in QEC scheme',\n", + " 'explanation': 'The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.',\n", + " 'label': 'Crossing prefactor',\n", + " 'path': 'jobParams/qecScheme/crossingPrefactor'},\n", + " {'description': 'Error correction threshold used in QEC scheme',\n", + " 'explanation': 'The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.',\n", + " 'label': 'Error correction threshold',\n", + " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", + " {'description': 'QEC scheme formula used to compute logical cycle time',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 5us 200ns.',\n", + " 'label': 'Logical cycle time formula',\n", + " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", + " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 338.',\n", + " 'label': 'Physical qubits formula',\n", + " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", + " 'title': 'Logical qubit parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of physical qubits for a single T factory',\n", + " 'explanation': 'This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'tfactory/physicalQubits'},\n", + " {'description': 'Runtime of a single T factory',\n", + " 'explanation': 'The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", + " {'description': 'Number of output T states produced in a single run of T factory',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.',\n", + " 'label': 'Number of output T states per run',\n", + " 'path': 'tfactory/numTstates'},\n", + " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", + " 'explanation': 'This value includes the physical input T states of all copies of the distillation unit in the first round.',\n", + " 'label': 'Number of input T states per run',\n", + " 'path': 'tfactory/numInputTstates'},\n", + " {'description': 'The number of distillation rounds',\n", + " 'explanation': 'This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.',\n", + " 'label': 'Distillation rounds',\n", + " 'path': 'tfactory/numRounds'},\n", + " {'description': 'The number of units in each round of distillation',\n", + " 'explanation': 'This is the number of copies for the distillation units per round.',\n", + " 'label': 'Distillation units per round',\n", + " 'path': 'physicalCountsFormatted/numUnitsPerRound'},\n", + " {'description': 'The types of distillation units',\n", + " 'explanation': 'These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.',\n", + " 'label': 'Distillation units',\n", + " 'path': 'physicalCountsFormatted/unitNamePerRound'},\n", + " {'description': 'The code distance in each round of distillation',\n", + " 'explanation': 'This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.',\n", + " 'label': 'Distillation code distances',\n", + " 'path': 'physicalCountsFormatted/codeDistancePerRound'},\n", + " {'description': 'The number of physical qubits used in each round of distillation',\n", + " 'explanation': 'The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.',\n", + " 'label': 'Number of physical qubits per round',\n", + " 'path': 'physicalCountsFormatted/physicalQubitsPerRound'},\n", + " {'description': 'The runtime of each distillation round',\n", + " 'explanation': 'The runtime of the T factory is the sum of the runtimes in all rounds.',\n", + " 'label': 'Runtime per round',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", + " {'description': 'Logical T state error rate',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.19e-6.',\n", + " 'label': 'Logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", + " 'title': 'T factory parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", + " 'explanation': 'We determine 42 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'label': 'Logical qubits (pre-layout)',\n", + " 'path': 'logicalCounts/numQubits'},\n", + " {'description': 'Number of T gates in the input quantum program',\n", + " 'explanation': 'This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.',\n", + " 'label': 'T gates',\n", + " 'path': 'logicalCounts/tCount'},\n", + " {'description': 'Number of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.',\n", + " 'label': 'Rotation gates',\n", + " 'path': 'logicalCounts/rotationCount'},\n", + " {'description': 'Depth of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.',\n", + " 'label': 'Rotation depth',\n", + " 'path': 'logicalCounts/rotationDepth'},\n", + " {'description': 'Number of CCZ-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCZ gates.',\n", + " 'label': 'CCZ gates',\n", + " 'path': 'logicalCounts/cczCount'},\n", + " {'description': 'Number of CCiX-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].',\n", + " 'label': 'CCiX gates',\n", + " 'path': 'logicalCounts/ccixCount'},\n", + " {'description': 'Number of single qubit measurements in the input quantum program',\n", + " 'explanation': 'This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.',\n", + " 'label': 'Measurement operations',\n", + " 'path': 'logicalCounts/measurementCount'}],\n", + " 'title': 'Pre-layout logical resources'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Total error budget for the algorithm',\n", + " 'explanation': \"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\n", + " 'label': 'Total error budget',\n", + " 'path': 'physicalCountsFormatted/errorBudget'},\n", + " {'description': 'Probability of at least one logical error',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'Logical error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetLogical'},\n", + " {'description': 'Probability of at least one faulty T distillation',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'T distillation error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetTstates'},\n", + " {'description': 'Probability of at least one failed rotation synthesis',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3.',\n", + " 'label': 'Rotation synthesis error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetRotations'}],\n", + " 'title': 'Assumed error budget'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Some descriptive name for the qubit model',\n", + " 'explanation': 'You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).',\n", + " 'label': 'Qubit name',\n", + " 'path': 'jobParams/qubitParams/name'},\n", + " {'description': 'Underlying qubit technology (gate-based or Majorana)',\n", + " 'explanation': 'When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.',\n", + " 'label': 'Instruction set',\n", + " 'path': 'jobParams/qubitParams/instructionSet'},\n", + " {'description': 'Operation time for single-qubit measurement (t_meas) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.',\n", + " 'label': 'Single-qubit measurement time',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementTime'},\n", + " {'description': 'Operation time for single-qubit gate (t_gate) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.',\n", + " 'label': 'Single-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateTime'},\n", + " {'description': 'Operation time for two-qubit gate in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.',\n", + " 'label': 'Two-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateTime'},\n", + " {'description': 'Operation time for a T gate',\n", + " 'explanation': 'This is the operation time in nanoseconds to execute a T gate.',\n", + " 'label': 'T gate time',\n", + " 'path': 'jobParams/qubitParams/tGateTime'},\n", + " {'description': 'Error rate for single-qubit measurement',\n", + " 'explanation': 'This is the probability in which a single-qubit measurement in the Pauli basis may fail.',\n", + " 'label': 'Single-qubit measurement error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementErrorRate'},\n", + " {'description': 'Error rate for single-qubit Clifford gate (p)',\n", + " 'explanation': 'This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.',\n", + " 'label': 'Single-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateErrorRate'},\n", + " {'description': 'Error rate for two-qubit Clifford gate',\n", + " 'explanation': 'This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.',\n", + " 'label': 'Two-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateErrorRate'},\n", + " {'description': 'Error rate to prepare single-qubit T state or apply a T gate (p_T)',\n", + " 'explanation': 'This is the probability in which executing a single T gate may fail.',\n", + " 'label': 'T gate error rate',\n", + " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", + " 'title': 'Physical qubit parameters'}]},\n", + " 'status': 'success',\n", + " 'tfactory': {'codeDistancePerRound': [11],\n", + " 'logicalErrorRate': 2.480000000000001e-07,\n", + " 'numInputTstates': 30,\n", + " 'numRounds': 1,\n", + " 'numTstates': 1,\n", + " 'numUnitsPerRound': [2],\n", + " 'physicalQubits': 9680,\n", + " 'physicalQubitsPerRound': [9680],\n", + " 'runtime': 57200.0,\n", + " 'runtimePerRound': [57200.0],\n", + " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", "# result = qsharp.azure.output(\"...\")\n", @@ -364,7 +8190,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, "metadata": { "collapsed": false, "jupyter": { @@ -391,7 +8217,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "metadata": { "collapsed": false, "jupyter": { @@ -404,10 +8230,37 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Logical algorithmic qubits = 42\n", + "Algorithmic depth = 405\n", + "Score = 17010\n" + ] + }, + { + "data": { + "text/plain": [ + "17010" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "evaluate_results(result)" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -415,9 +8268,9 @@ "name": "python3" }, "kernelspec": { - "display_name": "Python 3 [Default]", + "display_name": "Python 3 [Q#]", "language": "python", - "name": "python3" + "name": "python3_qsharp_b54crn" }, "language_info": { "codemirror_mode": { diff --git a/obj/__entrypoint__.dll b/obj/__entrypoint__.dll index 6f1942a7189b1fc25bfc0d930cb21e20dcb28868..d3b32702b1890d29d6cc018d6c45a0a04a5d29c6 100644 GIT binary patch delta 41062 zcmc(I2Ygjkw*ETj*4z|wZ+amKgc4F9l_b)l6h%QrK}2yNkf2}*5Nt#|K@icwf)|ZC z77(z3VkP**8Bi=UVjUG`U=$U5_c^1Zj{d*3_CDtpPnekqDvvG9JI;ilUqmWGUP{VklhDY3Fbgg;ET^~N)Ot%gvnp;|6b{ItN z(%z=xS<(Zx3KQm-C1}03y_k#k0m;1*0W95+OrRtG_cJKc;konw5T4)}l8i3YD;s8gcw1&h3)UdLK6rV3z&aCI zJFp~anU7_d{1F*e1ic>mS%%q-lTVL~|QO>4mN6QrJV0w@N%UT+(;18HuB+R6Ze 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zjfsxpXVQ4*{f4tgcc!58kl~EqQt84Eq8B+28_p&AQ7<~bWjN20&Of@u`EA2oDb3=0 z;`okF80IT|f5JR1y2N(MsJcW}t-r+l0hw*frFkX)?bA!yl|fhV{g8>Q z0e-G8GMIjJk@Eei<-;$pV?Bhs3HK2867D73N4TGGh;W$jEyA}6PY}LGc#7}?#H)L} znm*XVto-$-r%PE2cE6GG{~U;e5A|r=I+XMDU)~JE9X50}9{*x+=4^rDXZqn1mK5}E zZBg{c?`NSCO7AbvW$LePXIu2t8Wyd$^)b7id@pn8-Th4C-JdX7>^PFUc4vs z>->_kI`@KU{_If{HqFGGswSC zvYBK4wsNVe;_S|LTeW00|E*zMJl^)4#y>ss7(erwL$BMxDtg>5KGbW~m#COlS2s@DqvhEc*Z47Za;6ZvEb4A2*jL^`W(Fr(SV8dslzTgQ@P{<p5|bg z_w}+6TMA~G4$$JDJdk}i%MkA`l=YT-*(>8-VkgAG|yU~(anJO_NK;3nOE#gZ?9QtiX@Zpzyhf{yzd6qTl zb_TGWD^!_J+JXZ^N7)>a>`Rks)xTlPI*{=)OR-P1AF)@ec>9}C`r=`B=fKuC*sm2{ z^JU7wUx!&23)AG^`-NNbCVk^^7O%KA={t_IeENXgEev?|7zON> Date: Sun, 29 Jan 2023 13:56:08 +0000 Subject: [PATCH 5/7] final submission --- ...Hack-challenge-2023-task3-checkpoint.ipynb | 741 ++++++----- obj/__entrypoint__.dll | Bin 321536 -> 346112 bytes obj/__entrypoint__snippets__.dll | Bin 121344 -> 114688 bytes obj/__snippets__.dll | Bin 120832 -> 114176 bytes .../iQuHack-challenge-2023-task1.ipynb | 0 .../iQuHack-challenge-2023-task2.ipynb | 0 .../iQuHack-challenge-2023-task3.ipynb | 741 ++++++----- .../iQuHack-challenge-2023-task4.ipynb | 0 .../iQuHack-challenge-2023-task5.ipynb | 0 .../iQuHack-challenge-2023-task6.ipynb | 0 .../iQuHack-challenge-2023-task7.ipynb | 2 +- .../iQuHack-challenge-2023-task8.ipynb | 0 .../iQuHack-challenge-2023-task9.ipynb | 1105 +++++++++-------- 13 files changed, 1306 insertions(+), 1283 deletions(-) rename iQuHack-challenge-2023-task1.ipynb => team_solutions/schrodingers-duck/iQuHack-challenge-2023-task1.ipynb (100%) rename iQuHack-challenge-2023-task2.ipynb => team_solutions/schrodingers-duck/iQuHack-challenge-2023-task2.ipynb (100%) rename iQuHack-challenge-2023-task3.ipynb => team_solutions/schrodingers-duck/iQuHack-challenge-2023-task3.ipynb (85%) rename iQuHack-challenge-2023-task4.ipynb => team_solutions/schrodingers-duck/iQuHack-challenge-2023-task4.ipynb (100%) rename iQuHack-challenge-2023-task5.ipynb => team_solutions/schrodingers-duck/iQuHack-challenge-2023-task5.ipynb (100%) rename iQuHack-challenge-2023-task6.ipynb => team_solutions/schrodingers-duck/iQuHack-challenge-2023-task6.ipynb (100%) rename iQuHack-challenge-2023-task7.ipynb => team_solutions/schrodingers-duck/iQuHack-challenge-2023-task7.ipynb (99%) rename iQuHack-challenge-2023-task8.ipynb => team_solutions/schrodingers-duck/iQuHack-challenge-2023-task8.ipynb (100%) rename iQuHack-challenge-2023-task9.ipynb => team_solutions/schrodingers-duck/iQuHack-challenge-2023-task9.ipynb (92%) diff --git a/.ipynb_checkpoints/iQuHack-challenge-2023-task3-checkpoint.ipynb b/.ipynb_checkpoints/iQuHack-challenge-2023-task3-checkpoint.ipynb index 4d5561f..b151510 100644 --- a/.ipynb_checkpoints/iQuHack-challenge-2023-task3-checkpoint.ipynb +++ b/.ipynb_checkpoints/iQuHack-challenge-2023-task3-checkpoint.ipynb @@ -67,7 +67,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 38, "metadata": { "collapsed": false, "jupyter": { @@ -89,7 +89,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 39, "metadata": { "collapsed": false, "jupyter": { @@ -111,7 +111,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 40, "metadata": { "collapsed": false, "jupyter": { @@ -148,7 +148,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 41, "metadata": { "collapsed": false, "jupyter": { @@ -215,7 +215,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 42, "metadata": {}, "outputs": [], "source": [ @@ -224,7 +224,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 43, "metadata": { "collapsed": false, "jupyter": { @@ -281,7 +281,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 44, "metadata": { "collapsed": false, "jupyter": { @@ -326,12 +326,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -351,12 +351,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -376,12 +376,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -401,12 +401,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -426,12 +426,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -451,12 +451,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -476,12 +476,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -501,12 +501,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -526,12 +526,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -551,12 +551,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -576,12 +576,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -601,12 +601,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -626,12 +626,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -651,12 +651,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -676,12 +676,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -701,12 +701,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -726,12 +726,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -751,12 +751,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -776,12 +776,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -801,12 +801,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -826,12 +826,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -851,12 +851,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -876,12 +876,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -901,12 +901,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -926,12 +926,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -951,12 +951,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -976,12 +976,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1001,12 +1001,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1026,12 +1026,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1051,12 +1051,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1076,12 +1076,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1101,12 +1101,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1126,12 +1126,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1151,12 +1151,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1176,12 +1176,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1201,12 +1201,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1226,12 +1226,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1251,12 +1251,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1276,12 +1276,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1301,12 +1301,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1326,12 +1326,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1351,12 +1351,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1376,12 +1376,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1401,12 +1401,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1426,12 +1426,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1451,12 +1451,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1476,12 +1476,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1501,12 +1501,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1526,12 +1526,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1551,12 +1551,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1576,12 +1576,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1601,12 +1601,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1626,12 +1626,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1651,12 +1651,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1676,12 +1676,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1701,12 +1701,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1726,12 +1726,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1751,12 +1751,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1776,12 +1776,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1801,12 +1801,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1826,12 +1826,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1851,12 +1851,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1876,12 +1876,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1901,12 +1901,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1926,12 +1926,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1951,12 +1951,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1976,12 +1976,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2001,12 +2001,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2026,12 +2026,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2051,12 +2051,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2076,12 +2076,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2101,12 +2101,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2126,12 +2126,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2151,12 +2151,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2176,12 +2176,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2201,12 +2201,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2226,12 +2226,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2251,12 +2251,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2276,12 +2276,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2301,12 +2301,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2326,12 +2326,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2351,12 +2351,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2376,12 +2376,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2401,12 +2401,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2426,12 +2426,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

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\r\n", " \r\n", " \r\n", @@ -3657,7 +3657,7 @@ "()" ] }, - "execution_count": 18, + "execution_count": 44, "metadata": {}, "output_type": "execute_result" } @@ -3686,7 +3686,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 45, "metadata": { "collapsed": false, "jupyter": { @@ -3720,22 +3720,22 @@ { "data": { "text/plain": [ - "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 178144},\n", - " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 409698},\n", + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 181814},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 313983},\n", " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 4},\n", " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", - " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 109},\n", " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 168},\n", " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", - " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 109},\n", " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 168},\n", " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", @@ -3744,7 +3744,7 @@ " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" ] }, - "execution_count": 19, + "execution_count": 45, "metadata": {}, "output_type": "execute_result" } @@ -3760,7 +3760,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 46, "metadata": { "collapsed": false, "jupyter": { @@ -3788,7 +3788,7 @@ "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" ] }, - "execution_count": 20, + "execution_count": 46, "metadata": {}, "output_type": "execute_result" } @@ -3799,7 +3799,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 47, "metadata": { "collapsed": false, "jupyter": { @@ -3820,10 +3820,9 @@ "Submitting Task3_ResourceEstimationWrapper to target microsoft.estimator...\n", "Job successfully submitted.\n", " Job name: RE for the task 3\n", - " Job ID: 97de0812-1c25-4a9d-be97-55f936dc8c93\n", + " Job ID: 42702b8d-2ed2-47f0-8238-c9d2e88628f8\n", "Waiting up to 30 seconds for Azure Quantum job to complete...\n", - "[1:13:16 PM] Current job status: Executing\n", - "[1:13:21 PM] Current job status: Succeeded\n" + "[1:35:43 PM] Current job status: Succeeded\n" ] } ], @@ -3834,7 +3833,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 48, "metadata": { "collapsed": false, "jupyter": { @@ -3850,7 +3849,7 @@ "outputs": [ { "data": { - "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":80,\"cczCount\":20,\"measurementCount\":80,\"numQubits\":11,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":380,\"algorithmicLogicalQubits\":33,\"cliffordErrorRate\":0.001,\"logicalDepth\":380,\"numTfactories\":14,\"numTfactoryRuns\":29,\"numTsPerRotation\":null,\"numTstates\":400,\"physicalQubitsForAlgorithm\":7986,\"physicalQubitsForTfactories\":135520,\"requiredLogicalQubitErrorRate\":3.987240829346092E-08,\"requiredLogicalTstateErrorRate\":1.25E-06},\"physicalQubits\":143506,\"runtime\":1672000},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"11\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"94.44 %\",\"physicalQubitsPerRound\":\"9680\",\"requiredLogicalQubitErrorRate\":\"3.99e-8\",\"requiredLogicalTstateErrorRate\":\"1.25e-6\",\"runtime\":\"1ms 672us\",\"tfactoryRuntime\":\"57us 200ns\",\"tfactoryRuntimePerRound\":\"57us 200ns\",\"tstateLogicalErrorRate\":\"2.48e-7\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 7986 physical qubits to implement the algorithm logic, and 135520 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 380 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 11$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 33$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 80 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 20 CCZ and 80 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 380. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 20 CCZ and 80 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 400 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{400\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 1ms 672us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 400 T states, the 14 copies of the T factory are repeatedly invoked 29 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 7986 are the product of the 33 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 9680 physical qubits and we run 14 in parallel, therefore we need $135520 = 9680 \\\\cdot 14$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 380.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 400.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000003987240829346092)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[11],\"logicalErrorRate\":2.480000000000001E-07,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":9680,\"physicalQubitsPerRound\":[9680],\"runtime\":57200.0,\"runtimePerRound\":[57200.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":1,\"cczCount\":17,\"measurementCount\":1,\"numQubits\":13,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":55,\"algorithmicLogicalQubits\":38,\"cliffordErrorRate\":0.001,\"logicalDepth\":55,\"numTfactories\":14,\"numTfactoryRuns\":6,\"numTsPerRotation\":null,\"numTstates\":72,\"physicalQubitsForAlgorithm\":9196,\"physicalQubitsForTfactories\":90720,\"requiredLogicalQubitErrorRate\":2.3923444976076555E-07,\"requiredLogicalTstateErrorRate\":6.944444444444445E-06},\"physicalQubits\":99916,\"runtime\":242000},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"90.80 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"2.39e-7\",\"requiredLogicalTstateErrorRate\":\"6.94e-6\",\"runtime\":\"242us\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 9196 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 55 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 13$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 38$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 1 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 17 CCZ and 1 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 55. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 17 CCZ and 1 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 72 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{72\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 242us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 72 T states, the 14 copies of the T factory are repeatedly invoked 6 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 9196 are the product of the 38 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\\\cdot 14$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 55.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 72.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000023923444976076555)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.94e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", "text/html": [ "\r\n", "
\r\n", @@ -3862,24 +3861,24 @@ "\r\n", " \r\n", " Physical qubits\r\n", - " 143506\r\n", + " 99916\r\n", " \r\n", "

Number of physical qubits

\n", "\r\n", "
\r\n", - "

This value represents the total number of physical qubits, which is the sum of 7986 physical qubits to implement the algorithm logic, and 135520 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

\n", + "

This value represents the total number of physical qubits, which is the sum of 9196 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Runtime\r\n", - " 1ms 672us\r\n", + " 242us\r\n", " \r\n", "

Total runtime

\n", "\r\n", "
\r\n", - "

This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 380 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

\n", + "

This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 55 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

\n", "\r\n", " \r\n", " \n", @@ -3894,48 +3893,48 @@ "\r\n", " \r\n", " Logical algorithmic qubits\r\n", - " 33\r\n", + " 38\r\n", " \r\n", "

Number of logical qubits for the algorithm after layout

\n", "\r\n", "
\r\n", - "

Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 11\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 33$ logical qubits.

\n", + "

Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 13\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 38$ logical qubits.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Algorithmic depth\r\n", - " 380\r\n", + " 55\r\n", " \r\n", "

Number of logical cycles for the algorithm

\n", "\r\n", "
\r\n", - "

To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 80 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 20 CCZ and 80 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

\n", + "

To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 1 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 17 CCZ and 1 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Logical depth\r\n", - " 380\r\n", + " 55\r\n", " \r\n", "

Number of logical cycles performed

\n", "\r\n", "
\r\n", - "

This number is usually equal to the logical depth of the algorithm, which is 380. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", + "

This number is usually equal to the logical depth of the algorithm, which is 55. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Number of T states\r\n", - " 400\r\n", + " 72\r\n", " \r\n", "

Number of T states consumed by the algorithm

\n", "\r\n", "
\r\n", - "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 20 CCZ and 80 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", + "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 17 CCZ and 1 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", "\r\n", " \r\n", " \n", @@ -3944,70 +3943,70 @@ " Number of T factories\r\n", " 14\r\n", " \r\n", - "

Number of T factories capable of producing the demanded 400 T states during the algorithm's runtime

\n", + "

Number of T factories capable of producing the demanded 72 T states during the algorithm's runtime

\n", "\r\n", "
\r\n", - "

The total number of T factories 14 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{400\\;\\text{T states} \\cdot 57us 200ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 1ms 672us\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", + "

The total number of T factories 14 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{72\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 242us\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Number of T factory invocations\r\n", - " 29\r\n", + " 6\r\n", " \r\n", "

Number of times all T factories are invoked

\n", "\r\n", "
\r\n", - "

In order to prepare the 400 T states, the 14 copies of the T factory are repeatedly invoked 29 times.

\n", + "

In order to prepare the 72 T states, the 14 copies of the T factory are repeatedly invoked 6 times.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Physical algorithmic qubits\r\n", - " 7986\r\n", + " 9196\r\n", " \r\n", "

Number of physical qubits for the algorithm after layout

\n", "\r\n", "
\r\n", - "

The 7986 are the product of the 33 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.

\n", + "

The 9196 are the product of the 38 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Physical T factory qubits\r\n", - " 135520\r\n", + " 90720\r\n", " \r\n", "

Number of physical qubits for the T factories

\n", "\r\n", "
\r\n", - "

Each T factory requires 9680 physical qubits and we run 14 in parallel, therefore we need $135520 = 9680 \\cdot 14$ qubits.

\n", + "

Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\cdot 14$ qubits.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Required logical qubit error rate\r\n", - " 3.99e-8\r\n", + " 2.39e-7\r\n", " \r\n", "

The minimum logical qubit error rate required to run the algorithm within the error budget

\n", "\r\n", "
\r\n", - "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 380.

\n", + "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 55.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Required logical T state error rate\r\n", - " 1.25e-6\r\n", + " 6.94e-6\r\n", " \r\n", "

The minimum T state error rate required for distilled T states

\n", "\r\n", "
\r\n", - "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 400.

\n", + "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 72.

\n", "\r\n", " \r\n", " \n", @@ -4051,7 +4050,7 @@ "

Required code distance for error correction

\n", "\r\n", "
\r\n", - "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000003987240829346092)}{\\log(0.01/0.001)} - 1\\)

\n", + "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000023923444976076555)}{\\log(0.01/0.001)} - 1\\)

\n", "\r\n", " \r\n", " \n", @@ -4150,7 +4149,7 @@ "\r\n", " \r\n", " Physical qubits\r\n", - " 9680\r\n", + " 6480\r\n", " \r\n", "

Number of physical qubits for a single T factory

\n", "\r\n", @@ -4162,7 +4161,7 @@ "\r\n", " \r\n", " Runtime\r\n", - " 57us 200ns\r\n", + " 46us 800ns\r\n", " \r\n", "

Runtime of a single T factory

\n", "\r\n", @@ -4179,7 +4178,7 @@ "

Number of output T states produced in a single run of T factory

\n", "\r\n", "
\r\n", - "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.

\n", + "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.

\n", "\r\n", " \r\n", " \n", @@ -4234,7 +4233,7 @@ "\r\n", " \r\n", " Distillation code distances\r\n", - " 11\r\n", + " 9\r\n", " \r\n", "

The code distance in each round of distillation

\n", "\r\n", @@ -4246,7 +4245,7 @@ "\r\n", " \r\n", " Number of physical qubits per round\r\n", - " 9680\r\n", + " 6480\r\n", " \r\n", "

The number of physical qubits used in each round of distillation

\n", "\r\n", @@ -4258,7 +4257,7 @@ "\r\n", " \r\n", " Runtime per round\r\n", - " 57us 200ns\r\n", + " 46us 800ns\r\n", " \r\n", "

The runtime of each distillation round

\n", "\r\n", @@ -4270,12 +4269,12 @@ "\r\n", " \r\n", " Logical T state error rate\r\n", - " 2.48e-7\r\n", + " 2.17e-6\r\n", " \r\n", "

Logical T state error rate

\n", "\r\n", "
\r\n", - "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-6.

\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.94e-6.

\n", "\r\n", " \r\n", " \n", @@ -4290,12 +4289,12 @@ "\r\n", " \r\n", " Logical qubits (pre-layout)\r\n", - " 11\r\n", + " 13\r\n", " \r\n", "

Number of logical qubits in the input quantum program

\n", "\r\n", "
\r\n", - "

We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", + "

We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", "\r\n", " \r\n", " \n", @@ -4338,7 +4337,7 @@ "\r\n", " \r\n", " CCZ gates\r\n", - " 20\r\n", + " 17\r\n", " \r\n", "

Number of CCZ-gates in the input quantum program

\n", "\r\n", @@ -4350,7 +4349,7 @@ "\r\n", " \r\n", " CCiX gates\r\n", - " 80\r\n", + " 1\r\n", " \r\n", "

Number of CCiX-gates in the input quantum program

\n", "\r\n", @@ -4362,7 +4361,7 @@ "\r\n", " \r\n", " Measurement operations\r\n", - " 80\r\n", + " 1\r\n", " \r\n", "

Number of single qubit measurements in the input quantum program

\n", "\r\n", @@ -4593,10 +4592,10 @@ " 'tGateTime': '50 ns',\n", " 'twoQubitGateErrorRate': 0.001,\n", " 'twoQubitGateTime': '50 ns'}},\n", - " 'logicalCounts': {'ccixCount': 80,\n", - " 'cczCount': 20,\n", - " 'measurementCount': 80,\n", - " 'numQubits': 11,\n", + " 'logicalCounts': {'ccixCount': 1,\n", + " 'cczCount': 17,\n", + " 'measurementCount': 1,\n", + " 'numQubits': 13,\n", " 'rotationCount': 0,\n", " 'rotationDepth': 0,\n", " 'tCount': 0},\n", @@ -4604,21 +4603,21 @@ " 'logicalCycleTime': 4400.0,\n", " 'logicalErrorRate': 3.000000000000002e-08,\n", " 'physicalQubits': 242},\n", - " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 380,\n", - " 'algorithmicLogicalQubits': 33,\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 55,\n", + " 'algorithmicLogicalQubits': 38,\n", " 'cliffordErrorRate': 0.001,\n", - " 'logicalDepth': 380,\n", + " 'logicalDepth': 55,\n", " 'numTfactories': 14,\n", - " 'numTfactoryRuns': 29,\n", + " 'numTfactoryRuns': 6,\n", " 'numTsPerRotation': None,\n", - " 'numTstates': 400,\n", - " 'physicalQubitsForAlgorithm': 7986,\n", - " 'physicalQubitsForTfactories': 135520,\n", - " 'requiredLogicalQubitErrorRate': 3.987240829346092e-08,\n", - " 'requiredLogicalTstateErrorRate': 1.25e-06},\n", - " 'physicalQubits': 143506,\n", - " 'runtime': 1672000},\n", - " 'physicalCountsFormatted': {'codeDistancePerRound': '11',\n", + " 'numTstates': 72,\n", + " 'physicalQubitsForAlgorithm': 9196,\n", + " 'physicalQubitsForTfactories': 90720,\n", + " 'requiredLogicalQubitErrorRate': 2.3923444976076555e-07,\n", + " 'requiredLogicalTstateErrorRate': 6.944444444444445e-06},\n", + " 'physicalQubits': 99916,\n", + " 'runtime': 242000},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", " 'errorBudget': '1.00e-3',\n", " 'errorBudgetLogical': '5.00e-4',\n", " 'errorBudgetRotations': '0.00e0',\n", @@ -4627,14 +4626,14 @@ " 'logicalErrorRate': '3.00e-8',\n", " 'numTsPerRotation': 'No rotations in algorithm',\n", " 'numUnitsPerRound': '2',\n", - " 'physicalQubitsForTfactoriesPercentage': '94.44 %',\n", - " 'physicalQubitsPerRound': '9680',\n", - " 'requiredLogicalQubitErrorRate': '3.99e-8',\n", - " 'requiredLogicalTstateErrorRate': '1.25e-6',\n", - " 'runtime': '1ms 672us',\n", - " 'tfactoryRuntime': '57us 200ns',\n", - " 'tfactoryRuntimePerRound': '57us 200ns',\n", - " 'tstateLogicalErrorRate': '2.48e-7',\n", + " 'physicalQubitsForTfactoriesPercentage': '90.80 %',\n", + " 'physicalQubitsPerRound': '6480',\n", + " 'requiredLogicalQubitErrorRate': '2.39e-7',\n", + " 'requiredLogicalTstateErrorRate': '6.94e-6',\n", + " 'runtime': '242us',\n", + " 'tfactoryRuntime': '46us 800ns',\n", + " 'tfactoryRuntimePerRound': '46us 800ns',\n", + " 'tstateLogicalErrorRate': '2.17e-6',\n", " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", @@ -4645,53 +4644,53 @@ " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", " 'groups': [{'alwaysVisible': True,\n", " 'entries': [{'description': 'Number of physical qubits',\n", - " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 7986 physical qubits to implement the algorithm logic, and 135520 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 9196 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", " 'label': 'Physical qubits',\n", " 'path': 'physicalCounts/physicalQubits'},\n", " {'description': 'Total runtime',\n", - " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 380 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 55 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", " 'label': 'Runtime',\n", " 'path': 'physicalCountsFormatted/runtime'}],\n", " 'title': 'Physical resource estimates'},\n", " {'alwaysVisible': False,\n", " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", - " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 11$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 33$ logical qubits.',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 13$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 38$ logical qubits.',\n", " 'label': 'Logical algorithmic qubits',\n", " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", " {'description': 'Number of logical cycles for the algorithm',\n", - " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 80 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 20 CCZ and 80 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 1 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 17 CCZ and 1 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", " 'label': 'Algorithmic depth',\n", " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", " {'description': 'Number of logical cycles performed',\n", - " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 380. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 55. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", " 'label': 'Logical depth',\n", " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", " {'description': 'Number of T states consumed by the algorithm',\n", - " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 20 CCZ and 80 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 17 CCZ and 1 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", " 'label': 'Number of T states',\n", " 'path': 'physicalCounts/breakdown/numTstates'},\n", - " {'description': \"Number of T factories capable of producing the demanded 400 T states during the algorithm's runtime\",\n", - " 'explanation': 'The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{400\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 1ms 672us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " {'description': \"Number of T factories capable of producing the demanded 72 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{72\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 242us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", " 'label': 'Number of T factories',\n", " 'path': 'physicalCounts/breakdown/numTfactories'},\n", " {'description': 'Number of times all T factories are invoked',\n", - " 'explanation': 'In order to prepare the 400 T states, the 14 copies of the T factory are repeatedly invoked 29 times.',\n", + " 'explanation': 'In order to prepare the 72 T states, the 14 copies of the T factory are repeatedly invoked 6 times.',\n", " 'label': 'Number of T factory invocations',\n", " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", " {'description': 'Number of physical qubits for the algorithm after layout',\n", - " 'explanation': 'The 7986 are the product of the 33 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.',\n", + " 'explanation': 'The 9196 are the product of the 38 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.',\n", " 'label': 'Physical algorithmic qubits',\n", " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", " {'description': 'Number of physical qubits for the T factories',\n", - " 'explanation': 'Each T factory requires 9680 physical qubits and we run 14 in parallel, therefore we need $135520 = 9680 \\\\cdot 14$ qubits.',\n", + " 'explanation': 'Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\\\cdot 14$ qubits.',\n", " 'label': 'Physical T factory qubits',\n", " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", - " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 380.',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 55.',\n", " 'label': 'Required logical qubit error rate',\n", " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", " {'description': 'The minimum T state error rate required for distilled T states',\n", - " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 400.',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 72.',\n", " 'label': 'Required logical T state error rate',\n", " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", @@ -4705,7 +4704,7 @@ " 'label': 'QEC scheme',\n", " 'path': 'jobParams/qecScheme/name'},\n", " {'description': 'Required code distance for error correction',\n", - " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000003987240829346092)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000023923444976076555)}{\\\\log(0.01/0.001)} - 1$',\n", " 'label': 'Code distance',\n", " 'path': 'logicalQubit/codeDistance'},\n", " {'description': 'Number of physical qubits per logical qubit',\n", @@ -4747,7 +4746,7 @@ " 'label': 'Runtime',\n", " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", " {'description': 'Number of output T states produced in a single run of T factory',\n", - " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.',\n", " 'label': 'Number of output T states per run',\n", " 'path': 'tfactory/numTstates'},\n", " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", @@ -4779,13 +4778,13 @@ " 'label': 'Runtime per round',\n", " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", " {'description': 'Logical T state error rate',\n", - " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-6.',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.94e-6.',\n", " 'label': 'Logical T state error rate',\n", " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", " 'title': 'T factory parameters'},\n", " {'alwaysVisible': False,\n", " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", - " 'explanation': 'We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'explanation': 'We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", " 'label': 'Logical qubits (pre-layout)',\n", " 'path': 'logicalCounts/numQubits'},\n", " {'description': 'Number of T gates in the input quantum program',\n", @@ -4874,20 +4873,20 @@ " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", " 'title': 'Physical qubit parameters'}]},\n", " 'status': 'success',\n", - " 'tfactory': {'codeDistancePerRound': [11],\n", - " 'logicalErrorRate': 2.480000000000001e-07,\n", + " 'tfactory': {'codeDistancePerRound': [9],\n", + " 'logicalErrorRate': 2.165000000000001e-06,\n", " 'numInputTstates': 30,\n", " 'numRounds': 1,\n", " 'numTstates': 1,\n", " 'numUnitsPerRound': [2],\n", - " 'physicalQubits': 9680,\n", - " 'physicalQubitsPerRound': [9680],\n", - " 'runtime': 57200.0,\n", - " 'runtimePerRound': [57200.0],\n", + " 'physicalQubits': 6480,\n", + " 'physicalQubitsPerRound': [6480],\n", + " 'runtime': 46800.0,\n", + " 'runtimePerRound': [46800.0],\n", " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" ] }, - "execution_count": 22, + "execution_count": 48, "metadata": {}, "output_type": "execute_result" } @@ -4900,7 +4899,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 49, "metadata": { "collapsed": false, "jupyter": { @@ -4927,7 +4926,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 50, "metadata": { "collapsed": false, "jupyter": { @@ -4945,18 +4944,18 @@ "name": "stdout", "output_type": "stream", "text": [ - "Logical algorithmic qubits = 33\n", - "Algorithmic depth = 380\n", - "Score = 12540\n" + "Logical algorithmic qubits = 38\n", + "Algorithmic depth = 55\n", + "Score = 2090\n" ] }, { "data": { "text/plain": [ - "12540" + "2090" ] }, - "execution_count": 24, + "execution_count": 50, "metadata": {}, "output_type": "execute_result" } diff --git a/obj/__entrypoint__.dll b/obj/__entrypoint__.dll index 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\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -351,12 +351,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -376,12 +376,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -401,12 +401,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -426,12 +426,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -451,12 +451,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -476,12 +476,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -501,12 +501,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -526,12 +526,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -551,12 +551,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -576,12 +576,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -601,12 +601,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -626,12 +626,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -651,12 +651,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -676,12 +676,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -701,12 +701,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -726,12 +726,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -751,12 +751,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -776,12 +776,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -801,12 +801,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -826,12 +826,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -851,12 +851,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -876,12 +876,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -901,12 +901,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -926,12 +926,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -951,12 +951,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -976,12 +976,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1001,12 +1001,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1026,12 +1026,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1051,12 +1051,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1076,12 +1076,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1101,12 +1101,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1126,12 +1126,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1151,12 +1151,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1176,12 +1176,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1201,12 +1201,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1226,12 +1226,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1251,12 +1251,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1276,12 +1276,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1301,12 +1301,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1326,12 +1326,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1351,12 +1351,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1376,12 +1376,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1401,12 +1401,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1426,12 +1426,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1451,12 +1451,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1476,12 +1476,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1501,12 +1501,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1526,12 +1526,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1551,12 +1551,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1576,12 +1576,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1601,12 +1601,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1626,12 +1626,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1651,12 +1651,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1676,12 +1676,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1701,12 +1701,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1726,12 +1726,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1751,12 +1751,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1776,12 +1776,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1801,12 +1801,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1826,12 +1826,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1851,12 +1851,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1876,12 +1876,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1901,12 +1901,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1926,12 +1926,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1951,12 +1951,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1976,12 +1976,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2001,12 +2001,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2026,12 +2026,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2051,12 +2051,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2076,12 +2076,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2101,12 +2101,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2126,12 +2126,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2151,12 +2151,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2176,12 +2176,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2201,12 +2201,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2226,12 +2226,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2251,12 +2251,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2276,12 +2276,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2301,12 +2301,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2326,12 +2326,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2351,12 +2351,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2376,12 +2376,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2401,12 +2401,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2426,12 +2426,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2451,12 +2451,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2476,12 +2476,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2501,12 +2501,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2526,12 +2526,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2551,12 +2551,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2576,12 +2576,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2601,12 +2601,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2626,12 +2626,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2651,12 +2651,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2676,12 +2676,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2701,12 +2701,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2726,12 +2726,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2751,12 +2751,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2776,12 +2776,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2801,12 +2801,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2826,12 +2826,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2851,12 +2851,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2876,12 +2876,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2901,12 +2901,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2926,12 +2926,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2951,12 +2951,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2976,12 +2976,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3001,12 +3001,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3026,12 +3026,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3051,12 +3051,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3076,12 +3076,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3101,12 +3101,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3126,12 +3126,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3151,12 +3151,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3176,12 +3176,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3201,12 +3201,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3226,12 +3226,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3251,12 +3251,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3276,12 +3276,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3301,12 +3301,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3326,12 +3326,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3351,12 +3351,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3376,12 +3376,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3401,12 +3401,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3426,12 +3426,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3451,12 +3451,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3476,12 +3476,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3501,12 +3501,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3657,7 +3657,7 @@ "()" ] }, - "execution_count": 18, + "execution_count": 44, "metadata": {}, "output_type": "execute_result" } @@ -3686,7 +3686,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 45, "metadata": { "collapsed": false, "jupyter": { @@ -3720,22 +3720,22 @@ { "data": { "text/plain": [ - "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 178144},\n", - " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 409698},\n", + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 181814},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 313983},\n", " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 4},\n", " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", - " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 109},\n", " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 168},\n", " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", - " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 109},\n", " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 168},\n", " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", @@ -3744,7 +3744,7 @@ " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" ] }, - "execution_count": 19, + "execution_count": 45, "metadata": {}, "output_type": "execute_result" } @@ -3760,7 +3760,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 46, "metadata": { "collapsed": false, "jupyter": { @@ -3788,7 +3788,7 @@ "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" ] }, - "execution_count": 20, + "execution_count": 46, "metadata": {}, "output_type": "execute_result" } @@ -3799,7 +3799,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 47, "metadata": { "collapsed": false, "jupyter": { @@ -3820,10 +3820,9 @@ "Submitting Task3_ResourceEstimationWrapper to target microsoft.estimator...\n", "Job successfully submitted.\n", " Job name: RE for the task 3\n", - " Job ID: 97de0812-1c25-4a9d-be97-55f936dc8c93\n", + " Job ID: 42702b8d-2ed2-47f0-8238-c9d2e88628f8\n", "Waiting up to 30 seconds for Azure Quantum job to complete...\n", - "[1:13:16 PM] Current job status: Executing\n", - "[1:13:21 PM] Current job status: Succeeded\n" + "[1:35:43 PM] Current job status: Succeeded\n" ] } ], @@ -3834,7 +3833,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 48, "metadata": { "collapsed": false, "jupyter": { @@ -3850,7 +3849,7 @@ "outputs": [ { "data": { - "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":80,\"cczCount\":20,\"measurementCount\":80,\"numQubits\":11,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":380,\"algorithmicLogicalQubits\":33,\"cliffordErrorRate\":0.001,\"logicalDepth\":380,\"numTfactories\":14,\"numTfactoryRuns\":29,\"numTsPerRotation\":null,\"numTstates\":400,\"physicalQubitsForAlgorithm\":7986,\"physicalQubitsForTfactories\":135520,\"requiredLogicalQubitErrorRate\":3.987240829346092E-08,\"requiredLogicalTstateErrorRate\":1.25E-06},\"physicalQubits\":143506,\"runtime\":1672000},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"11\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"94.44 %\",\"physicalQubitsPerRound\":\"9680\",\"requiredLogicalQubitErrorRate\":\"3.99e-8\",\"requiredLogicalTstateErrorRate\":\"1.25e-6\",\"runtime\":\"1ms 672us\",\"tfactoryRuntime\":\"57us 200ns\",\"tfactoryRuntimePerRound\":\"57us 200ns\",\"tstateLogicalErrorRate\":\"2.48e-7\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 7986 physical qubits to implement the algorithm logic, and 135520 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 380 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 11$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 33$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 80 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 20 CCZ and 80 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 380. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 20 CCZ and 80 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 400 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{400\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 1ms 672us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 400 T states, the 14 copies of the T factory are repeatedly invoked 29 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 7986 are the product of the 33 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 9680 physical qubits and we run 14 in parallel, therefore we need $135520 = 9680 \\\\cdot 14$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 380.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 400.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000003987240829346092)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 33 from this number by assuming to align them in a 2D grid. 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Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. 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"{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":1,\"cczCount\":17,\"measurementCount\":1,\"numQubits\":13,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":55,\"algorithmicLogicalQubits\":38,\"cliffordErrorRate\":0.001,\"logicalDepth\":55,\"numTfactories\":14,\"numTfactoryRuns\":6,\"numTsPerRotation\":null,\"numTstates\":72,\"physicalQubitsForAlgorithm\":9196,\"physicalQubitsForTfactories\":90720,\"requiredLogicalQubitErrorRate\":2.3923444976076555E-07,\"requiredLogicalTstateErrorRate\":6.944444444444445E-06},\"physicalQubits\":99916,\"runtime\":242000},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"90.80 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"2.39e-7\",\"requiredLogicalTstateErrorRate\":\"6.94e-6\",\"runtime\":\"242us\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 9196 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 55 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 13$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 38$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 1 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 17 CCZ and 1 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 55. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 17 CCZ and 1 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 72 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{72\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 242us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 72 T states, the 14 copies of the T factory are repeatedly invoked 6 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 9196 are the product of the 38 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\\\cdot 14$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 55.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 72.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000023923444976076555)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.94e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", "text/html": [ "\r\n", "
\r\n", @@ -3862,24 +3861,24 @@ "\r\n", " \r\n", " Physical qubits\r\n", - " 143506\r\n", + " 99916\r\n", " \r\n", "

Number of physical qubits

\n", "\r\n", "
\r\n", - "

This value represents the total number of physical qubits, which is the sum of 7986 physical qubits to implement the algorithm logic, and 135520 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

\n", + "

This value represents the total number of physical qubits, which is the sum of 9196 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Runtime\r\n", - " 1ms 672us\r\n", + " 242us\r\n", " \r\n", "

Total runtime

\n", "\r\n", "
\r\n", - "

This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 380 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

\n", + "

This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 55 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

\n", "\r\n", " \r\n", " \n", @@ -3894,48 +3893,48 @@ "\r\n", " \r\n", " Logical algorithmic qubits\r\n", - " 33\r\n", + " 38\r\n", " \r\n", "

Number of logical qubits for the algorithm after layout

\n", "\r\n", "
\r\n", - "

Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 11\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 33$ logical qubits.

\n", + "

Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 13\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 38$ logical qubits.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Algorithmic depth\r\n", - " 380\r\n", + " 55\r\n", " \r\n", "

Number of logical cycles for the algorithm

\n", "\r\n", "
\r\n", - "

To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 80 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 20 CCZ and 80 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

\n", + "

To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 1 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 17 CCZ and 1 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Logical depth\r\n", - " 380\r\n", + " 55\r\n", " \r\n", "

Number of logical cycles performed

\n", "\r\n", "
\r\n", - "

This number is usually equal to the logical depth of the algorithm, which is 380. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", + "

This number is usually equal to the logical depth of the algorithm, which is 55. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Number of T states\r\n", - " 400\r\n", + " 72\r\n", " \r\n", "

Number of T states consumed by the algorithm

\n", "\r\n", "
\r\n", - "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 20 CCZ and 80 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", + "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 17 CCZ and 1 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", "\r\n", " \r\n", " \n", @@ -3944,70 +3943,70 @@ " Number of T factories\r\n", " 14\r\n", " \r\n", - "

Number of T factories capable of producing the demanded 400 T states during the algorithm's runtime

\n", + "

Number of T factories capable of producing the demanded 72 T states during the algorithm's runtime

\n", "\r\n", "
\r\n", - "

The total number of T factories 14 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{400\\;\\text{T states} \\cdot 57us 200ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 1ms 672us\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", + "

The total number of T factories 14 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{72\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 242us\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Number of T factory invocations\r\n", - " 29\r\n", + " 6\r\n", " \r\n", "

Number of times all T factories are invoked

\n", "\r\n", "
\r\n", - "

In order to prepare the 400 T states, the 14 copies of the T factory are repeatedly invoked 29 times.

\n", + "

In order to prepare the 72 T states, the 14 copies of the T factory are repeatedly invoked 6 times.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Physical algorithmic qubits\r\n", - " 7986\r\n", + " 9196\r\n", " \r\n", "

Number of physical qubits for the algorithm after layout

\n", "\r\n", "
\r\n", - "

The 7986 are the product of the 33 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.

\n", + "

The 9196 are the product of the 38 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Physical T factory qubits\r\n", - " 135520\r\n", + " 90720\r\n", " \r\n", "

Number of physical qubits for the T factories

\n", "\r\n", "
\r\n", - "

Each T factory requires 9680 physical qubits and we run 14 in parallel, therefore we need $135520 = 9680 \\cdot 14$ qubits.

\n", + "

Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\cdot 14$ qubits.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Required logical qubit error rate\r\n", - " 3.99e-8\r\n", + " 2.39e-7\r\n", " \r\n", "

The minimum logical qubit error rate required to run the algorithm within the error budget

\n", "\r\n", "
\r\n", - "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 380.

\n", + "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 55.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Required logical T state error rate\r\n", - " 1.25e-6\r\n", + " 6.94e-6\r\n", " \r\n", "

The minimum T state error rate required for distilled T states

\n", "\r\n", "
\r\n", - "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 400.

\n", + "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 72.

\n", "\r\n", " \r\n", " \n", @@ -4051,7 +4050,7 @@ "

Required code distance for error correction

\n", "\r\n", "
\r\n", - "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000003987240829346092)}{\\log(0.01/0.001)} - 1\\)

\n", + "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000023923444976076555)}{\\log(0.01/0.001)} - 1\\)

\n", "\r\n", " \r\n", " \n", @@ -4150,7 +4149,7 @@ "\r\n", " \r\n", " Physical qubits\r\n", - " 9680\r\n", + " 6480\r\n", " \r\n", "

Number of physical qubits for a single T factory

\n", "\r\n", @@ -4162,7 +4161,7 @@ "\r\n", " \r\n", " Runtime\r\n", - " 57us 200ns\r\n", + " 46us 800ns\r\n", " \r\n", "

Runtime of a single T factory

\n", "\r\n", @@ -4179,7 +4178,7 @@ "

Number of output T states produced in a single run of T factory

\n", "\r\n", "
\r\n", - "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.

\n", + "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.

\n", "\r\n", " \r\n", " \n", @@ -4234,7 +4233,7 @@ "\r\n", " \r\n", " Distillation code distances\r\n", - " 11\r\n", + " 9\r\n", " \r\n", "

The code distance in each round of distillation

\n", "\r\n", @@ -4246,7 +4245,7 @@ "\r\n", " \r\n", " Number of physical qubits per round\r\n", - " 9680\r\n", + " 6480\r\n", " \r\n", "

The number of physical qubits used in each round of distillation

\n", "\r\n", @@ -4258,7 +4257,7 @@ "\r\n", " \r\n", " Runtime per round\r\n", - " 57us 200ns\r\n", + " 46us 800ns\r\n", " \r\n", "

The runtime of each distillation round

\n", "\r\n", @@ -4270,12 +4269,12 @@ "\r\n", " \r\n", " Logical T state error rate\r\n", - " 2.48e-7\r\n", + " 2.17e-6\r\n", " \r\n", "

Logical T state error rate

\n", "\r\n", "
\r\n", - "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-6.

\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.94e-6.

\n", "\r\n", " \r\n", " \n", @@ -4290,12 +4289,12 @@ "\r\n", " \r\n", " Logical qubits (pre-layout)\r\n", - " 11\r\n", + " 13\r\n", " \r\n", "

Number of logical qubits in the input quantum program

\n", "\r\n", "
\r\n", - "

We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", + "

We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", "\r\n", " \r\n", " \n", @@ -4338,7 +4337,7 @@ "\r\n", " \r\n", " CCZ gates\r\n", - " 20\r\n", + " 17\r\n", " \r\n", "

Number of CCZ-gates in the input quantum program

\n", "\r\n", @@ -4350,7 +4349,7 @@ "\r\n", " \r\n", " CCiX gates\r\n", - " 80\r\n", + " 1\r\n", " \r\n", "

Number of CCiX-gates in the input quantum program

\n", "\r\n", @@ -4362,7 +4361,7 @@ "\r\n", " \r\n", " Measurement operations\r\n", - " 80\r\n", + " 1\r\n", " \r\n", "

Number of single qubit measurements in the input quantum program

\n", "\r\n", @@ -4593,10 +4592,10 @@ " 'tGateTime': '50 ns',\n", " 'twoQubitGateErrorRate': 0.001,\n", " 'twoQubitGateTime': '50 ns'}},\n", - " 'logicalCounts': {'ccixCount': 80,\n", - " 'cczCount': 20,\n", - " 'measurementCount': 80,\n", - " 'numQubits': 11,\n", + " 'logicalCounts': {'ccixCount': 1,\n", + " 'cczCount': 17,\n", + " 'measurementCount': 1,\n", + " 'numQubits': 13,\n", " 'rotationCount': 0,\n", " 'rotationDepth': 0,\n", " 'tCount': 0},\n", @@ -4604,21 +4603,21 @@ " 'logicalCycleTime': 4400.0,\n", " 'logicalErrorRate': 3.000000000000002e-08,\n", " 'physicalQubits': 242},\n", - " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 380,\n", - " 'algorithmicLogicalQubits': 33,\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 55,\n", + " 'algorithmicLogicalQubits': 38,\n", " 'cliffordErrorRate': 0.001,\n", - " 'logicalDepth': 380,\n", + " 'logicalDepth': 55,\n", " 'numTfactories': 14,\n", - " 'numTfactoryRuns': 29,\n", + " 'numTfactoryRuns': 6,\n", " 'numTsPerRotation': None,\n", - " 'numTstates': 400,\n", - " 'physicalQubitsForAlgorithm': 7986,\n", - " 'physicalQubitsForTfactories': 135520,\n", - " 'requiredLogicalQubitErrorRate': 3.987240829346092e-08,\n", - " 'requiredLogicalTstateErrorRate': 1.25e-06},\n", - " 'physicalQubits': 143506,\n", - " 'runtime': 1672000},\n", - " 'physicalCountsFormatted': {'codeDistancePerRound': '11',\n", + " 'numTstates': 72,\n", + " 'physicalQubitsForAlgorithm': 9196,\n", + " 'physicalQubitsForTfactories': 90720,\n", + " 'requiredLogicalQubitErrorRate': 2.3923444976076555e-07,\n", + " 'requiredLogicalTstateErrorRate': 6.944444444444445e-06},\n", + " 'physicalQubits': 99916,\n", + " 'runtime': 242000},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", " 'errorBudget': '1.00e-3',\n", " 'errorBudgetLogical': '5.00e-4',\n", " 'errorBudgetRotations': '0.00e0',\n", @@ -4627,14 +4626,14 @@ " 'logicalErrorRate': '3.00e-8',\n", " 'numTsPerRotation': 'No rotations in algorithm',\n", " 'numUnitsPerRound': '2',\n", - " 'physicalQubitsForTfactoriesPercentage': '94.44 %',\n", - " 'physicalQubitsPerRound': '9680',\n", - " 'requiredLogicalQubitErrorRate': '3.99e-8',\n", - " 'requiredLogicalTstateErrorRate': '1.25e-6',\n", - " 'runtime': '1ms 672us',\n", - " 'tfactoryRuntime': '57us 200ns',\n", - " 'tfactoryRuntimePerRound': '57us 200ns',\n", - " 'tstateLogicalErrorRate': '2.48e-7',\n", + " 'physicalQubitsForTfactoriesPercentage': '90.80 %',\n", + " 'physicalQubitsPerRound': '6480',\n", + " 'requiredLogicalQubitErrorRate': '2.39e-7',\n", + " 'requiredLogicalTstateErrorRate': '6.94e-6',\n", + " 'runtime': '242us',\n", + " 'tfactoryRuntime': '46us 800ns',\n", + " 'tfactoryRuntimePerRound': '46us 800ns',\n", + " 'tstateLogicalErrorRate': '2.17e-6',\n", " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", @@ -4645,53 +4644,53 @@ " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", " 'groups': [{'alwaysVisible': True,\n", " 'entries': [{'description': 'Number of physical qubits',\n", - " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 7986 physical qubits to implement the algorithm logic, and 135520 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 9196 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", " 'label': 'Physical qubits',\n", " 'path': 'physicalCounts/physicalQubits'},\n", " {'description': 'Total runtime',\n", - " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 380 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 55 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", " 'label': 'Runtime',\n", " 'path': 'physicalCountsFormatted/runtime'}],\n", " 'title': 'Physical resource estimates'},\n", " {'alwaysVisible': False,\n", " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", - " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 11$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 33$ logical qubits.',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 13$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 38$ logical qubits.',\n", " 'label': 'Logical algorithmic qubits',\n", " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", " {'description': 'Number of logical cycles for the algorithm',\n", - " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 80 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 20 CCZ and 80 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 1 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 17 CCZ and 1 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", " 'label': 'Algorithmic depth',\n", " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", " {'description': 'Number of logical cycles performed',\n", - " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 380. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 55. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", " 'label': 'Logical depth',\n", " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", " {'description': 'Number of T states consumed by the algorithm',\n", - " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 20 CCZ and 80 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 17 CCZ and 1 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", " 'label': 'Number of T states',\n", " 'path': 'physicalCounts/breakdown/numTstates'},\n", - " {'description': \"Number of T factories capable of producing the demanded 400 T states during the algorithm's runtime\",\n", - " 'explanation': 'The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{400\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 1ms 672us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " {'description': \"Number of T factories capable of producing the demanded 72 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{72\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 242us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", " 'label': 'Number of T factories',\n", " 'path': 'physicalCounts/breakdown/numTfactories'},\n", " {'description': 'Number of times all T factories are invoked',\n", - " 'explanation': 'In order to prepare the 400 T states, the 14 copies of the T factory are repeatedly invoked 29 times.',\n", + " 'explanation': 'In order to prepare the 72 T states, the 14 copies of the T factory are repeatedly invoked 6 times.',\n", " 'label': 'Number of T factory invocations',\n", " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", " {'description': 'Number of physical qubits for the algorithm after layout',\n", - " 'explanation': 'The 7986 are the product of the 33 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.',\n", + " 'explanation': 'The 9196 are the product of the 38 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.',\n", " 'label': 'Physical algorithmic qubits',\n", " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", " {'description': 'Number of physical qubits for the T factories',\n", - " 'explanation': 'Each T factory requires 9680 physical qubits and we run 14 in parallel, therefore we need $135520 = 9680 \\\\cdot 14$ qubits.',\n", + " 'explanation': 'Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\\\cdot 14$ qubits.',\n", " 'label': 'Physical T factory qubits',\n", " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", - " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 380.',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 55.',\n", " 'label': 'Required logical qubit error rate',\n", " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", " {'description': 'The minimum T state error rate required for distilled T states',\n", - " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 400.',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 72.',\n", " 'label': 'Required logical T state error rate',\n", " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", @@ -4705,7 +4704,7 @@ " 'label': 'QEC scheme',\n", " 'path': 'jobParams/qecScheme/name'},\n", " {'description': 'Required code distance for error correction',\n", - " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000003987240829346092)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000023923444976076555)}{\\\\log(0.01/0.001)} - 1$',\n", " 'label': 'Code distance',\n", " 'path': 'logicalQubit/codeDistance'},\n", " {'description': 'Number of physical qubits per logical qubit',\n", @@ -4747,7 +4746,7 @@ " 'label': 'Runtime',\n", " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", " {'description': 'Number of output T states produced in a single run of T factory',\n", - " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.',\n", " 'label': 'Number of output T states per run',\n", " 'path': 'tfactory/numTstates'},\n", " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", @@ -4779,13 +4778,13 @@ " 'label': 'Runtime per round',\n", " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", " {'description': 'Logical T state error rate',\n", - " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.25e-6.',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.94e-6.',\n", " 'label': 'Logical T state error rate',\n", " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", " 'title': 'T factory parameters'},\n", " {'alwaysVisible': False,\n", " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", - " 'explanation': 'We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'explanation': 'We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", " 'label': 'Logical qubits (pre-layout)',\n", " 'path': 'logicalCounts/numQubits'},\n", " {'description': 'Number of T gates in the input quantum program',\n", @@ -4874,20 +4873,20 @@ " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", " 'title': 'Physical qubit parameters'}]},\n", " 'status': 'success',\n", - " 'tfactory': {'codeDistancePerRound': [11],\n", - " 'logicalErrorRate': 2.480000000000001e-07,\n", + " 'tfactory': {'codeDistancePerRound': [9],\n", + " 'logicalErrorRate': 2.165000000000001e-06,\n", " 'numInputTstates': 30,\n", " 'numRounds': 1,\n", " 'numTstates': 1,\n", " 'numUnitsPerRound': [2],\n", - " 'physicalQubits': 9680,\n", - " 'physicalQubitsPerRound': [9680],\n", - " 'runtime': 57200.0,\n", - " 'runtimePerRound': [57200.0],\n", + " 'physicalQubits': 6480,\n", + " 'physicalQubitsPerRound': [6480],\n", + " 'runtime': 46800.0,\n", + " 'runtimePerRound': [46800.0],\n", " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" ] }, - "execution_count": 22, + "execution_count": 48, "metadata": {}, "output_type": "execute_result" } @@ -4900,7 +4899,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 49, "metadata": { "collapsed": false, "jupyter": { @@ -4927,7 +4926,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 50, "metadata": { "collapsed": false, "jupyter": { @@ -4945,18 +4944,18 @@ "name": "stdout", "output_type": "stream", "text": [ - "Logical algorithmic qubits = 33\n", - "Algorithmic depth = 380\n", - "Score = 12540\n" + "Logical algorithmic qubits = 38\n", + "Algorithmic depth = 55\n", + "Score = 2090\n" ] }, { "data": { "text/plain": [ - "12540" + "2090" ] }, - "execution_count": 24, + "execution_count": 50, "metadata": {}, "output_type": "execute_result" } diff --git a/iQuHack-challenge-2023-task4.ipynb b/team_solutions/schrodingers-duck/iQuHack-challenge-2023-task4.ipynb similarity index 100% rename from iQuHack-challenge-2023-task4.ipynb rename to team_solutions/schrodingers-duck/iQuHack-challenge-2023-task4.ipynb diff --git a/iQuHack-challenge-2023-task5.ipynb b/team_solutions/schrodingers-duck/iQuHack-challenge-2023-task5.ipynb similarity index 100% rename from iQuHack-challenge-2023-task5.ipynb rename to team_solutions/schrodingers-duck/iQuHack-challenge-2023-task5.ipynb diff --git a/iQuHack-challenge-2023-task6.ipynb b/team_solutions/schrodingers-duck/iQuHack-challenge-2023-task6.ipynb similarity index 100% rename from iQuHack-challenge-2023-task6.ipynb rename to team_solutions/schrodingers-duck/iQuHack-challenge-2023-task6.ipynb diff --git a/iQuHack-challenge-2023-task7.ipynb b/team_solutions/schrodingers-duck/iQuHack-challenge-2023-task7.ipynb similarity index 99% rename from iQuHack-challenge-2023-task7.ipynb rename to team_solutions/schrodingers-duck/iQuHack-challenge-2023-task7.ipynb index 89a785e..029dfd4 100644 --- a/iQuHack-challenge-2023-task7.ipynb +++ b/team_solutions/schrodingers-duck/iQuHack-challenge-2023-task7.ipynb @@ -104,7 +104,7 @@ }, "outputs": [], "source": [ - "teamname=\"schrodingers-cat\" # Update this field with your team name\n", + "teamname=\"schrodingers-duck\" # Update this field with your team name\n", "task=[\"task7\"]\n", "slack_id=\"U04L3SFUCQ2\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" ] diff --git a/iQuHack-challenge-2023-task8.ipynb b/team_solutions/schrodingers-duck/iQuHack-challenge-2023-task8.ipynb similarity index 100% rename from iQuHack-challenge-2023-task8.ipynb rename to team_solutions/schrodingers-duck/iQuHack-challenge-2023-task8.ipynb diff --git a/iQuHack-challenge-2023-task9.ipynb b/team_solutions/schrodingers-duck/iQuHack-challenge-2023-task9.ipynb similarity index 92% rename from iQuHack-challenge-2023-task9.ipynb rename to team_solutions/schrodingers-duck/iQuHack-challenge-2023-task9.ipynb index 2f3bf93..a21494d 100644 --- a/iQuHack-challenge-2023-task9.ipynb +++ b/team_solutions/schrodingers-duck/iQuHack-challenge-2023-task9.ipynb @@ -67,7 +67,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 21, "metadata": { "collapsed": false, "jupyter": { @@ -89,7 +89,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 22, "metadata": { "collapsed": false, "jupyter": { @@ -105,13 +105,13 @@ "outputs": [], "source": [ "teamname=\"schrodingers-duck\" # Update this field with your team name\n", - "task=[\"task8\"]\n", + "task=[\"task9\"]\n", "slack_id=\"U04L3SFUCQ2\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 23, "metadata": { "collapsed": false, "jupyter": { @@ -148,7 +148,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 24, "metadata": { "collapsed": false, "jupyter": { @@ -169,9 +169,11 @@ "%%qsharp\n", "open Microsoft.Quantum.Canon;\n", "open Microsoft.Quantum.Diagnostics;\n", + "open Microsoft.Quantum.Arrays;\n", "\n", "// Task 9. \n", "// (input will contain 8 qubits)\n", + "\n", "operation original(input : Qubit[], target : Qubit) : Unit is Adj {\n", " for i in [31,46,61,76,91,106,121,136,151,166,181,196,211,226,241] {\n", " ControlledOnInt(i, X)(input, target);\n", @@ -179,15 +181,37 @@ "}\n", "\n", "operation Task9(input : Qubit[], target : Qubit) : Unit is Adj {\n", - " for i in [31,46,61,76,91,106,121,136,151,166,181,196,211,226,241] {\n", + " for i in [31, 136, 241]{\n", " ControlledOnInt(i, X)(input, target);\n", " }\n", - "}" + " for i in [46,61,76,91,106,121] {\n", + " ControlledOnInt(i, X)(input, target);\n", + " SWAP(input[0], input[4]); SWAP(input[1], input[5]); SWAP(input[2], input[6]); SWAP(input[3],input[7]);\n", + " ControlledOnInt(i, X)(input, target);\n", + " }\n", + "}\n", + "\n", + "operation QubitArrayWrapperOperation (op : ((Qubit[], Qubit) => Unit is Adj), qs : Qubit[]) : Unit is Adj { \n", + " op(Most(qs), Tail(qs));\n", + "}\n", + "\n", + "operation TestCompoundGate () : Unit {\n", + " AssertOperationsEqualReferenced(8+1, QubitArrayWrapperOperation(Task9, _), QubitArrayWrapperOperation (original, _));\n", + "}\n" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [], + "source": [ + "TestCompoundGate();" ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 26, "metadata": { "collapsed": false, "jupyter": { @@ -244,7 +268,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 27, "metadata": { "collapsed": false, "jupyter": { @@ -289,12 +313,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -314,12 +338,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -339,12 +363,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -364,12 +388,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -389,12 +413,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -414,12 +438,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -439,12 +463,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -464,12 +488,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -489,12 +513,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -514,12 +538,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -539,12 +563,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -564,12 +588,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -589,12 +613,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -614,12 +638,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -639,12 +663,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -664,12 +688,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -689,12 +713,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -714,12 +738,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -739,12 +763,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -764,12 +788,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -789,12 +813,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -814,12 +838,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -839,12 +863,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -864,12 +888,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -889,12 +913,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -914,12 +938,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -939,12 +963,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -964,12 +988,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -989,12 +1013,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1014,12 +1038,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1039,12 +1063,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1064,12 +1088,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1089,12 +1113,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1114,12 +1138,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1139,12 +1163,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1164,12 +1188,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1189,12 +1213,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1214,12 +1238,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1239,12 +1263,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1264,12 +1288,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1289,12 +1313,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1314,12 +1338,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1339,12 +1363,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1364,12 +1388,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1389,12 +1413,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1414,12 +1438,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1439,12 +1463,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1464,12 +1488,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1489,12 +1513,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1514,12 +1538,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1539,12 +1563,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1564,12 +1588,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1589,12 +1613,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1614,12 +1638,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1639,12 +1663,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1664,12 +1688,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1689,12 +1713,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1714,12 +1738,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1739,12 +1763,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1764,12 +1788,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1789,12 +1813,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1814,12 +1838,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1839,12 +1863,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1864,12 +1888,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1889,12 +1913,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1914,12 +1938,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1939,12 +1963,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1964,12 +1988,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1989,12 +2013,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2014,12 +2038,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2039,12 +2063,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2064,12 +2088,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2089,12 +2113,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2114,12 +2138,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2139,12 +2163,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2164,12 +2188,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2189,12 +2213,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2214,12 +2238,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2239,12 +2263,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2264,12 +2288,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2289,12 +2313,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2314,12 +2338,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2339,12 +2363,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2364,12 +2388,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2389,12 +2413,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2414,12 +2438,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2439,12 +2463,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2464,12 +2488,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2489,12 +2513,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2514,12 +2538,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2539,12 +2563,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2564,12 +2588,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2589,12 +2613,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2614,12 +2638,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2639,12 +2663,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2664,12 +2688,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2689,12 +2713,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2714,12 +2738,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2739,12 +2763,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2764,12 +2788,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2789,12 +2813,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2814,12 +2838,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2839,12 +2863,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2864,12 +2888,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2889,12 +2913,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2914,12 +2938,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2939,12 +2963,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2964,12 +2988,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2989,12 +3013,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3014,12 +3038,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3039,12 +3063,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3064,12 +3088,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3089,12 +3113,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3114,12 +3138,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3139,12 +3163,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3164,12 +3188,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3189,12 +3213,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3214,12 +3238,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3239,12 +3263,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3264,12 +3288,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3289,12 +3313,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3314,12 +3338,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3339,12 +3363,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3364,12 +3388,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3389,12 +3413,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3414,12 +3438,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3439,12 +3463,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3464,12 +3488,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3489,12 +3513,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3514,12 +3538,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3539,12 +3563,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3564,12 +3588,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3589,12 +3613,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3614,12 +3638,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3639,12 +3663,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3664,12 +3688,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3689,12 +3713,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3714,12 +3738,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3739,12 +3763,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3764,12 +3788,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3789,12 +3813,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3814,12 +3838,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3839,12 +3863,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3864,12 +3888,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3889,12 +3913,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3914,12 +3938,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3939,12 +3963,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3964,12 +3988,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3989,12 +4013,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4014,12 +4038,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4039,12 +4063,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4064,12 +4088,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4089,12 +4113,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4114,12 +4138,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4139,12 +4163,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4164,12 +4188,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4189,12 +4213,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4214,12 +4238,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4239,12 +4263,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4264,12 +4288,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4289,12 +4313,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4314,12 +4338,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4339,12 +4363,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4364,12 +4388,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4389,12 +4413,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4414,12 +4438,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4439,12 +4463,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4464,12 +4488,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4489,12 +4513,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4514,12 +4538,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4539,12 +4563,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4564,12 +4588,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4589,12 +4613,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4614,12 +4638,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4639,12 +4663,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4664,12 +4688,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4689,12 +4713,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4714,12 +4738,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4739,12 +4763,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4764,12 +4788,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4789,12 +4813,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4814,12 +4838,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4839,12 +4863,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4864,12 +4888,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4889,12 +4913,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4914,12 +4938,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4939,12 +4963,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4964,12 +4988,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4989,12 +5013,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5014,12 +5038,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5039,12 +5063,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5064,12 +5088,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5089,12 +5113,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5114,12 +5138,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5139,12 +5163,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5164,12 +5188,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5189,12 +5213,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5214,12 +5238,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5239,12 +5263,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5264,12 +5288,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5289,12 +5313,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5314,12 +5338,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5339,12 +5363,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5364,12 +5388,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5389,12 +5413,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5414,12 +5438,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5439,12 +5463,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5464,12 +5488,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5489,12 +5513,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5514,12 +5538,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5539,12 +5563,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5564,12 +5588,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5589,12 +5613,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5614,12 +5638,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5639,12 +5663,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5664,12 +5688,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5689,12 +5713,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5714,12 +5738,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5739,12 +5763,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5764,12 +5788,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5789,12 +5813,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5814,12 +5838,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5839,12 +5863,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5864,12 +5888,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5889,12 +5913,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5914,12 +5938,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5939,12 +5963,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5964,12 +5988,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5989,12 +6013,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6014,12 +6038,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6039,12 +6063,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6064,12 +6088,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6089,12 +6113,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6114,12 +6138,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6139,12 +6163,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6164,12 +6188,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6189,12 +6213,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6214,12 +6238,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6239,12 +6263,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6264,12 +6288,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6289,12 +6313,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6314,12 +6338,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6339,12 +6363,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6364,12 +6388,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6389,12 +6413,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6414,12 +6438,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6439,12 +6463,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6464,12 +6488,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6489,12 +6513,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6514,12 +6538,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6539,12 +6563,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6564,12 +6588,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6589,12 +6613,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6614,12 +6638,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6639,12 +6663,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6664,12 +6688,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6948,7 +6972,7 @@ "()" ] }, - "execution_count": 6, + "execution_count": 27, "metadata": {}, "output_type": "execute_result" } @@ -6977,7 +7001,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 28, "metadata": { "collapsed": false, "jupyter": { @@ -7011,23 +7035,23 @@ { "data": { "text/plain": [ - "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 178414},\n", - " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 303167},\n", + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 181200},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 356642},\n", " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 4},\n", " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", - " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", - " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 166},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 193},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 167},\n", " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", - " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", - " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 166},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 193},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 167},\n", " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", @@ -7035,7 +7059,7 @@ " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" ] }, - "execution_count": 7, + "execution_count": 28, "metadata": {}, "output_type": "execute_result" } @@ -7051,7 +7075,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 29, "metadata": { "collapsed": false, "jupyter": { @@ -7079,7 +7103,7 @@ "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" ] }, - "execution_count": 8, + "execution_count": 29, "metadata": {}, "output_type": "execute_result" } @@ -7090,7 +7114,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 30, "metadata": { "collapsed": false, "jupyter": { @@ -7111,9 +7135,10 @@ "Submitting Task9_ResourceEstimationWrapper to target microsoft.estimator...\n", "Job successfully submitted.\n", " Job name: RE for the task 9\n", - " Job ID: ae3e32d3-3d41-40d0-8170-61957fdfc5ca\n", + " Job ID: 7ace3952-b323-4e0a-b110-cd1d4bfc1c6a\n", "Waiting up to 30 seconds for Azure Quantum job to complete...\n", - "[12:43:18 PM] Current job status: Succeeded\n" + "[1:47:12 PM] Current job status: Executing\n", + "[1:47:17 PM] Current job status: Succeeded\n" ] } ], @@ -7124,7 +7149,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 31, "metadata": { "collapsed": false, "jupyter": { @@ -8177,7 +8202,7 @@ " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" ] }, - "execution_count": 10, + "execution_count": 31, "metadata": {}, "output_type": "execute_result" } @@ -8190,7 +8215,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 32, "metadata": { "collapsed": false, "jupyter": { @@ -8217,7 +8242,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 33, "metadata": { "collapsed": false, "jupyter": { @@ -8246,7 +8271,7 @@ "17010" ] }, - "execution_count": 12, + "execution_count": 33, "metadata": {}, "output_type": "execute_result" } From 9ce72e08af69aa352c3b6671c4ebf7618e279a61 Mon Sep 17 00:00:00 2001 From: Hamish Hall Date: Sun, 29 Jan 2023 14:19:17 +0000 Subject: [PATCH 6/7] completed some outputs --- ...Hack-challenge-2023-task2-checkpoint.ipynb | 3374 +++++++ ...Hack-challenge-2023-task5-checkpoint.ipynb | 3402 +++++++ ...Hack-challenge-2023-task6-checkpoint.ipynb | 8327 +++++++++++++++++ ...Hack-challenge-2023-task7-checkpoint.ipynb | 4993 ++++++++++ ...Hack-challenge-2023-task8-checkpoint.ipynb | 5018 ++++++++++ .../iQuHack-challenge-2023-task5.ipynb | 363 +- .../iQuHack-challenge-2023-task6.ipynb | 1306 +-- .../iQuHack-challenge-2023-task7.ipynb | 568 +- .../schrodingers-duck/obj/__entrypoint__.dll | Bin 0 -> 321536 bytes .../obj/__entrypoint__snippets__.dll | Bin 0 -> 121344 bytes .../schrodingers-duck/obj/__snippets__.dll | Bin 0 -> 120832 bytes 11 files changed, 26203 insertions(+), 1148 deletions(-) create mode 100644 team_solutions/schrodingers-duck/.ipynb_checkpoints/iQuHack-challenge-2023-task2-checkpoint.ipynb create mode 100644 team_solutions/schrodingers-duck/.ipynb_checkpoints/iQuHack-challenge-2023-task5-checkpoint.ipynb create mode 100644 team_solutions/schrodingers-duck/.ipynb_checkpoints/iQuHack-challenge-2023-task6-checkpoint.ipynb create mode 100644 team_solutions/schrodingers-duck/.ipynb_checkpoints/iQuHack-challenge-2023-task7-checkpoint.ipynb create mode 100644 team_solutions/schrodingers-duck/.ipynb_checkpoints/iQuHack-challenge-2023-task8-checkpoint.ipynb create mode 100644 team_solutions/schrodingers-duck/obj/__entrypoint__.dll create mode 100644 team_solutions/schrodingers-duck/obj/__entrypoint__snippets__.dll create mode 100644 team_solutions/schrodingers-duck/obj/__snippets__.dll diff --git a/team_solutions/schrodingers-duck/.ipynb_checkpoints/iQuHack-challenge-2023-task2-checkpoint.ipynb b/team_solutions/schrodingers-duck/.ipynb_checkpoints/iQuHack-challenge-2023-task2-checkpoint.ipynb new file mode 100644 index 0000000..c41a4bc --- /dev/null +++ b/team_solutions/schrodingers-duck/.ipynb_checkpoints/iQuHack-challenge-2023-task2-checkpoint.ipynb @@ -0,0 +1,3374 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "# MIT iQuHack Microsoft Challenge: Optimizing Quantum Oracles, Task 2\n", + "\n", + "To work on this task,\n", + "1. Use the notebook for this task. Each of the notebooks in the repository has the code of the corresponding task.\n", + "2. Update your team name and Slack ID variables in the next code cell (you can use different Slack IDs for different tasks if different team members work on them, but make sure to use the same team name throughout the Hackathon). Do not change the task variable!\n", + "3. Work on your task in the cell that contains operation `Task2`! Your goal is to rewrite the code so that it maintains its correctness, but requires as few resources as possible. See `evaluate_results` function for details on how your absolute score for the task is calculated.\n", + "4. Submit your task using qBraid. Use the Share Notebook feature on qBraid (See File > Share Notebook) and enter the email rickyyoung@qbraid.com. Once you click submit, if the share notebook feature works correctly, it should show that you receive no errors and the email you entered will disappear. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "Log in to Azure (once per session, don't need to do it if running from Azure workspace)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\u001b[93mTo sign in, use a web browser to open the page https://microsoft.com/devicelogin and enter the code F2JVHXWME to authenticate.\u001b[0m\n", + "[\n", + " {\n", + " \"cloudName\": \"AzureCloud\",\n", + " \"homeTenantId\": \"b4e518fe-3bdc-4371-a4be-7f3d83d7acbd\",\n", + " \"id\": \"7fc54e95-14cf-4a6f-b50e-d6155c241309\",\n", + " \"isDefault\": true,\n", + " \"managedByTenants\": [\n", + " {\n", + " \"tenantId\": \"d0ecd01b-d782-448e-bae0-c3cad0e0543a\"\n", + " },\n", + " {\n", + " \"tenantId\": \"94c4857e-1130-4ab8-8eac-069b40c9db20\"\n", + " },\n", + " {\n", + " \"tenantId\": \"f702a9dc-ae48-4dc7-8f0a-8155a6dfa4e5\"\n", + " }\n", + " ],\n", + " \"name\": \"Azure subscription 1\",\n", + " \"state\": \"Enabled\",\n", + " \"tenantId\": \"b4e518fe-3bdc-4371-a4be-7f3d83d7acbd\",\n", + " \"user\": {\n", + " \"name\": \"hachall@hotmail.com\",\n", + " \"type\": \"user\"\n", + " }\n", + " }\n", + "]\n" + ] + } + ], + "source": [ + "!az login" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 1. Write the code" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Run this code cell to import the modules required to work with Q# and Azure\n", + "import qsharp\n", + "from qsharp import azure" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "teamname=\"schrodingers-duck\" # Update this field with your team name\n", + "task=[\"task2\"]\n", + "slack_id=\"U04L3SFUCQ2\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# You don't need to run this cell, it defines Q# operations as Python types to keep IntelliSense happy\n", + "Task2_DumpMachineWrapper : qsharp.QSharpCallable = None\n", + "Task2_ResourceEstimationWrapper : qsharp.QSharpCallable = None" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "**The complete code for Task 2 should be in this cell.** \n", + "This cell can include additional open statements and helper operations and functions if your solution needs them. \n", + "If you define helper operations in other cells, they will not be picked up by the grader!" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "open Microsoft.Quantum.Canon;\n", + "open Microsoft.Quantum.Bitwise;\n", + "open Microsoft.Quantum.Diagnostics;\n", + "open Microsoft.Quantum.Arrays;\n", + "\n", + "// Task 2. Celebrate MIT iQuHack!\n", + "// (input will contain 5 qubits)\n", + "\n", + "operation old(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " ControlledOnInt(13, X)(input, target); // M\n", + " ControlledOnInt( 9, X)(input, target); // I\n", + " ControlledOnInt(20, X)(input, target); // T\n", + "\n", + " ControlledOnInt( 9, X)(input, target); // I\n", + " ControlledOnInt(17, X)(input, target); // Q\n", + " ControlledOnInt(21, X)(input, target); // U\n", + " ControlledOnInt( 8, X)(input, target); // H\n", + " ControlledOnInt( 1, X)(input, target); // A\n", + " ControlledOnInt( 3, X)(input, target); // C\n", + " ControlledOnInt(11, X)(input, target); // K\n", + "}\n", + "\n", + "operation Task2(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " ControlledOnInt(13, X)(input, target); // M\n", + " ControlledOnInt(20, X)(input, target); // T\n", + " ControlledOnInt( 8, X)(input, target); // H\n", + " ControlledOnInt( 1, X)(input, target); // A\n", + " ControlledOnInt(9, X)([input[0],input[1],input[3],input[4]], target);\n", + " ControlledOnInt(3, X)([input[0],input[1],input[2],input[4]], target);\n", + "}\n", + "\n", + "operation QubitArrayWrapperOperation (op : ((Qubit[], Qubit) => Unit is Adj), qs : Qubit[]) : Unit is Adj { \n", + " op(Most(qs), Tail(qs));\n", + "}\n", + "\n", + "operation TestCompoundGate () : Unit {\n", + " AssertOperationsEqualReferenced(5+1, QubitArrayWrapperOperation(Task2, _), QubitArrayWrapperOperation (old, _));\n", + "}\n" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [], + "source": [ + "TestCompoundGate();" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "// Wrapper operation that allows you to observe the effects of the marking oracle by running it on a simulator.\n", + "operation Task2_DumpMachineWrapper() : Unit {\n", + " let N = 5;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " // Prepare an equal superposition of all input states in the input register.\n", + " ApplyToEach(H, input);\n", + " // Apply the oracle.\n", + " Task2(input, target);\n", + " // Print the state of the system after the oracle application.\n", + " DumpMachine();\n", + " ResetAll(input + [target]);\n", + "}\n", + "\n", + "// Wrapper operation that allows to run resource estimation for the task.\n", + "// This operation only allocates the qubits and applies the oracle once, not using any additional gates or measurements.\n", + "operation Task2_ResourceEstimationWrapper() : Unit {\n", + " let N = 5;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " Task2(input, target);\n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 2. Run the code on a simulator to see what it does\n", + "You can also write your own code to explore the effects of the oracle (for example, applying it to different basis states and measuring the results)." + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "data": { + "application/x-qsharp-data": 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Qubit IDs0, 1, 2, 3, 4, 5
Basis state (bitstring)AmplitudeMeas. Pr.
$\\left|000000\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|000001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|000010\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|000011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|000100\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|000101\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|000110\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|000111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|001000\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|001001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|001010\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|001011\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|001100\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|001101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|001110\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|001111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010000\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010010\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010100\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010110\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|011000\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|011001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|011010\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|011011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|011100\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|011101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|011110\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|011111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|100000\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|100001\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|100010\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|100011\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|100100\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|100101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|100110\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|100111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101000\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101010\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101011\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101100\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101101\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101110\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110000\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110001\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110010\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110100\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110101\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110110\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111000\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111001\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111010\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111011\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111100\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111101\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111110\\right\\rangle$$0.1768 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111111\\right\\rangle$$0.0000 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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Evaluate the code using resource estimation" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "data": { + "application/x-qsharp-data": "\"Connecting to Azure Quantum...\"", + "text/plain": [ + "Connecting to Azure Quantum..." + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Connected to Azure Quantum workspace azure-q in location uksouth.\n" + ] + }, + { + "data": { + "text/plain": [ + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 178071},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 409594},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 4},\n", + " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 167},\n", + " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 167},\n", + " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.qpu.aspen-m-2', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", + "# If you're using this notebook in qBraid, keep it\n", + "qsharp.azure.connect(\n", + " resourceId=\"/subscriptions/7fc54e95-14cf-4a6f-b50e-d6155c241309/resourceGroups/AzureQuantum/providers/Microsoft.Quantum/Workspaces/azure-q\",\n", + " location=\"UK South\",\n", + " credential=\"CLI\")" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loading package Microsoft.Quantum.Providers.Core and dependencies...\n", + "Active target is now microsoft.estimator\n" + ] + }, + { + "data": { + "text/plain": [ + "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qsharp.azure.target(\"microsoft.estimator\")" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Submitting Task2_ResourceEstimationWrapper to target microsoft.estimator...\n", + "Job successfully submitted.\n", + " Job name: RE for the task 2\n", + " Job ID: 4e3f0c4e-e8f0-49d5-99bf-d4d7d51bc4f7\n", + "Waiting up to 30 seconds for Azure Quantum job to complete...\n", + "[1:12:00 PM] Current job status: Executing\n", + "[1:12:06 PM] Current job status: Succeeded\n" + ] + } + ], + "source": [ + "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", + "result = qsharp.azure.execute(Task2_ResourceEstimationWrapper, jobName=\"RE for the task 2\")" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "data": { + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":30,\"cczCount\":10,\"measurementCount\":30,\"numQubits\":9,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":150,\"algorithmicLogicalQubits\":28,\"cliffordErrorRate\":0.001,\"logicalDepth\":150,\"numTfactories\":12,\"numTfactoryRuns\":14,\"numTsPerRotation\":null,\"numTstates\":160,\"physicalQubitsForAlgorithm\":6776,\"physicalQubitsForTfactories\":77760,\"requiredLogicalQubitErrorRate\":1.1904761904761904E-07,\"requiredLogicalTstateErrorRate\":3.125E-06},\"physicalQubits\":84536,\"runtime\":660000},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"91.98 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"1.19e-7\",\"requiredLogicalTstateErrorRate\":\"3.13e-6\",\"runtime\":\"660us\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 6776 physical qubits to implement the algorithm logic, and 77760 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 150 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 9$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 28$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 30 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 10 CCZ and 30 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 150. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 10 CCZ and 30 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 160 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{160\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 660us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 160 T states, the 12 copies of the T factory are repeatedly invoked 14 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 6776 are the product of the 28 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 12 in parallel, therefore we need $77760 = 6480 \\\\cdot 12$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 28 logical qubits and the total cycle count 150.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 160.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000011904761904761904)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 3.13e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 28 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or ¬µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "text/html": [ + "\r\n", + "
\r\n", + " \r\n", + " Physical resource estimates\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits84536\r\n", + "

Number of physical qubits

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This value represents the total number of physical qubits, which is the sum of 6776 physical qubits to implement the algorithm logic, and 77760 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

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Runtime660us\r\n", + "

Total runtime

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This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 150 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

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\r\n", + " \r\n", + " Resource estimates breakdown\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Logical algorithmic qubits28\r\n", + "

Number of logical qubits for the algorithm after layout

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Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 9\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 28$ logical qubits.

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Algorithmic depth150\r\n", + "

Number of logical cycles for the algorithm

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To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 30 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 10 CCZ and 30 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

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Logical depth150\r\n", + "

Number of logical cycles performed

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This number is usually equal to the logical depth of the algorithm, which is 150. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

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Number of T states160\r\n", + "

Number of T states consumed by the algorithm

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To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 10 CCZ and 30 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

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Number of T factories12\r\n", + "

Number of T factories capable of producing the demanded 160 T states during the algorithm's runtime

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The total number of T factories 12 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{160\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 660us\\;\\text{algorithm runtime}}\\right\\rceil\\)

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Number of T factory invocations14\r\n", + "

Number of times all T factories are invoked

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In order to prepare the 160 T states, the 12 copies of the T factory are repeatedly invoked 14 times.

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Physical algorithmic qubits6776\r\n", + "

Number of physical qubits for the algorithm after layout

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The 6776 are the product of the 28 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.

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Physical T factory qubits77760\r\n", + "

Number of physical qubits for the T factories

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Each T factory requires 6480 physical qubits and we run 12 in parallel, therefore we need $77760 = 6480 \\cdot 12$ qubits.

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Required logical qubit error rate1.19e-7\r\n", + "

The minimum logical qubit error rate required to run the algorithm within the error budget

\n", + "\r\n", + "
\r\n", + "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 28 logical qubits and the total cycle count 150.

\n", + "\r\n", + "
Required logical T state error rate3.13e-6\r\n", + "

The minimum T state error rate required for distilled T states

\n", + "\r\n", + "
\r\n", + "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 160.

\n", + "\r\n", + "
Number of T states per rotationNo rotations in algorithm\r\n", + "

Number of T states to implement a rotation with an arbitrary angle

\n", + "\r\n", + "
\r\n", + "

The number of T states to implement a rotation with an arbitrary angle is \\(\\lceil 0.53 \\log_2(0 / 0) + 5.3\\rceil\\) [arXiv:2203.10064]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Logical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
QEC schemesurface_code\r\n", + "

Name of QEC scheme

\n", + "\r\n", + "
\r\n", + "

You can load pre-defined QEC schemes by using the name surface_code or floquet_code. The latter only works with Majorana qubits.

\n", + "\r\n", + "
Code distance11\r\n", + "

Required code distance for error correction

\n", + "\r\n", + "
\r\n", + "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000011904761904761904)}{\\log(0.01/0.001)} - 1\\)

\n", + "\r\n", + "
Physical qubits242\r\n", + "

Number of physical qubits per logical qubit

\n", + "\r\n", + "
\r\n", + "

The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.

\n", + "\r\n", + "
Logical cycle time4us 400ns\r\n", + "

Duration of a logical cycle in nanoseconds

\n", + "\r\n", + "
\r\n", + "

The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.

\n", + "\r\n", + "
Logical qubit error rate3.00e-8\r\n", + "

Logical qubit error rate

\n", + "\r\n", + "
\r\n", + "

The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{11 + 1}{2}$

\n", + "\r\n", + "
Crossing prefactor0.03\r\n", + "

Crossing prefactor used in QEC scheme

\n", + "\r\n", + "
\r\n", + "

The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.

\n", + "\r\n", + "
Error correction threshold0.01\r\n", + "

Error correction threshold used in QEC scheme

\n", + "\r\n", + "
\r\n", + "

The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.

\n", + "\r\n", + "
Logical cycle time formula(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\r\n", + "

QEC scheme formula used to compute logical cycle time

\n", + "\r\n", + "
\r\n", + "

This is the formula that is used to compute the logical cycle time 4us 400ns.

\n", + "\r\n", + "
Physical qubits formula2 * codeDistance * codeDistance\r\n", + "

QEC scheme formula used to compute number of physical qubits per logical qubit

\n", + "\r\n", + "
\r\n", + "

This is the formula that is used to compute the number of physical qubits per logical qubits 242.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " T factory parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits6480\r\n", + "

Number of physical qubits for a single T factory

\n", + "\r\n", + "
\r\n", + "

This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.

\n", + "\r\n", + "
Runtime46us 800ns\r\n", + "

Runtime of a single T factory

\n", + "\r\n", + "
\r\n", + "

The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.

\n", + "\r\n", + "
Number of output T states per run1\r\n", + "

Number of output T states produced in a single run of T factory

\n", + "\r\n", + "
\r\n", + "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.

\n", + "\r\n", + "
Number of input T states per run30\r\n", + "

Number of physical input T states consumed in a single run of a T factory

\n", + "\r\n", + "
\r\n", + "

This value includes the physical input T states of all copies of the distillation unit in the first round.

\n", + "\r\n", + "
Distillation rounds1\r\n", + "

The number of distillation rounds

\n", + "\r\n", + "
\r\n", + "

This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.

\n", + "\r\n", + "
Distillation units per round2\r\n", + "

The number of units in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the number of copies for the distillation units per round.

\n", + "\r\n", + "
Distillation units15-to-1 space efficient logical\r\n", + "

The types of distillation units

\n", + "\r\n", + "
\r\n", + "

These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.

\n", + "\r\n", + "
Distillation code distances9\r\n", + "

The code distance in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.

\n", + "\r\n", + "
Number of physical qubits per round6480\r\n", + "

The number of physical qubits used in each round of distillation

\n", + "\r\n", + "
\r\n", + "

The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.

\n", + "\r\n", + "
Runtime per round46us 800ns\r\n", + "

The runtime of each distillation round

\n", + "\r\n", + "
\r\n", + "

The runtime of the T factory is the sum of the runtimes in all rounds.

\n", + "\r\n", + "
Logical T state error rate2.17e-6\r\n", + "

Logical T state error rate

\n", + "\r\n", + "
\r\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 3.13e-6.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Pre-layout logical resources\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Logical qubits (pre-layout)9\r\n", + "

Number of logical qubits in the input quantum program

\n", + "\r\n", + "
\r\n", + "

We determine 28 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", + "\r\n", + "
T gates0\r\n", + "

Number of T gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.

\n", + "\r\n", + "
Rotation gates0\r\n", + "

Number of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.

\n", + "\r\n", + "
Rotation depth0\r\n", + "

Depth of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.

\n", + "\r\n", + "
CCZ gates10\r\n", + "

Number of CCZ-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCZ gates.

\n", + "\r\n", + "
CCiX gates30\r\n", + "

Number of CCiX-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCiX gates, which applies \\(-iX\\) controlled on two control qubits [1212.5069].

\n", + "\r\n", + "
Measurement operations30\r\n", + "

Number of single qubit measurements in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Assumed error budget\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Total error budget1.00e-3\r\n", + "

Total error budget for the algorithm

\n", + "\r\n", + "
\r\n", + "

The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget \\(\\epsilon = \\epsilon_{\\log} + \\epsilon_{\\rm dis} + \\epsilon_{\\rm syn}\\) is uniformly distributed and applies to errors \\(\\epsilon_{\\log}\\) to implement logical qubits, an error budget \\(\\epsilon_{\\rm dis}\\) to produce T states through distillation, and an error budget \\(\\epsilon_{\\rm syn}\\) to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets \\(\\epsilon_{\\rm dis}\\) and \\(\\epsilon_{\\rm syn}\\) are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.

\n", + "\r\n", + "
Logical error probability5.00e-4\r\n", + "

Probability of at least one logical error

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
T distillation error probability5.00e-4\r\n", + "

Probability of at least one faulty T distillation

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
Rotation synthesis error probability0.00e0\r\n", + "

Probability of at least one failed rotation synthesis

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Physical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Qubit namequbit_gate_ns_e3\r\n", + "

Some descriptive name for the qubit model

\n", + "\r\n", + "
\r\n", + "

You can load pre-defined qubit parameters by using the names qubit_gate_ns_e3, qubit_gate_ns_e4, qubit_gate_us_e3, qubit_gate_us_e4, qubit_maj_ns_e4, or qubit_maj_ns_e6. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).

\n", + "\r\n", + "
Instruction setGateBased\r\n", + "

Underlying qubit technology (gate-based or Majorana)

\n", + "\r\n", + "
\r\n", + "

When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either gate-based or Majorana. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.

\n", + "\r\n", + "
Single-qubit measurement time100 ns\r\n", + "

Operation time for single-qubit measurement (t_meas) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.

\n", + "\r\n", + "
Single-qubit gate time50 ns\r\n", + "

Operation time for single-qubit gate (t_gate) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.

\n", + "\r\n", + "
Two-qubit gate time50 ns\r\n", + "

Operation time for two-qubit gate in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.

\n", + "\r\n", + "
T gate time50 ns\r\n", + "

Operation time for a T gate

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to execute a T gate.

\n", + "\r\n", + "
Single-qubit measurement error rate0.001\r\n", + "

Error rate for single-qubit measurement

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit measurement in the Pauli basis may fail.

\n", + "\r\n", + "
Single-qubit error rate0.001\r\n", + "

Error rate for single-qubit Clifford gate (p)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.

\n", + "\r\n", + "
Two-qubit error rate0.001\r\n", + "

Error rate for two-qubit Clifford gate

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.

\n", + "\r\n", + "
T gate error rate0.001\r\n", + "

Error rate to prepare single-qubit T state or apply a T gate (p_T)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which executing a single T gate may fail.

\n", + "\r\n", + "
\n", + "
\r\n", + " Assumptions\r\n", + "
    \n", + "

  • More details on the following lists of assumptions can be found in the paper Accessing requirements for scaling quantum computers and their applications.

    \n", + "
    • \n", + "

  • Uniform independent physical noise. We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.

    \n", + "
    • \n", + "

  • Efficient classical computation. We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.

    \n", + "
    • \n", + "

  • Extraction circuits for planar quantum ISA. We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).

    \n", + "
    • \n", + "

  • Uniform independent logical noise. We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.

    \n", + "
    • \n", + "

  • Negligible Clifford costs for synthesis. We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.

    \n", + "
    • \n", + "

  • Smooth magic state consumption rate. We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.

    \n", + "
    • \n", + "
\n" + ], + "text/plain": [ + "{'errorBudget': {'logical': 0.0005, 'rotations': 0.0, 'tstates': 0.0005},\n", + " 'jobParams': {'errorBudget': 0.001,\n", + " 'qecScheme': {'crossingPrefactor': 0.03,\n", + " 'errorCorrectionThreshold': 0.01,\n", + " 'logicalCycleTime': '(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance',\n", + " 'name': 'surface_code',\n", + " 'physicalQubitsPerLogicalQubit': '2 * codeDistance * codeDistance'},\n", + " 'qubitParams': {'instructionSet': 'GateBased',\n", + " 'name': 'qubit_gate_ns_e3',\n", + " 'oneQubitGateErrorRate': 0.001,\n", + " 'oneQubitGateTime': '50 ns',\n", + " 'oneQubitMeasurementErrorRate': 0.001,\n", + " 'oneQubitMeasurementTime': '100 ns',\n", + " 'tGateErrorRate': 0.001,\n", + " 'tGateTime': '50 ns',\n", + " 'twoQubitGateErrorRate': 0.001,\n", + " 'twoQubitGateTime': '50 ns'}},\n", + " 'logicalCounts': {'ccixCount': 30,\n", + " 'cczCount': 10,\n", + " 'measurementCount': 30,\n", + " 'numQubits': 9,\n", + " 'rotationCount': 0,\n", + " 'rotationDepth': 0,\n", + " 'tCount': 0},\n", + " 'logicalQubit': {'codeDistance': 11,\n", + " 'logicalCycleTime': 4400.0,\n", + " 'logicalErrorRate': 3.000000000000002e-08,\n", + " 'physicalQubits': 242},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 150,\n", + " 'algorithmicLogicalQubits': 28,\n", + " 'cliffordErrorRate': 0.001,\n", + " 'logicalDepth': 150,\n", + " 'numTfactories': 12,\n", + " 'numTfactoryRuns': 14,\n", + " 'numTsPerRotation': None,\n", + " 'numTstates': 160,\n", + " 'physicalQubitsForAlgorithm': 6776,\n", + " 'physicalQubitsForTfactories': 77760,\n", + " 'requiredLogicalQubitErrorRate': 1.1904761904761904e-07,\n", + " 'requiredLogicalTstateErrorRate': 3.125e-06},\n", + " 'physicalQubits': 84536,\n", + " 'runtime': 660000},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", + " 'errorBudget': '1.00e-3',\n", + " 'errorBudgetLogical': '5.00e-4',\n", + " 'errorBudgetRotations': '0.00e0',\n", + " 'errorBudgetTstates': '5.00e-4',\n", + " 'logicalCycleTime': '4us 400ns',\n", + " 'logicalErrorRate': '3.00e-8',\n", + " 'numTsPerRotation': 'No rotations in algorithm',\n", + " 'numUnitsPerRound': '2',\n", + " 'physicalQubitsForTfactoriesPercentage': '91.98 %',\n", + " 'physicalQubitsPerRound': '6480',\n", + " 'requiredLogicalQubitErrorRate': '1.19e-7',\n", + " 'requiredLogicalTstateErrorRate': '3.13e-6',\n", + " 'runtime': '660us',\n", + " 'tfactoryRuntime': '46us 800ns',\n", + " 'tfactoryRuntimePerRound': '46us 800ns',\n", + " 'tstateLogicalErrorRate': '2.17e-6',\n", + " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", + " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", + " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", + " '**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.',\n", + " '**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).',\n", + " '**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.',\n", + " '**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.',\n", + " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", + " 'groups': [{'alwaysVisible': True,\n", + " 'entries': [{'description': 'Number of physical qubits',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 6776 physical qubits to implement the algorithm logic, and 77760 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'physicalCounts/physicalQubits'},\n", + " {'description': 'Total runtime',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 150 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/runtime'}],\n", + " 'title': 'Physical resource estimates'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 9$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 28$ logical qubits.',\n", + " 'label': 'Logical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", + " {'description': 'Number of logical cycles for the algorithm',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 30 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 10 CCZ and 30 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'label': 'Algorithmic depth',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", + " {'description': 'Number of logical cycles performed',\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 150. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'label': 'Logical depth',\n", + " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", + " {'description': 'Number of T states consumed by the algorithm',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 10 CCZ and 30 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'label': 'Number of T states',\n", + " 'path': 'physicalCounts/breakdown/numTstates'},\n", + " {'description': \"Number of T factories capable of producing the demanded 160 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{160\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 660us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " 'label': 'Number of T factories',\n", + " 'path': 'physicalCounts/breakdown/numTfactories'},\n", + " {'description': 'Number of times all T factories are invoked',\n", + " 'explanation': 'In order to prepare the 160 T states, the 12 copies of the T factory are repeatedly invoked 14 times.',\n", + " 'label': 'Number of T factory invocations',\n", + " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", + " {'description': 'Number of physical qubits for the algorithm after layout',\n", + " 'explanation': 'The 6776 are the product of the 28 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.',\n", + " 'label': 'Physical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", + " {'description': 'Number of physical qubits for the T factories',\n", + " 'explanation': 'Each T factory requires 6480 physical qubits and we run 12 in parallel, therefore we need $77760 = 6480 \\\\cdot 12$ qubits.',\n", + " 'label': 'Physical T factory qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", + " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 28 logical qubits and the total cycle count 150.',\n", + " 'label': 'Required logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", + " {'description': 'The minimum T state error rate required for distilled T states',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 160.',\n", + " 'label': 'Required logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", + " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", + " 'explanation': 'The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.',\n", + " 'label': 'Number of T states per rotation',\n", + " 'path': 'physicalCountsFormatted/numTsPerRotation'}],\n", + " 'title': 'Resource estimates breakdown'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Name of QEC scheme',\n", + " 'explanation': 'You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.',\n", + " 'label': 'QEC scheme',\n", + " 'path': 'jobParams/qecScheme/name'},\n", + " {'description': 'Required code distance for error correction',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000011904761904761904)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'label': 'Code distance',\n", + " 'path': 'logicalQubit/codeDistance'},\n", + " {'description': 'Number of physical qubits per logical qubit',\n", + " 'explanation': 'The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'logicalQubit/physicalQubits'},\n", + " {'description': 'Duration of a logical cycle in nanoseconds',\n", + " 'explanation': 'The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.',\n", + " 'label': 'Logical cycle time',\n", + " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", + " {'description': 'Logical qubit error rate',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$',\n", + " 'label': 'Logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", + " {'description': 'Crossing prefactor used in QEC scheme',\n", + " 'explanation': 'The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.',\n", + " 'label': 'Crossing prefactor',\n", + " 'path': 'jobParams/qecScheme/crossingPrefactor'},\n", + " {'description': 'Error correction threshold used in QEC scheme',\n", + " 'explanation': 'The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.',\n", + " 'label': 'Error correction threshold',\n", + " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", + " {'description': 'QEC scheme formula used to compute logical cycle time',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 4us 400ns.',\n", + " 'label': 'Logical cycle time formula',\n", + " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", + " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 242.',\n", + " 'label': 'Physical qubits formula',\n", + " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", + " 'title': 'Logical qubit parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of physical qubits for a single T factory',\n", + " 'explanation': 'This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'tfactory/physicalQubits'},\n", + " {'description': 'Runtime of a single T factory',\n", + " 'explanation': 'The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", + " {'description': 'Number of output T states produced in a single run of T factory',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.',\n", + " 'label': 'Number of output T states per run',\n", + " 'path': 'tfactory/numTstates'},\n", + " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", + " 'explanation': 'This value includes the physical input T states of all copies of the distillation unit in the first round.',\n", + " 'label': 'Number of input T states per run',\n", + " 'path': 'tfactory/numInputTstates'},\n", + " {'description': 'The number of distillation rounds',\n", + " 'explanation': 'This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.',\n", + " 'label': 'Distillation rounds',\n", + " 'path': 'tfactory/numRounds'},\n", + " {'description': 'The number of units in each round of distillation',\n", + " 'explanation': 'This is the number of copies for the distillation units per round.',\n", + " 'label': 'Distillation units per round',\n", + " 'path': 'physicalCountsFormatted/numUnitsPerRound'},\n", + " {'description': 'The types of distillation units',\n", + " 'explanation': 'These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.',\n", + " 'label': 'Distillation units',\n", + " 'path': 'physicalCountsFormatted/unitNamePerRound'},\n", + " {'description': 'The code distance in each round of distillation',\n", + " 'explanation': 'This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.',\n", + " 'label': 'Distillation code distances',\n", + " 'path': 'physicalCountsFormatted/codeDistancePerRound'},\n", + " {'description': 'The number of physical qubits used in each round of distillation',\n", + " 'explanation': 'The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.',\n", + " 'label': 'Number of physical qubits per round',\n", + " 'path': 'physicalCountsFormatted/physicalQubitsPerRound'},\n", + " {'description': 'The runtime of each distillation round',\n", + " 'explanation': 'The runtime of the T factory is the sum of the runtimes in all rounds.',\n", + " 'label': 'Runtime per round',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", + " {'description': 'Logical T state error rate',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 3.13e-6.',\n", + " 'label': 'Logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", + " 'title': 'T factory parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", + " 'explanation': 'We determine 28 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'label': 'Logical qubits (pre-layout)',\n", + " 'path': 'logicalCounts/numQubits'},\n", + " {'description': 'Number of T gates in the input quantum program',\n", + " 'explanation': 'This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.',\n", + " 'label': 'T gates',\n", + " 'path': 'logicalCounts/tCount'},\n", + " {'description': 'Number of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.',\n", + " 'label': 'Rotation gates',\n", + " 'path': 'logicalCounts/rotationCount'},\n", + " {'description': 'Depth of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.',\n", + " 'label': 'Rotation depth',\n", + " 'path': 'logicalCounts/rotationDepth'},\n", + " {'description': 'Number of CCZ-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCZ gates.',\n", + " 'label': 'CCZ gates',\n", + " 'path': 'logicalCounts/cczCount'},\n", + " {'description': 'Number of CCiX-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].',\n", + " 'label': 'CCiX gates',\n", + " 'path': 'logicalCounts/ccixCount'},\n", + " {'description': 'Number of single qubit measurements in the input quantum program',\n", + " 'explanation': 'This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.',\n", + " 'label': 'Measurement operations',\n", + " 'path': 'logicalCounts/measurementCount'}],\n", + " 'title': 'Pre-layout logical resources'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Total error budget for the algorithm',\n", + " 'explanation': \"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\n", + " 'label': 'Total error budget',\n", + " 'path': 'physicalCountsFormatted/errorBudget'},\n", + " {'description': 'Probability of at least one logical error',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'Logical error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetLogical'},\n", + " {'description': 'Probability of at least one faulty T distillation',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'T distillation error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetTstates'},\n", + " {'description': 'Probability of at least one failed rotation synthesis',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3.',\n", + " 'label': 'Rotation synthesis error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetRotations'}],\n", + " 'title': 'Assumed error budget'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Some descriptive name for the qubit model',\n", + " 'explanation': 'You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).',\n", + " 'label': 'Qubit name',\n", + " 'path': 'jobParams/qubitParams/name'},\n", + " {'description': 'Underlying qubit technology (gate-based or Majorana)',\n", + " 'explanation': 'When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.',\n", + " 'label': 'Instruction set',\n", + " 'path': 'jobParams/qubitParams/instructionSet'},\n", + " {'description': 'Operation time for single-qubit measurement (t_meas) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.',\n", + " 'label': 'Single-qubit measurement time',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementTime'},\n", + " {'description': 'Operation time for single-qubit gate (t_gate) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.',\n", + " 'label': 'Single-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateTime'},\n", + " {'description': 'Operation time for two-qubit gate in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.',\n", + " 'label': 'Two-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateTime'},\n", + " {'description': 'Operation time for a T gate',\n", + " 'explanation': 'This is the operation time in nanoseconds to execute a T gate.',\n", + " 'label': 'T gate time',\n", + " 'path': 'jobParams/qubitParams/tGateTime'},\n", + " {'description': 'Error rate for single-qubit measurement',\n", + " 'explanation': 'This is the probability in which a single-qubit measurement in the Pauli basis may fail.',\n", + " 'label': 'Single-qubit measurement error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementErrorRate'},\n", + " {'description': 'Error rate for single-qubit Clifford gate (p)',\n", + " 'explanation': 'This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.',\n", + " 'label': 'Single-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateErrorRate'},\n", + " {'description': 'Error rate for two-qubit Clifford gate',\n", + " 'explanation': 'This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.',\n", + " 'label': 'Two-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateErrorRate'},\n", + " {'description': 'Error rate to prepare single-qubit T state or apply a T gate (p_T)',\n", + " 'explanation': 'This is the probability in which executing a single T gate may fail.',\n", + " 'label': 'T gate error rate',\n", + " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", + " 'title': 'Physical qubit parameters'}]},\n", + " 'status': 'success',\n", + " 'tfactory': {'codeDistancePerRound': [9],\n", + " 'logicalErrorRate': 2.165000000000001e-06,\n", + " 'numInputTstates': 30,\n", + " 'numRounds': 1,\n", + " 'numTstates': 1,\n", + " 'numUnitsPerRound': [2],\n", + " 'physicalQubits': 6480,\n", + " 'physicalQubitsPerRound': [6480],\n", + " 'runtime': 46800.0,\n", + " 'runtimePerRound': [46800.0],\n", + " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", + "# result = qsharp.azure.output(\"...\")\n", + "result" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# The function that extracts the relevant resource information from the resource estimation job results and produces your absolute score.\n", + "def evaluate_results(res) : \n", + " width = res['physicalCounts']['breakdown']['algorithmicLogicalQubits']\n", + " depth = res['physicalCounts']['breakdown']['algorithmicLogicalDepth']\n", + " print(f\"Logical algorithmic qubits = {width}\")\n", + " print(f\"Algorithmic depth = {depth}\")\n", + " print(f\"Score = {width * depth}\")\n", + " return width * depth\n" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Logical algorithmic qubits = 28\n", + "Algorithmic depth = 150\n", + "Score = 4200\n" + ] + }, + { + "data": { + "text/plain": [ + "4200" + ] + }, + "execution_count": 47, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "evaluate_results(result)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernel_info": { + "name": "python3" + }, + "kernelspec": { + "display_name": "Python 3 [Q#]", + "language": "python", + "name": "python3_qsharp_b54crn" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.10" + }, + "nteract": { + "version": "nteract-front-end@1.0.0" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/team_solutions/schrodingers-duck/.ipynb_checkpoints/iQuHack-challenge-2023-task5-checkpoint.ipynb b/team_solutions/schrodingers-duck/.ipynb_checkpoints/iQuHack-challenge-2023-task5-checkpoint.ipynb new file mode 100644 index 0000000..9d4c433 --- /dev/null +++ b/team_solutions/schrodingers-duck/.ipynb_checkpoints/iQuHack-challenge-2023-task5-checkpoint.ipynb @@ -0,0 +1,3402 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "# MIT iQuHack Microsoft Challenge: Optimizing Quantum Oracles, Task 5\n", + "\n", + "To work on this task,\n", + "1. Use the notebook for this task. Each of the notebooks in the repository has the code of the corresponding task.\n", + "2. Update your team name and Slack ID variables in the next code cell (you can use different Slack IDs for different tasks if different team members work on them, but make sure to use the same team name throughout the Hackathon). Do not change the task variable!\n", + "3. Work on your task in the cell that contains operation `Task5`! Your goal is to rewrite the code so that it maintains its correctness, but requires as few resources as possible. See `evaluate_results` function for details on how your absolute score for the task is calculated.\n", + "4. Submit your task using qBraid. Use the Share Notebook feature on qBraid (See File > Share Notebook) and enter the email rickyyoung@qbraid.com. Once you click submit, if the share notebook feature works correctly, it should show that you receive no errors and the email you entered will disappear. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "Log in to Azure (once per session, don't need to do it if running from Azure workspace)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "!az login" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 1. Write the code" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Run this code cell to import the modules required to work with Q# and Azure\n", + "import qsharp\n", + "from qsharp import azure" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "teamname=\"schrodingers-duck\" # Update this field with your team name\n", + "task=[\"task5\"]\n", + "slack_id=\"U04L3SFUCQ2\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# You don't need to run this cell, it defines Q# operations as Python types to keep IntelliSense happy\n", + "Task5_DumpMachineWrapper : qsharp.QSharpCallable = None\n", + "Task5_ResourceEstimationWrapper : qsharp.QSharpCallable = None" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "**The complete code for Task 5 should be in this cell.** \n", + "This cell can include additional open statements and helper operations and functions if your solution needs them. \n", + "If you define helper operations in other cells, they will not be picked up by the grader!" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "open Microsoft.Quantum.Canon;\n", + "open Microsoft.Quantum.Diagnostics;\n", + "open Microsoft.Quantum.Arrays;\n", + "\n", + "\n", + "// Task 5. \n", + "// (input will contain 6 qubits)\n", + "operation Task5(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " for i in [21,42] {\n", + " ControlledOnInt(i, X)(input, target);\n", + " }\n", + " use equality = Qubit[3];\n", + " use storageWire = Qubit[1];\n", + " within {\n", + " CNOT(input[0], equality[0]);\n", + " CNOT(input[3], equality[0]);\n", + " CNOT(input[1], equality[1]);\n", + " CNOT(input[4], equality[1]);\n", + " CNOT(input[2], equality[2]);\n", + " CNOT(input[5], equality[2]);\n", + " X(equality[0]); X(equality[1]); X(equality[2]);\n", + " CCNOT(equality[0], equality[1], storageWire[0]);\n", + " } apply {\n", + " CCNOT(equality[2], storageWire[0], target);\n", + " }\n", + "}\n", + "\n", + "operation original(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " for i in [0, 9, 18, 21, 27, 36, 42, 45, 54, 63] {\n", + " ControlledOnInt(i, X)(input, target);\n", + " }\n", + "}\n", + "\n", + "operation QubitArrayWrapperOperation (op : ((Qubit[], Qubit) => Unit is Adj), qs : Qubit[]) : Unit is Adj { \n", + " op(Most(qs), Tail(qs));\n", + "}\n", + "\n", + "operation TestCompoundGate () : Unit {\n", + " AssertOperationsEqualReferenced(6+1, QubitArrayWrapperOperation(Task5, _), QubitArrayWrapperOperation (original, _));\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "\r\n", + "
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SourceCallable
(notebook)Task5
(notebook)QubitArrayWrapperOperation
/home/jovyan/2023_microsoft/D:\\a\\1\\s\\submodules\\qsharp-runtime\\src\\Simulation\\TargetDefinitions\\Decompositions\\AssertOperationsEqualReferenced.qs:0Microsoft.Quantum.Diagnostics.AssertOperationsEqualReferenced
(notebook)TestCompoundGate
\r\n", + "
\r\n", + " " + ], + "text/plain": [ + "Unhandled exception. System.ArgumentOutOfRangeException: Specified argument was out of the range of valid values.\n", + " ---> SNIPPET.Task5 on /snippet_.qs:line 0\n", + " at SNIPPET.QubitArrayWrapperOperation on /snippet_.qs:line 0\n", + " at Microsoft.Quantum.Diagnostics.AssertOperationsEqualReferenced on /home/jovyan/2023_microsoft/D:\\a\\1\\s\\submodules\\qsharp-runtime\\src\\Simulation\\TargetDefinitions\\Decompositions\\AssertOperationsEqualReferenced.qs:line 0\n", + " at SNIPPET.TestCompoundGate on /snippet_.qs:line 0\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Specified argument was out of the range of valid values.\n" + ] + } + ], + "source": [ + "TestCompoundGate();" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "// Wrapper operation that allows you to observe the effects of the marking oracle by running it on a simulator.\n", + "operation Task5_DumpMachineWrapper() : Unit {\n", + " let N = 6;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " // Prepare an equal superposition of all input states in the input register.\n", + " ApplyToEach(H, input);\n", + " // Apply the oracle.\n", + " Task5(input, target);\n", + " // Print the state of the system after the oracle application.\n", + " DumpMachine();\n", + " ResetAll(input + [target]);\n", + "}\n", + "\n", + "// Wrapper operation that allows to run resource estimation for the task.\n", + "// This operation only allocates the qubits and applies the oracle once, not using any additional gates or measurements.\n", + "operation Task5_ResourceEstimationWrapper() : Unit {\n", + " let N = 6;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " Task5(input, target);\n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 2. Run the code on a simulator to see what it does\n", + "You can also write your own code to explore the effects of the oracle (for example, applying it to different basis states and measuring the results)." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "data": { + "application/x-qsharp-data": 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Qubit IDs0, 1, 2, 3, 4, 5, 6
Basis state (bitstring)AmplitudeMeas. Pr.
$\\left|0000001\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

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$\\left|0000010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0000100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0000110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0001000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0001010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0001100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0001110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0010000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0010011\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0010100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0010110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0011000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0011010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0011100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0011110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0100000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0100010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0100101\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0100110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0101000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0101011\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0101100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0101110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0110000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0110010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0110100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0110111\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0111000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0111010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0111100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0111110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1000000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1000010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1000100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1000110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1001001\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1001010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1001100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1001110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1010000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1010010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|1010101\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1010110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1011000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1011011\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1011100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1011110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1100000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1100010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1100100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1100110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1101000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1101010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1101101\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1101110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1110000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1110010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1110100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1110110\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1111000\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1111010\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1111100\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|1111111\\right\\rangle$$0.1250 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
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Evaluate the code using resource estimation" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "data": { + "application/x-qsharp-data": "\"Connecting to Azure Quantum...\"", + "text/plain": [ + "Connecting to Azure Quantum..." + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Connected to Azure Quantum workspace azure-q in location uksouth.\n" + ] + }, + { + "data": { + "text/plain": [ + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 284985},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 412930},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 2},\n", + " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 257411},\n", + " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 4298},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 137},\n", + " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 257411},\n", + " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 4298},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 137},\n", + " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.qpu.aspen-m-2', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", + "# If you're using this notebook in qBraid, keep it\n", + "qsharp.azure.connect(\n", + " resourceId=\"/subscriptions/7fc54e95-14cf-4a6f-b50e-d6155c241309/resourceGroups/AzureQuantum/providers/Microsoft.Quantum/Workspaces/azure-q\",\n", + " location=\"UK South\",\n", + " credential=\"CLI\")" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loading package Microsoft.Quantum.Providers.Core and dependencies...\n", + "Active target is now microsoft.estimator\n" + ] + }, + { + "data": { + "text/plain": [ + "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qsharp.azure.target(\"microsoft.estimator\")" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Submitting Task5_ResourceEstimationWrapper to target microsoft.estimator...\n", + "Job successfully submitted.\n", + " Job name: RE for the task 5\n", + " Job ID: ce9dd9e8-528c-46ec-94d2-289b8fed02a7\n", + "Waiting up to 30 seconds for Azure Quantum job to complete...\n", + "[11:30:22 PM] Current job status: Executing\n", + "[11:30:27 PM] Current job status: Succeeded\n" + ] + } + ], + "source": [ + "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", + "result = qsharp.azure.execute(Task5_ResourceEstimationWrapper, jobName=\"RE for the task 5\")" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "data": { + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":8,\"cczCount\":5,\"measurementCount\":8,\"numQubits\":11,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":9,\"logicalCycleTime\":3600.0,\"logicalErrorRate\":3.0000000000000015E-07,\"physicalQubits\":162},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":47,\"algorithmicLogicalQubits\":33,\"cliffordErrorRate\":0.001,\"logicalDepth\":47,\"numTfactories\":15,\"numTfactoryRuns\":4,\"numTsPerRotation\":null,\"numTstates\":52,\"physicalQubitsForAlgorithm\":5346,\"physicalQubitsForTfactories\":97200,\"requiredLogicalQubitErrorRate\":3.2237266279819474E-07,\"requiredLogicalTstateErrorRate\":9.615384615384616E-06},\"physicalQubits\":102546,\"runtime\":169200},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"3us 600ns\",\"logicalErrorRate\":\"3.00e-7\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"94.79 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"3.22e-7\",\"requiredLogicalTstateErrorRate\":\"9.62e-6\",\"runtime\":\"169us 200ns\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 5346 physical qubits to implement the algorithm logic, and 97200 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 47 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 11$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 33$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 8 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 5 CCZ and 8 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 47. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 5 CCZ and 8 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 52 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 15 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{52\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 169us 200ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 52 T states, the 15 copies of the T factory are repeatedly invoked 4 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 5346 are the product of the 33 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 15 in parallel, therefore we need $97200 = 6480 \\\\cdot 15$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 47.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 52.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000032237266279819474)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{9 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 3us 600ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 162.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 9.62e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or ¬µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "text/html": [ + "\r\n", + "
\r\n", + " \r\n", + " Physical resource estimates\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits102546\r\n", + "

Number of physical qubits

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This value represents the total number of physical qubits, which is the sum of 5346 physical qubits to implement the algorithm logic, and 97200 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

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Runtime169us 200ns\r\n", + "

Total runtime

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This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 47 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

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\r\n", + " \r\n", + " Resource estimates breakdown\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Logical algorithmic qubits33\r\n", + "

Number of logical qubits for the algorithm after layout

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Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 11\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 33$ logical qubits.

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Algorithmic depth47\r\n", + "

Number of logical cycles for the algorithm

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To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 8 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 5 CCZ and 8 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

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Logical depth47\r\n", + "

Number of logical cycles performed

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This number is usually equal to the logical depth of the algorithm, which is 47. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

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Number of T states52\r\n", + "

Number of T states consumed by the algorithm

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To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 5 CCZ and 8 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

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Number of T factories15\r\n", + "

Number of T factories capable of producing the demanded 52 T states during the algorithm's runtime

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The total number of T factories 15 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{52\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 169us 200ns\\;\\text{algorithm runtime}}\\right\\rceil\\)

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Number of T factory invocations4\r\n", + "

Number of times all T factories are invoked

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In order to prepare the 52 T states, the 15 copies of the T factory are repeatedly invoked 4 times.

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Physical algorithmic qubits5346\r\n", + "

Number of physical qubits for the algorithm after layout

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The 5346 are the product of the 33 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.

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Physical T factory qubits97200\r\n", + "

Number of physical qubits for the T factories

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Each T factory requires 6480 physical qubits and we run 15 in parallel, therefore we need $97200 = 6480 \\cdot 15$ qubits.

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Required logical qubit error rate3.22e-7\r\n", + "

The minimum logical qubit error rate required to run the algorithm within the error budget

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The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 47.

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Required logical T state error rate9.62e-6\r\n", + "

The minimum T state error rate required for distilled T states

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The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 52.

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Number of T states per rotationNo rotations in algorithm\r\n", + "

Number of T states to implement a rotation with an arbitrary angle

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The number of T states to implement a rotation with an arbitrary angle is \\(\\lceil 0.53 \\log_2(0 / 0) + 5.3\\rceil\\) [arXiv:2203.10064]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.

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\r\n", + " \r\n", + " Logical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
QEC schemesurface_code\r\n", + "

Name of QEC scheme

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You can load pre-defined QEC schemes by using the name surface_code or floquet_code. The latter only works with Majorana qubits.

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Code distance9\r\n", + "

Required code distance for error correction

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The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000032237266279819474)}{\\log(0.01/0.001)} - 1\\)

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Physical qubits162\r\n", + "

Number of physical qubits per logical qubit

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The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.

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Logical cycle time3us 600ns\r\n", + "

Duration of a logical cycle in nanoseconds

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The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.

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Logical qubit error rate3.00e-7\r\n", + "

Logical qubit error rate

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The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{9 + 1}{2}$

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Crossing prefactor0.03\r\n", + "

Crossing prefactor used in QEC scheme

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The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.

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Error correction threshold0.01\r\n", + "

Error correction threshold used in QEC scheme

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The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.

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Logical cycle time formula(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\r\n", + "

QEC scheme formula used to compute logical cycle time

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This is the formula that is used to compute the logical cycle time 3us 600ns.

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Physical qubits formula2 * codeDistance * codeDistance\r\n", + "

QEC scheme formula used to compute number of physical qubits per logical qubit

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This is the formula that is used to compute the number of physical qubits per logical qubits 162.

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Physical qubits6480\r\n", + "

Number of physical qubits for a single T factory

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This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.

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Runtime46us 800ns\r\n", + "

Runtime of a single T factory

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The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.

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Number of output T states per run1\r\n", + "

Number of output T states produced in a single run of T factory

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The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.

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Number of input T states per run30\r\n", + "

Number of physical input T states consumed in a single run of a T factory

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This value includes the physical input T states of all copies of the distillation unit in the first round.

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Distillation rounds1\r\n", + "

The number of distillation rounds

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This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.

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Distillation units per round2\r\n", + "

The number of units in each round of distillation

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This is the number of copies for the distillation units per round.

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Distillation units15-to-1 space efficient logical\r\n", + "

The types of distillation units

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These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.

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Distillation code distances9\r\n", + "

The code distance in each round of distillation

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This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.

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Number of physical qubits per round6480\r\n", + "

The number of physical qubits used in each round of distillation

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The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.

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Runtime per round46us 800ns\r\n", + "

The runtime of each distillation round

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The runtime of the T factory is the sum of the runtimes in all rounds.

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Logical T state error rate2.17e-6\r\n", + "

Logical T state error rate

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This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 9.62e-6.

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Logical qubits (pre-layout)11\r\n", + "

Number of logical qubits in the input quantum program

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We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

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T gates0\r\n", + "

Number of T gates in the input quantum program

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This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.

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Rotation gates0\r\n", + "

Number of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.

\n", + "\r\n", + "
Rotation depth0\r\n", + "

Depth of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.

\n", + "\r\n", + "
CCZ gates5\r\n", + "

Number of CCZ-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCZ gates.

\n", + "\r\n", + "
CCiX gates8\r\n", + "

Number of CCiX-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCiX gates, which applies \\(-iX\\) controlled on two control qubits [1212.5069].

\n", + "\r\n", + "
Measurement operations8\r\n", + "

Number of single qubit measurements in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Assumed error budget\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Total error budget1.00e-3\r\n", + "

Total error budget for the algorithm

\n", + "\r\n", + "
\r\n", + "

The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget \\(\\epsilon = \\epsilon_{\\log} + \\epsilon_{\\rm dis} + \\epsilon_{\\rm syn}\\) is uniformly distributed and applies to errors \\(\\epsilon_{\\log}\\) to implement logical qubits, an error budget \\(\\epsilon_{\\rm dis}\\) to produce T states through distillation, and an error budget \\(\\epsilon_{\\rm syn}\\) to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets \\(\\epsilon_{\\rm dis}\\) and \\(\\epsilon_{\\rm syn}\\) are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.

\n", + "\r\n", + "
Logical error probability5.00e-4\r\n", + "

Probability of at least one logical error

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
T distillation error probability5.00e-4\r\n", + "

Probability of at least one faulty T distillation

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
Rotation synthesis error probability0.00e0\r\n", + "

Probability of at least one failed rotation synthesis

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Physical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Qubit namequbit_gate_ns_e3\r\n", + "

Some descriptive name for the qubit model

\n", + "\r\n", + "
\r\n", + "

You can load pre-defined qubit parameters by using the names qubit_gate_ns_e3, qubit_gate_ns_e4, qubit_gate_us_e3, qubit_gate_us_e4, qubit_maj_ns_e4, or qubit_maj_ns_e6. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).

\n", + "\r\n", + "
Instruction setGateBased\r\n", + "

Underlying qubit technology (gate-based or Majorana)

\n", + "\r\n", + "
\r\n", + "

When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either gate-based or Majorana. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.

\n", + "\r\n", + "
Single-qubit measurement time100 ns\r\n", + "

Operation time for single-qubit measurement (t_meas) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.

\n", + "\r\n", + "
Single-qubit gate time50 ns\r\n", + "

Operation time for single-qubit gate (t_gate) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.

\n", + "\r\n", + "
Two-qubit gate time50 ns\r\n", + "

Operation time for two-qubit gate in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.

\n", + "\r\n", + "
T gate time50 ns\r\n", + "

Operation time for a T gate

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to execute a T gate.

\n", + "\r\n", + "
Single-qubit measurement error rate0.001\r\n", + "

Error rate for single-qubit measurement

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit measurement in the Pauli basis may fail.

\n", + "\r\n", + "
Single-qubit error rate0.001\r\n", + "

Error rate for single-qubit Clifford gate (p)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.

\n", + "\r\n", + "
Two-qubit error rate0.001\r\n", + "

Error rate for two-qubit Clifford gate

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.

\n", + "\r\n", + "
T gate error rate0.001\r\n", + "

Error rate to prepare single-qubit T state or apply a T gate (p_T)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which executing a single T gate may fail.

\n", + "\r\n", + "
\n", + "
\r\n", + " Assumptions\r\n", + "
    \n", + "

  • More details on the following lists of assumptions can be found in the paper Accessing requirements for scaling quantum computers and their applications.

    \n", + "
    • \n", + "

  • Uniform independent physical noise. We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.

    \n", + "
    • \n", + "

  • Efficient classical computation. We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.

    \n", + "
    • \n", + "

  • Extraction circuits for planar quantum ISA. We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).

    \n", + "
    • \n", + "

  • Uniform independent logical noise. We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.

    \n", + "
    • \n", + "

  • Negligible Clifford costs for synthesis. We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.

    \n", + "
    • \n", + "

  • Smooth magic state consumption rate. We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.

    \n", + "
    • \n", + "
\n" + ], + "text/plain": [ + "{'errorBudget': {'logical': 0.0005, 'rotations': 0.0, 'tstates': 0.0005},\n", + " 'jobParams': {'errorBudget': 0.001,\n", + " 'qecScheme': {'crossingPrefactor': 0.03,\n", + " 'errorCorrectionThreshold': 0.01,\n", + " 'logicalCycleTime': '(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance',\n", + " 'name': 'surface_code',\n", + " 'physicalQubitsPerLogicalQubit': '2 * codeDistance * codeDistance'},\n", + " 'qubitParams': {'instructionSet': 'GateBased',\n", + " 'name': 'qubit_gate_ns_e3',\n", + " 'oneQubitGateErrorRate': 0.001,\n", + " 'oneQubitGateTime': '50 ns',\n", + " 'oneQubitMeasurementErrorRate': 0.001,\n", + " 'oneQubitMeasurementTime': '100 ns',\n", + " 'tGateErrorRate': 0.001,\n", + " 'tGateTime': '50 ns',\n", + " 'twoQubitGateErrorRate': 0.001,\n", + " 'twoQubitGateTime': '50 ns'}},\n", + " 'logicalCounts': {'ccixCount': 8,\n", + " 'cczCount': 5,\n", + " 'measurementCount': 8,\n", + " 'numQubits': 11,\n", + " 'rotationCount': 0,\n", + " 'rotationDepth': 0,\n", + " 'tCount': 0},\n", + " 'logicalQubit': {'codeDistance': 9,\n", + " 'logicalCycleTime': 3600.0,\n", + " 'logicalErrorRate': 3.0000000000000015e-07,\n", + " 'physicalQubits': 162},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 47,\n", + " 'algorithmicLogicalQubits': 33,\n", + " 'cliffordErrorRate': 0.001,\n", + " 'logicalDepth': 47,\n", + " 'numTfactories': 15,\n", + " 'numTfactoryRuns': 4,\n", + " 'numTsPerRotation': None,\n", + " 'numTstates': 52,\n", + " 'physicalQubitsForAlgorithm': 5346,\n", + " 'physicalQubitsForTfactories': 97200,\n", + " 'requiredLogicalQubitErrorRate': 3.2237266279819474e-07,\n", + " 'requiredLogicalTstateErrorRate': 9.615384615384616e-06},\n", + " 'physicalQubits': 102546,\n", + " 'runtime': 169200},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", + " 'errorBudget': '1.00e-3',\n", + " 'errorBudgetLogical': '5.00e-4',\n", + " 'errorBudgetRotations': '0.00e0',\n", + " 'errorBudgetTstates': '5.00e-4',\n", + " 'logicalCycleTime': '3us 600ns',\n", + " 'logicalErrorRate': '3.00e-7',\n", + " 'numTsPerRotation': 'No rotations in algorithm',\n", + " 'numUnitsPerRound': '2',\n", + " 'physicalQubitsForTfactoriesPercentage': '94.79 %',\n", + " 'physicalQubitsPerRound': '6480',\n", + " 'requiredLogicalQubitErrorRate': '3.22e-7',\n", + " 'requiredLogicalTstateErrorRate': '9.62e-6',\n", + " 'runtime': '169us 200ns',\n", + " 'tfactoryRuntime': '46us 800ns',\n", + " 'tfactoryRuntimePerRound': '46us 800ns',\n", + " 'tstateLogicalErrorRate': '2.17e-6',\n", + " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", + " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", + " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", + " '**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.',\n", + " '**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).',\n", + " '**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.',\n", + " '**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.',\n", + " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", + " 'groups': [{'alwaysVisible': True,\n", + " 'entries': [{'description': 'Number of physical qubits',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 5346 physical qubits to implement the algorithm logic, and 97200 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'physicalCounts/physicalQubits'},\n", + " {'description': 'Total runtime',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 47 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/runtime'}],\n", + " 'title': 'Physical resource estimates'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 11$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 33$ logical qubits.',\n", + " 'label': 'Logical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", + " {'description': 'Number of logical cycles for the algorithm',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 8 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 5 CCZ and 8 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'label': 'Algorithmic depth',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", + " {'description': 'Number of logical cycles performed',\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 47. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'label': 'Logical depth',\n", + " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", + " {'description': 'Number of T states consumed by the algorithm',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 5 CCZ and 8 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'label': 'Number of T states',\n", + " 'path': 'physicalCounts/breakdown/numTstates'},\n", + " {'description': \"Number of T factories capable of producing the demanded 52 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 15 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{52\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 169us 200ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " 'label': 'Number of T factories',\n", + " 'path': 'physicalCounts/breakdown/numTfactories'},\n", + " {'description': 'Number of times all T factories are invoked',\n", + " 'explanation': 'In order to prepare the 52 T states, the 15 copies of the T factory are repeatedly invoked 4 times.',\n", + " 'label': 'Number of T factory invocations',\n", + " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", + " {'description': 'Number of physical qubits for the algorithm after layout',\n", + " 'explanation': 'The 5346 are the product of the 33 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.',\n", + " 'label': 'Physical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", + " {'description': 'Number of physical qubits for the T factories',\n", + " 'explanation': 'Each T factory requires 6480 physical qubits and we run 15 in parallel, therefore we need $97200 = 6480 \\\\cdot 15$ qubits.',\n", + " 'label': 'Physical T factory qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", + " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 33 logical qubits and the total cycle count 47.',\n", + " 'label': 'Required logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", + " {'description': 'The minimum T state error rate required for distilled T states',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 52.',\n", + " 'label': 'Required logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", + " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", + " 'explanation': 'The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.',\n", + " 'label': 'Number of T states per rotation',\n", + " 'path': 'physicalCountsFormatted/numTsPerRotation'}],\n", + " 'title': 'Resource estimates breakdown'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Name of QEC scheme',\n", + " 'explanation': 'You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.',\n", + " 'label': 'QEC scheme',\n", + " 'path': 'jobParams/qecScheme/name'},\n", + " {'description': 'Required code distance for error correction',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000032237266279819474)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'label': 'Code distance',\n", + " 'path': 'logicalQubit/codeDistance'},\n", + " {'description': 'Number of physical qubits per logical qubit',\n", + " 'explanation': 'The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'logicalQubit/physicalQubits'},\n", + " {'description': 'Duration of a logical cycle in nanoseconds',\n", + " 'explanation': 'The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.',\n", + " 'label': 'Logical cycle time',\n", + " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", + " {'description': 'Logical qubit error rate',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{9 + 1}{2}$',\n", + " 'label': 'Logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", + " {'description': 'Crossing prefactor used in QEC scheme',\n", + " 'explanation': 'The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.',\n", + " 'label': 'Crossing prefactor',\n", + " 'path': 'jobParams/qecScheme/crossingPrefactor'},\n", + " {'description': 'Error correction threshold used in QEC scheme',\n", + " 'explanation': 'The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.',\n", + " 'label': 'Error correction threshold',\n", + " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", + " {'description': 'QEC scheme formula used to compute logical cycle time',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 3us 600ns.',\n", + " 'label': 'Logical cycle time formula',\n", + " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", + " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 162.',\n", + " 'label': 'Physical qubits formula',\n", + " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", + " 'title': 'Logical qubit parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of physical qubits for a single T factory',\n", + " 'explanation': 'This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'tfactory/physicalQubits'},\n", + " {'description': 'Runtime of a single T factory',\n", + " 'explanation': 'The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", + " {'description': 'Number of output T states produced in a single run of T factory',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.',\n", + " 'label': 'Number of output T states per run',\n", + " 'path': 'tfactory/numTstates'},\n", + " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", + " 'explanation': 'This value includes the physical input T states of all copies of the distillation unit in the first round.',\n", + " 'label': 'Number of input T states per run',\n", + " 'path': 'tfactory/numInputTstates'},\n", + " {'description': 'The number of distillation rounds',\n", + " 'explanation': 'This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.',\n", + " 'label': 'Distillation rounds',\n", + " 'path': 'tfactory/numRounds'},\n", + " {'description': 'The number of units in each round of distillation',\n", + " 'explanation': 'This is the number of copies for the distillation units per round.',\n", + " 'label': 'Distillation units per round',\n", + " 'path': 'physicalCountsFormatted/numUnitsPerRound'},\n", + " {'description': 'The types of distillation units',\n", + " 'explanation': 'These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.',\n", + " 'label': 'Distillation units',\n", + " 'path': 'physicalCountsFormatted/unitNamePerRound'},\n", + " {'description': 'The code distance in each round of distillation',\n", + " 'explanation': 'This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.',\n", + " 'label': 'Distillation code distances',\n", + " 'path': 'physicalCountsFormatted/codeDistancePerRound'},\n", + " {'description': 'The number of physical qubits used in each round of distillation',\n", + " 'explanation': 'The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.',\n", + " 'label': 'Number of physical qubits per round',\n", + " 'path': 'physicalCountsFormatted/physicalQubitsPerRound'},\n", + " {'description': 'The runtime of each distillation round',\n", + " 'explanation': 'The runtime of the T factory is the sum of the runtimes in all rounds.',\n", + " 'label': 'Runtime per round',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", + " {'description': 'Logical T state error rate',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 9.62e-6.',\n", + " 'label': 'Logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", + " 'title': 'T factory parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", + " 'explanation': 'We determine 33 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'label': 'Logical qubits (pre-layout)',\n", + " 'path': 'logicalCounts/numQubits'},\n", + " {'description': 'Number of T gates in the input quantum program',\n", + " 'explanation': 'This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.',\n", + " 'label': 'T gates',\n", + " 'path': 'logicalCounts/tCount'},\n", + " {'description': 'Number of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.',\n", + " 'label': 'Rotation gates',\n", + " 'path': 'logicalCounts/rotationCount'},\n", + " {'description': 'Depth of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.',\n", + " 'label': 'Rotation depth',\n", + " 'path': 'logicalCounts/rotationDepth'},\n", + " {'description': 'Number of CCZ-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCZ gates.',\n", + " 'label': 'CCZ gates',\n", + " 'path': 'logicalCounts/cczCount'},\n", + " {'description': 'Number of CCiX-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].',\n", + " 'label': 'CCiX gates',\n", + " 'path': 'logicalCounts/ccixCount'},\n", + " {'description': 'Number of single qubit measurements in the input quantum program',\n", + " 'explanation': 'This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.',\n", + " 'label': 'Measurement operations',\n", + " 'path': 'logicalCounts/measurementCount'}],\n", + " 'title': 'Pre-layout logical resources'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Total error budget for the algorithm',\n", + " 'explanation': \"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\n", + " 'label': 'Total error budget',\n", + " 'path': 'physicalCountsFormatted/errorBudget'},\n", + " {'description': 'Probability of at least one logical error',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'Logical error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetLogical'},\n", + " {'description': 'Probability of at least one faulty T distillation',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'T distillation error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetTstates'},\n", + " {'description': 'Probability of at least one failed rotation synthesis',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3.',\n", + " 'label': 'Rotation synthesis error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetRotations'}],\n", + " 'title': 'Assumed error budget'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Some descriptive name for the qubit model',\n", + " 'explanation': 'You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).',\n", + " 'label': 'Qubit name',\n", + " 'path': 'jobParams/qubitParams/name'},\n", + " {'description': 'Underlying qubit technology (gate-based or Majorana)',\n", + " 'explanation': 'When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.',\n", + " 'label': 'Instruction set',\n", + " 'path': 'jobParams/qubitParams/instructionSet'},\n", + " {'description': 'Operation time for single-qubit measurement (t_meas) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.',\n", + " 'label': 'Single-qubit measurement time',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementTime'},\n", + " {'description': 'Operation time for single-qubit gate (t_gate) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.',\n", + " 'label': 'Single-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateTime'},\n", + " {'description': 'Operation time for two-qubit gate in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.',\n", + " 'label': 'Two-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateTime'},\n", + " {'description': 'Operation time for a T gate',\n", + " 'explanation': 'This is the operation time in nanoseconds to execute a T gate.',\n", + " 'label': 'T gate time',\n", + " 'path': 'jobParams/qubitParams/tGateTime'},\n", + " {'description': 'Error rate for single-qubit measurement',\n", + " 'explanation': 'This is the probability in which a single-qubit measurement in the Pauli basis may fail.',\n", + " 'label': 'Single-qubit measurement error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementErrorRate'},\n", + " {'description': 'Error rate for single-qubit Clifford gate (p)',\n", + " 'explanation': 'This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.',\n", + " 'label': 'Single-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateErrorRate'},\n", + " {'description': 'Error rate for two-qubit Clifford gate',\n", + " 'explanation': 'This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.',\n", + " 'label': 'Two-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateErrorRate'},\n", + " {'description': 'Error rate to prepare single-qubit T state or apply a T gate (p_T)',\n", + " 'explanation': 'This is the probability in which executing a single T gate may fail.',\n", + " 'label': 'T gate error rate',\n", + " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", + " 'title': 'Physical qubit parameters'}]},\n", + " 'status': 'success',\n", + " 'tfactory': {'codeDistancePerRound': [9],\n", + " 'logicalErrorRate': 2.165000000000001e-06,\n", + " 'numInputTstates': 30,\n", + " 'numRounds': 1,\n", + " 'numTstates': 1,\n", + " 'numUnitsPerRound': [2],\n", + " 'physicalQubits': 6480,\n", + " 'physicalQubitsPerRound': [6480],\n", + " 'runtime': 46800.0,\n", + " 'runtimePerRound': [46800.0],\n", + " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", + "# result = qsharp.azure.output(\"...\")\n", + "result" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# The function that extracts the relevant resource information from the resource estimation job results and produces your absolute score.\n", + "def evaluate_results(res) : \n", + " width = res['physicalCounts']['breakdown']['algorithmicLogicalQubits']\n", + " depth = res['physicalCounts']['breakdown']['algorithmicLogicalDepth']\n", + " print(f\"Logical algorithmic qubits = {width}\")\n", + " print(f\"Algorithmic depth = {depth}\")\n", + " print(f\"Score = {width * depth}\")\n", + " return width * depth\n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Logical algorithmic qubits = 33\n", + "Algorithmic depth = 47\n", + "Score = 1551\n" + ] + }, + { + "data": { + "text/plain": [ + "1551" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "evaluate_results(result)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernel_info": { + "name": "python3" + }, + "kernelspec": { + "display_name": "Python 3 [Q#]", + "language": "python", + "name": "python3_qsharp_b54crn" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.10" + }, + "nteract": { + "version": "nteract-front-end@1.0.0" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/team_solutions/schrodingers-duck/.ipynb_checkpoints/iQuHack-challenge-2023-task6-checkpoint.ipynb b/team_solutions/schrodingers-duck/.ipynb_checkpoints/iQuHack-challenge-2023-task6-checkpoint.ipynb new file mode 100644 index 0000000..f811e97 --- /dev/null +++ b/team_solutions/schrodingers-duck/.ipynb_checkpoints/iQuHack-challenge-2023-task6-checkpoint.ipynb @@ -0,0 +1,8327 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "# MIT iQuHack Microsoft Challenge: Optimizing Quantum Oracles, Task 6\n", + "\n", + "To work on this task,\n", + "1. Use the notebook for this task. Each of the notebooks in the repository has the code of the corresponding task.\n", + "2. Update your team name and Slack ID variables in the next code cell (you can use different Slack IDs for different tasks if different team members work on them, but make sure to use the same team name throughout the Hackathon). Do not change the task variable!\n", + "3. Work on your task in the cell that contains operation `Task6`! Your goal is to rewrite the code so that it maintains its correctness, but requires as few resources as possible. See `evaluate_results` function for details on how your absolute score for the task is calculated.\n", + "4. Submit your task using qBraid. Use the Share Notebook feature on qBraid (See File > Share Notebook) and enter the email rickyyoung@qbraid.com. Once you click submit, if the share notebook feature works correctly, it should show that you receive no errors and the email you entered will disappear. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "Log in to Azure (once per session, don't need to do it if running from Azure workspace)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "!az login" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 1. Write the code" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Preparing Q# environment...\n" + ] + } + ], + "source": [ + "# Run this code cell to import the modules required to work with Q# and Azure\n", + "import qsharp\n", + "from qsharp import azure" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "teamname=\"schrodingers-duck\" # Update this field with your team name\n", + "task=[\"task6\"]\n", + "slack_id=\"U04L3SFUCQ2\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# You don't need to run this cell, it defines Q# operations as Python types to keep IntelliSense happy\n", + "Task6_DumpMachineWrapper : qsharp.QSharpCallable = None\n", + "Task6_ResourceEstimationWrapper : qsharp.QSharpCallable = None" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "**The complete code for Task 6 should be in this cell.** \n", + "This cell can include additional open statements and helper operations and functions if your solution needs them. \n", + "If you define helper operations in other cells, they will not be picked up by the grader!" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "open Microsoft.Quantum.Canon;\n", + "open Microsoft.Quantum.Diagnostics;\n", + "open Microsoft.Quantum.Arrays;\n", + "\n", + "// Task 6. \n", + "// (input will contain 8 qubits)\n", + "operation original(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " for i in [144, 145, 148, 149, 152, 153, 156, 157, 208, 209, 212, 213, 216, 217, 220, 221] {\n", + " ControlledOnInt(i, X)(input, target);\n", + " }\n", + "}\n", + "\n", + "operation Task6(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " for i in [20,22] {\n", + " ControlledOnInt(i, X)([input[1],input[2],input[4], input[5], input[7]], target);\n", + " }\n", + "}\n", + "\n", + "operation QubitArrayWrapperOperation (op : ((Qubit[], Qubit) => Unit is Adj), qs : Qubit[]) : Unit is Adj { \n", + " op(Most(qs), Tail(qs));\n", + "}\n", + "\n", + "operation TestCompoundGate () : Unit {\n", + " AssertOperationsEqualReferenced(8+1, QubitArrayWrapperOperation(Task6, _), QubitArrayWrapperOperation (original, _));\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "TestCompoundGate();" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "// Wrapper operation that allows you to observe the effects of the marking oracle by running it on a simulator.\n", + "operation Task6_DumpMachineWrapper() : Unit {\n", + " let N = 8;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " // Prepare an equal superposition of all input states in the input register.\n", + " ApplyToEach(H, input);\n", + " // Apply the oracle.\n", + " Task6(input, target);\n", + " // Print the state of the system after the oracle application.\n", + " DumpMachine();\n", + " ResetAll(input + [target]);\n", + "}\n", + "\n", + "// Wrapper operation that allows to run resource estimation for the task.\n", + "// This operation only allocates the qubits and applies the oracle once, not using any additional gates or measurements.\n", + "operation Task6_ResourceEstimationWrapper() : Unit {\n", + " let N = 8;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " Task6(input, target);\n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 2. Run the code on a simulator to see what it does\n", + "You can also write your own code to explore the effects of the oracle (for example, applying it to different basis states and measuring the results)." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "data": { + "application/x-qsharp-data": 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Qubit IDs0, 1, 2, 3, 4, 5, 6, 7, 8
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$\\left|001000110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001001000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001001010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001001100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001001110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001010000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001010010100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001010100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001010110100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001011000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001011010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001011100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001011110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001100000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001100010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001100100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001100110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001101000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001101010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001101100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001101110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001110000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001110010100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001110100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001110110100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001111000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001111010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001111100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|001111110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010000010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010000100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010000110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010001000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010001010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010001100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010001110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010010000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|010010010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010010100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010010110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010011000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010011010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010011100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010011110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010100000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010100010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010100100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010100110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010101000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010101010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|010101100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|010101110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|010110000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|010110010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010110100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010110110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010111000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|010111010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|010111100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|010111110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011000010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011000100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011000110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011001000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|011001010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011001100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011001110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011010000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011010010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011010100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011010110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011011000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011011010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011011100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011011110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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$\\left|011101010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|011101110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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\r\n", + "
$\\left|011110010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|011110110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
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\r\n", + "
$\\left|011111010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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\r\n", + "
$\\left|011111110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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\r\n", + "
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\r\n", + "

\r\n", + "
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\r\n", + "

\r\n", + "
$\\left|100000110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
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\r\n", + "

\r\n", + "
$\\left|100001010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|100001100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
$\\left|100001110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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\r\n", + "
$\\left|100010010100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

\r\n", + "
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\r\n", + "
$\\left|100010110100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|100011000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100011010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100011100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100011110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100100000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100100010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100100100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100100110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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\r\n", + "
$\\left|100101010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100101100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100101110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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\r\n", + "
$\\left|100110010100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100110100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100110110100000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100111000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|100111010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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\r\n", + "
$\\left|100111110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
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\r\n", + "
$\\left|101000010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|101000100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|101000110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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\r\n", + "
$\\left|101001000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101011000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101011100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101011110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101100000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101111000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101111010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|101111100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110000010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110000100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110010000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110010010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110010100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110010110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110011000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110011010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110011100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110011110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110100000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110100010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110100100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110100110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110101000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110101010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

\r\n", + "

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$\\left|110101100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110101110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110110000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110110010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110110100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110110110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110111000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110111010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110111100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|110111110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111000010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111000100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111000110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111001000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111001010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111001100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111001110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111010010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111010110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111011000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111011010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111011100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111011110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111100010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111100110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111101000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111101010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111101110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111110000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111110010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111110100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111110110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111111000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111111010000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111111100\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|111111110000000000\\right\\rangle$$0.0625 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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"output_type": "execute_result" + } + ], + "source": [ + "# Note that in the output of this cell the target qubit corresponds to the rightmost bit\n", + "qsharp.config[\"dump.basisStateLabelingConvention\"]=\"Bitstring\"\n", + "qsharp.config[\"dump.phaseDisplayStyle\"]=\"None\"\n", + "# Uncomment the following line if you want to see only the entries with non-zero amplitudes\n", + "qsharp.config[\"dump.truncateSmallAmplitudes\"]=True\n", + "Task6_DumpMachineWrapper.simulate()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 3. Evaluate the code using resource estimation" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "data": { + "application/x-qsharp-data": "\"Connecting to Azure Quantum...\"", + "text/plain": [ + "Connecting to Azure Quantum..." + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Connected to Azure Quantum workspace azure-q in location uksouth.\n" + ] + }, + { + "data": { + "text/plain": [ + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 180106},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 429377},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 2},\n", + " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 445},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 163},\n", + " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 445},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 163},\n", + " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.qpu.aspen-m-2', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", + "# If you're using this notebook in qBraid, keep it\n", + "qsharp.azure.connect(\n", + " resourceId=\"/subscriptions/7fc54e95-14cf-4a6f-b50e-d6155c241309/resourceGroups/AzureQuantum/providers/Microsoft.Quantum/Workspaces/azure-q\",\n", + " location=\"UK South\",\n", + " credential=\"CLI\")" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loading package Microsoft.Quantum.Providers.Core and dependencies...\n", + "Active target is now microsoft.estimator\n" + ] + }, + { + "data": { + "text/plain": [ + "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qsharp.azure.target(\"microsoft.estimator\")" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Submitting Task6_ResourceEstimationWrapper to target microsoft.estimator...\n", + "Job successfully submitted.\n", + " Job name: RE for the task 6\n", + " Job ID: 9acb26ad-ff11-4b7d-8502-bc6a6f2ca438\n", + "Waiting up to 30 seconds for Azure Quantum job to complete...\n", + "[2:12:45 PM] Current job status: Executing\n", + "[2:12:50 PM] Current job status: Succeeded\n" + ] + } + ], + "source": [ + "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", + "result = qsharp.azure.execute(Task6_ResourceEstimationWrapper, jobName=\"RE for the task 6\")" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "data": { + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":6,\"cczCount\":2,\"measurementCount\":6,\"numQubits\":12,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":9,\"logicalCycleTime\":3600.0,\"logicalErrorRate\":3.0000000000000015E-07,\"physicalQubits\":162},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":30,\"algorithmicLogicalQubits\":35,\"cliffordErrorRate\":0.001,\"logicalDepth\":30,\"numTfactories\":14,\"numTfactoryRuns\":3,\"numTsPerRotation\":null,\"numTstates\":32,\"physicalQubitsForAlgorithm\":5670,\"physicalQubitsForTfactories\":90720,\"requiredLogicalQubitErrorRate\":4.761904761904762E-07,\"requiredLogicalTstateErrorRate\":1.5625E-05},\"physicalQubits\":96390,\"runtime\":108000},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"3us 600ns\",\"logicalErrorRate\":\"3.00e-7\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"94.12 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"4.76e-7\",\"requiredLogicalTstateErrorRate\":\"1.56e-5\",\"runtime\":\"108us\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 5670 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 30 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 12$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 35$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 6 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 2 CCZ and 6 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 30. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 2 CCZ and 6 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 32 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{32\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 108us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 32 T states, the 14 copies of the T factory are repeatedly invoked 3 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 5670 are the product of the 35 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\\\cdot 14$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 35 logical qubits and the total cycle count 30.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 32.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.0000004761904761904762)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{9 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 3us 600ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 162.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.56e-5.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 35 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or ¬µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "text/html": [ + "\r\n", + "
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Physical qubits96390\r\n", + "

Number of physical qubits

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This value represents the total number of physical qubits, which is the sum of 5670 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

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Runtime108us\r\n", + "

Total runtime

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This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 30 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

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Logical algorithmic qubits35\r\n", + "

Number of logical qubits for the algorithm after layout

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Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 12\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 35$ logical qubits.

\n", + "\r\n", + "
Algorithmic depth30\r\n", + "

Number of logical cycles for the algorithm

\n", + "\r\n", + "
\r\n", + "

To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 6 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 2 CCZ and 6 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

\n", + "\r\n", + "
Logical depth30\r\n", + "

Number of logical cycles performed

\n", + "\r\n", + "
\r\n", + "

This number is usually equal to the logical depth of the algorithm, which is 30. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", + "\r\n", + "
Number of T states32\r\n", + "

Number of T states consumed by the algorithm

\n", + "\r\n", + "
\r\n", + "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 2 CCZ and 6 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", + "\r\n", + "
Number of T factories14\r\n", + "

Number of T factories capable of producing the demanded 32 T states during the algorithm's runtime

\n", + "\r\n", + "
\r\n", + "

The total number of T factories 14 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{32\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 108us\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", + "\r\n", + "
Number of T factory invocations3\r\n", + "

Number of times all T factories are invoked

\n", + "\r\n", + "
\r\n", + "

In order to prepare the 32 T states, the 14 copies of the T factory are repeatedly invoked 3 times.

\n", + "\r\n", + "
Physical algorithmic qubits5670\r\n", + "

Number of physical qubits for the algorithm after layout

\n", + "\r\n", + "
\r\n", + "

The 5670 are the product of the 35 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.

\n", + "\r\n", + "
Physical T factory qubits90720\r\n", + "

Number of physical qubits for the T factories

\n", + "\r\n", + "
\r\n", + "

Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\cdot 14$ qubits.

\n", + "\r\n", + "
Required logical qubit error rate4.76e-7\r\n", + "

The minimum logical qubit error rate required to run the algorithm within the error budget

\n", + "\r\n", + "
\r\n", + "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 35 logical qubits and the total cycle count 30.

\n", + "\r\n", + "
Required logical T state error rate1.56e-5\r\n", + "

The minimum T state error rate required for distilled T states

\n", + "\r\n", + "
\r\n", + "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 32.

\n", + "\r\n", + "
Number of T states per rotationNo rotations in algorithm\r\n", + "

Number of T states to implement a rotation with an arbitrary angle

\n", + "\r\n", + "
\r\n", + "

The number of T states to implement a rotation with an arbitrary angle is \\(\\lceil 0.53 \\log_2(0 / 0) + 5.3\\rceil\\) [arXiv:2203.10064]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Logical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
QEC schemesurface_code\r\n", + "

Name of QEC scheme

\n", + "\r\n", + "
\r\n", + "

You can load pre-defined QEC schemes by using the name surface_code or floquet_code. The latter only works with Majorana qubits.

\n", + "\r\n", + "
Code distance9\r\n", + "

Required code distance for error correction

\n", + "\r\n", + "
\r\n", + "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.0000004761904761904762)}{\\log(0.01/0.001)} - 1\\)

\n", + "\r\n", + "
Physical qubits162\r\n", + "

Number of physical qubits per logical qubit

\n", + "\r\n", + "
\r\n", + "

The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.

\n", + "\r\n", + "
Logical cycle time3us 600ns\r\n", + "

Duration of a logical cycle in nanoseconds

\n", + "\r\n", + "
\r\n", + "

The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.

\n", + "\r\n", + "
Logical qubit error rate3.00e-7\r\n", + "

Logical qubit error rate

\n", + "\r\n", + "
\r\n", + "

The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{9 + 1}{2}$

\n", + "\r\n", + "
Crossing prefactor0.03\r\n", + "

Crossing prefactor used in QEC scheme

\n", + "\r\n", + "
\r\n", + "

The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.

\n", + "\r\n", + "
Error correction threshold0.01\r\n", + "

Error correction threshold used in QEC scheme

\n", + "\r\n", + "
\r\n", + "

The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.

\n", + "\r\n", + "
Logical cycle time formula(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\r\n", + "

QEC scheme formula used to compute logical cycle time

\n", + "\r\n", + "
\r\n", + "

This is the formula that is used to compute the logical cycle time 3us 600ns.

\n", + "\r\n", + "
Physical qubits formula2 * codeDistance * codeDistance\r\n", + "

QEC scheme formula used to compute number of physical qubits per logical qubit

\n", + "\r\n", + "
\r\n", + "

This is the formula that is used to compute the number of physical qubits per logical qubits 162.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " T factory parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits6480\r\n", + "

Number of physical qubits for a single T factory

\n", + "\r\n", + "
\r\n", + "

This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.

\n", + "\r\n", + "
Runtime46us 800ns\r\n", + "

Runtime of a single T factory

\n", + "\r\n", + "
\r\n", + "

The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.

\n", + "\r\n", + "
Number of output T states per run1\r\n", + "

Number of output T states produced in a single run of T factory

\n", + "\r\n", + "
\r\n", + "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.

\n", + "\r\n", + "
Number of input T states per run30\r\n", + "

Number of physical input T states consumed in a single run of a T factory

\n", + "\r\n", + "
\r\n", + "

This value includes the physical input T states of all copies of the distillation unit in the first round.

\n", + "\r\n", + "
Distillation rounds1\r\n", + "

The number of distillation rounds

\n", + "\r\n", + "
\r\n", + "

This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.

\n", + "\r\n", + "
Distillation units per round2\r\n", + "

The number of units in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the number of copies for the distillation units per round.

\n", + "\r\n", + "
Distillation units15-to-1 space efficient logical\r\n", + "

The types of distillation units

\n", + "\r\n", + "
\r\n", + "

These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.

\n", + "\r\n", + "
Distillation code distances9\r\n", + "

The code distance in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.

\n", + "\r\n", + "
Number of physical qubits per round6480\r\n", + "

The number of physical qubits used in each round of distillation

\n", + "\r\n", + "
\r\n", + "

The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.

\n", + "\r\n", + "
Runtime per round46us 800ns\r\n", + "

The runtime of each distillation round

\n", + "\r\n", + "
\r\n", + "

The runtime of the T factory is the sum of the runtimes in all rounds.

\n", + "\r\n", + "
Logical T state error rate2.17e-6\r\n", + "

Logical T state error rate

\n", + "\r\n", + "
\r\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.56e-5.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Pre-layout logical resources\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Logical qubits (pre-layout)12\r\n", + "

Number of logical qubits in the input quantum program

\n", + "\r\n", + "
\r\n", + "

We determine 35 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", + "\r\n", + "
T gates0\r\n", + "

Number of T gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.

\n", + "\r\n", + "
Rotation gates0\r\n", + "

Number of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.

\n", + "\r\n", + "
Rotation depth0\r\n", + "

Depth of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.

\n", + "\r\n", + "
CCZ gates2\r\n", + "

Number of CCZ-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCZ gates.

\n", + "\r\n", + "
CCiX gates6\r\n", + "

Number of CCiX-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCiX gates, which applies \\(-iX\\) controlled on two control qubits [1212.5069].

\n", + "\r\n", + "
Measurement operations6\r\n", + "

Number of single qubit measurements in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Assumed error budget\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Total error budget1.00e-3\r\n", + "

Total error budget for the algorithm

\n", + "\r\n", + "
\r\n", + "

The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget \\(\\epsilon = \\epsilon_{\\log} + \\epsilon_{\\rm dis} + \\epsilon_{\\rm syn}\\) is uniformly distributed and applies to errors \\(\\epsilon_{\\log}\\) to implement logical qubits, an error budget \\(\\epsilon_{\\rm dis}\\) to produce T states through distillation, and an error budget \\(\\epsilon_{\\rm syn}\\) to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets \\(\\epsilon_{\\rm dis}\\) and \\(\\epsilon_{\\rm syn}\\) are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.

\n", + "\r\n", + "
Logical error probability5.00e-4\r\n", + "

Probability of at least one logical error

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
T distillation error probability5.00e-4\r\n", + "

Probability of at least one faulty T distillation

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
Rotation synthesis error probability0.00e0\r\n", + "

Probability of at least one failed rotation synthesis

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Physical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Qubit namequbit_gate_ns_e3\r\n", + "

Some descriptive name for the qubit model

\n", + "\r\n", + "
\r\n", + "

You can load pre-defined qubit parameters by using the names qubit_gate_ns_e3, qubit_gate_ns_e4, qubit_gate_us_e3, qubit_gate_us_e4, qubit_maj_ns_e4, or qubit_maj_ns_e6. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).

\n", + "\r\n", + "
Instruction setGateBased\r\n", + "

Underlying qubit technology (gate-based or Majorana)

\n", + "\r\n", + "
\r\n", + "

When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either gate-based or Majorana. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.

\n", + "\r\n", + "
Single-qubit measurement time100 ns\r\n", + "

Operation time for single-qubit measurement (t_meas) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.

\n", + "\r\n", + "
Single-qubit gate time50 ns\r\n", + "

Operation time for single-qubit gate (t_gate) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.

\n", + "\r\n", + "
Two-qubit gate time50 ns\r\n", + "

Operation time for two-qubit gate in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.

\n", + "\r\n", + "
T gate time50 ns\r\n", + "

Operation time for a T gate

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to execute a T gate.

\n", + "\r\n", + "
Single-qubit measurement error rate0.001\r\n", + "

Error rate for single-qubit measurement

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit measurement in the Pauli basis may fail.

\n", + "\r\n", + "
Single-qubit error rate0.001\r\n", + "

Error rate for single-qubit Clifford gate (p)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.

\n", + "\r\n", + "
Two-qubit error rate0.001\r\n", + "

Error rate for two-qubit Clifford gate

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.

\n", + "\r\n", + "
T gate error rate0.001\r\n", + "

Error rate to prepare single-qubit T state or apply a T gate (p_T)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which executing a single T gate may fail.

\n", + "\r\n", + "
\n", + "
\r\n", + " Assumptions\r\n", + "
    \n", + "

  • More details on the following lists of assumptions can be found in the paper Accessing requirements for scaling quantum computers and their applications.

    \n", + "
    • \n", + "

  • Uniform independent physical noise. We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.

    \n", + "
    • \n", + "

  • Efficient classical computation. We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.

    \n", + "
    • \n", + "

  • Extraction circuits for planar quantum ISA. We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).

    \n", + "
    • \n", + "

  • Uniform independent logical noise. We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.

    \n", + "
    • \n", + "

  • Negligible Clifford costs for synthesis. We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.

    \n", + "
    • \n", + "

  • Smooth magic state consumption rate. We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.

    \n", + "
    • \n", + "
\n" + ], + "text/plain": [ + "{'errorBudget': {'logical': 0.0005, 'rotations': 0.0, 'tstates': 0.0005},\n", + " 'jobParams': {'errorBudget': 0.001,\n", + " 'qecScheme': {'crossingPrefactor': 0.03,\n", + " 'errorCorrectionThreshold': 0.01,\n", + " 'logicalCycleTime': '(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance',\n", + " 'name': 'surface_code',\n", + " 'physicalQubitsPerLogicalQubit': '2 * codeDistance * codeDistance'},\n", + " 'qubitParams': {'instructionSet': 'GateBased',\n", + " 'name': 'qubit_gate_ns_e3',\n", + " 'oneQubitGateErrorRate': 0.001,\n", + " 'oneQubitGateTime': '50 ns',\n", + " 'oneQubitMeasurementErrorRate': 0.001,\n", + " 'oneQubitMeasurementTime': '100 ns',\n", + " 'tGateErrorRate': 0.001,\n", + " 'tGateTime': '50 ns',\n", + " 'twoQubitGateErrorRate': 0.001,\n", + " 'twoQubitGateTime': '50 ns'}},\n", + " 'logicalCounts': {'ccixCount': 6,\n", + " 'cczCount': 2,\n", + " 'measurementCount': 6,\n", + " 'numQubits': 12,\n", + " 'rotationCount': 0,\n", + " 'rotationDepth': 0,\n", + " 'tCount': 0},\n", + " 'logicalQubit': {'codeDistance': 9,\n", + " 'logicalCycleTime': 3600.0,\n", + " 'logicalErrorRate': 3.0000000000000015e-07,\n", + " 'physicalQubits': 162},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 30,\n", + " 'algorithmicLogicalQubits': 35,\n", + " 'cliffordErrorRate': 0.001,\n", + " 'logicalDepth': 30,\n", + " 'numTfactories': 14,\n", + " 'numTfactoryRuns': 3,\n", + " 'numTsPerRotation': None,\n", + " 'numTstates': 32,\n", + " 'physicalQubitsForAlgorithm': 5670,\n", + " 'physicalQubitsForTfactories': 90720,\n", + " 'requiredLogicalQubitErrorRate': 4.761904761904762e-07,\n", + " 'requiredLogicalTstateErrorRate': 1.5625e-05},\n", + " 'physicalQubits': 96390,\n", + " 'runtime': 108000},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", + " 'errorBudget': '1.00e-3',\n", + " 'errorBudgetLogical': '5.00e-4',\n", + " 'errorBudgetRotations': '0.00e0',\n", + " 'errorBudgetTstates': '5.00e-4',\n", + " 'logicalCycleTime': '3us 600ns',\n", + " 'logicalErrorRate': '3.00e-7',\n", + " 'numTsPerRotation': 'No rotations in algorithm',\n", + " 'numUnitsPerRound': '2',\n", + " 'physicalQubitsForTfactoriesPercentage': '94.12 %',\n", + " 'physicalQubitsPerRound': '6480',\n", + " 'requiredLogicalQubitErrorRate': '4.76e-7',\n", + " 'requiredLogicalTstateErrorRate': '1.56e-5',\n", + " 'runtime': '108us',\n", + " 'tfactoryRuntime': '46us 800ns',\n", + " 'tfactoryRuntimePerRound': '46us 800ns',\n", + " 'tstateLogicalErrorRate': '2.17e-6',\n", + " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", + " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", + " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", + " '**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.',\n", + " '**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).',\n", + " '**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.',\n", + " '**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.',\n", + " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", + " 'groups': [{'alwaysVisible': True,\n", + " 'entries': [{'description': 'Number of physical qubits',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 5670 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'physicalCounts/physicalQubits'},\n", + " {'description': 'Total runtime',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 30 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/runtime'}],\n", + " 'title': 'Physical resource estimates'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 12$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 35$ logical qubits.',\n", + " 'label': 'Logical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", + " {'description': 'Number of logical cycles for the algorithm',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 6 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 2 CCZ and 6 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'label': 'Algorithmic depth',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", + " {'description': 'Number of logical cycles performed',\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 30. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'label': 'Logical depth',\n", + " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", + " {'description': 'Number of T states consumed by the algorithm',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 2 CCZ and 6 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'label': 'Number of T states',\n", + " 'path': 'physicalCounts/breakdown/numTstates'},\n", + " {'description': \"Number of T factories capable of producing the demanded 32 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{32\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 108us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " 'label': 'Number of T factories',\n", + " 'path': 'physicalCounts/breakdown/numTfactories'},\n", + " {'description': 'Number of times all T factories are invoked',\n", + " 'explanation': 'In order to prepare the 32 T states, the 14 copies of the T factory are repeatedly invoked 3 times.',\n", + " 'label': 'Number of T factory invocations',\n", + " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", + " {'description': 'Number of physical qubits for the algorithm after layout',\n", + " 'explanation': 'The 5670 are the product of the 35 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.',\n", + " 'label': 'Physical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", + " {'description': 'Number of physical qubits for the T factories',\n", + " 'explanation': 'Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\\\cdot 14$ qubits.',\n", + " 'label': 'Physical T factory qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", + " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 35 logical qubits and the total cycle count 30.',\n", + " 'label': 'Required logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", + " {'description': 'The minimum T state error rate required for distilled T states',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 32.',\n", + " 'label': 'Required logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", + " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", + " 'explanation': 'The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.',\n", + " 'label': 'Number of T states per rotation',\n", + " 'path': 'physicalCountsFormatted/numTsPerRotation'}],\n", + " 'title': 'Resource estimates breakdown'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Name of QEC scheme',\n", + " 'explanation': 'You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.',\n", + " 'label': 'QEC scheme',\n", + " 'path': 'jobParams/qecScheme/name'},\n", + " {'description': 'Required code distance for error correction',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.0000004761904761904762)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'label': 'Code distance',\n", + " 'path': 'logicalQubit/codeDistance'},\n", + " {'description': 'Number of physical qubits per logical qubit',\n", + " 'explanation': 'The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'logicalQubit/physicalQubits'},\n", + " {'description': 'Duration of a logical cycle in nanoseconds',\n", + " 'explanation': 'The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.',\n", + " 'label': 'Logical cycle time',\n", + " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", + " {'description': 'Logical qubit error rate',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{9 + 1}{2}$',\n", + " 'label': 'Logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", + " {'description': 'Crossing prefactor used in QEC scheme',\n", + " 'explanation': 'The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.',\n", + " 'label': 'Crossing prefactor',\n", + " 'path': 'jobParams/qecScheme/crossingPrefactor'},\n", + " {'description': 'Error correction threshold used in QEC scheme',\n", + " 'explanation': 'The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.',\n", + " 'label': 'Error correction threshold',\n", + " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", + " {'description': 'QEC scheme formula used to compute logical cycle time',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 3us 600ns.',\n", + " 'label': 'Logical cycle time formula',\n", + " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", + " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 162.',\n", + " 'label': 'Physical qubits formula',\n", + " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", + " 'title': 'Logical qubit parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of physical qubits for a single T factory',\n", + " 'explanation': 'This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'tfactory/physicalQubits'},\n", + " {'description': 'Runtime of a single T factory',\n", + " 'explanation': 'The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", + " {'description': 'Number of output T states produced in a single run of T factory',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.',\n", + " 'label': 'Number of output T states per run',\n", + " 'path': 'tfactory/numTstates'},\n", + " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", + " 'explanation': 'This value includes the physical input T states of all copies of the distillation unit in the first round.',\n", + " 'label': 'Number of input T states per run',\n", + " 'path': 'tfactory/numInputTstates'},\n", + " {'description': 'The number of distillation rounds',\n", + " 'explanation': 'This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.',\n", + " 'label': 'Distillation rounds',\n", + " 'path': 'tfactory/numRounds'},\n", + " {'description': 'The number of units in each round of distillation',\n", + " 'explanation': 'This is the number of copies for the distillation units per round.',\n", + " 'label': 'Distillation units per round',\n", + " 'path': 'physicalCountsFormatted/numUnitsPerRound'},\n", + " {'description': 'The types of distillation units',\n", + " 'explanation': 'These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.',\n", + " 'label': 'Distillation units',\n", + " 'path': 'physicalCountsFormatted/unitNamePerRound'},\n", + " {'description': 'The code distance in each round of distillation',\n", + " 'explanation': 'This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.',\n", + " 'label': 'Distillation code distances',\n", + " 'path': 'physicalCountsFormatted/codeDistancePerRound'},\n", + " {'description': 'The number of physical qubits used in each round of distillation',\n", + " 'explanation': 'The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.',\n", + " 'label': 'Number of physical qubits per round',\n", + " 'path': 'physicalCountsFormatted/physicalQubitsPerRound'},\n", + " {'description': 'The runtime of each distillation round',\n", + " 'explanation': 'The runtime of the T factory is the sum of the runtimes in all rounds.',\n", + " 'label': 'Runtime per round',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", + " {'description': 'Logical T state error rate',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.56e-5.',\n", + " 'label': 'Logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", + " 'title': 'T factory parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", + " 'explanation': 'We determine 35 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'label': 'Logical qubits (pre-layout)',\n", + " 'path': 'logicalCounts/numQubits'},\n", + " {'description': 'Number of T gates in the input quantum program',\n", + " 'explanation': 'This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.',\n", + " 'label': 'T gates',\n", + " 'path': 'logicalCounts/tCount'},\n", + " {'description': 'Number of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.',\n", + " 'label': 'Rotation gates',\n", + " 'path': 'logicalCounts/rotationCount'},\n", + " {'description': 'Depth of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.',\n", + " 'label': 'Rotation depth',\n", + " 'path': 'logicalCounts/rotationDepth'},\n", + " {'description': 'Number of CCZ-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCZ gates.',\n", + " 'label': 'CCZ gates',\n", + " 'path': 'logicalCounts/cczCount'},\n", + " {'description': 'Number of CCiX-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].',\n", + " 'label': 'CCiX gates',\n", + " 'path': 'logicalCounts/ccixCount'},\n", + " {'description': 'Number of single qubit measurements in the input quantum program',\n", + " 'explanation': 'This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.',\n", + " 'label': 'Measurement operations',\n", + " 'path': 'logicalCounts/measurementCount'}],\n", + " 'title': 'Pre-layout logical resources'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Total error budget for the algorithm',\n", + " 'explanation': \"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\n", + " 'label': 'Total error budget',\n", + " 'path': 'physicalCountsFormatted/errorBudget'},\n", + " {'description': 'Probability of at least one logical error',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'Logical error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetLogical'},\n", + " {'description': 'Probability of at least one faulty T distillation',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'T distillation error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetTstates'},\n", + " {'description': 'Probability of at least one failed rotation synthesis',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3.',\n", + " 'label': 'Rotation synthesis error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetRotations'}],\n", + " 'title': 'Assumed error budget'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Some descriptive name for the qubit model',\n", + " 'explanation': 'You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).',\n", + " 'label': 'Qubit name',\n", + " 'path': 'jobParams/qubitParams/name'},\n", + " {'description': 'Underlying qubit technology (gate-based or Majorana)',\n", + " 'explanation': 'When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.',\n", + " 'label': 'Instruction set',\n", + " 'path': 'jobParams/qubitParams/instructionSet'},\n", + " {'description': 'Operation time for single-qubit measurement (t_meas) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.',\n", + " 'label': 'Single-qubit measurement time',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementTime'},\n", + " {'description': 'Operation time for single-qubit gate (t_gate) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.',\n", + " 'label': 'Single-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateTime'},\n", + " {'description': 'Operation time for two-qubit gate in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.',\n", + " 'label': 'Two-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateTime'},\n", + " {'description': 'Operation time for a T gate',\n", + " 'explanation': 'This is the operation time in nanoseconds to execute a T gate.',\n", + " 'label': 'T gate time',\n", + " 'path': 'jobParams/qubitParams/tGateTime'},\n", + " {'description': 'Error rate for single-qubit measurement',\n", + " 'explanation': 'This is the probability in which a single-qubit measurement in the Pauli basis may fail.',\n", + " 'label': 'Single-qubit measurement error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementErrorRate'},\n", + " {'description': 'Error rate for single-qubit Clifford gate (p)',\n", + " 'explanation': 'This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.',\n", + " 'label': 'Single-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateErrorRate'},\n", + " {'description': 'Error rate for two-qubit Clifford gate',\n", + " 'explanation': 'This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.',\n", + " 'label': 'Two-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateErrorRate'},\n", + " {'description': 'Error rate to prepare single-qubit T state or apply a T gate (p_T)',\n", + " 'explanation': 'This is the probability in which executing a single T gate may fail.',\n", + " 'label': 'T gate error rate',\n", + " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", + " 'title': 'Physical qubit parameters'}]},\n", + " 'status': 'success',\n", + " 'tfactory': {'codeDistancePerRound': [9],\n", + " 'logicalErrorRate': 2.165000000000001e-06,\n", + " 'numInputTstates': 30,\n", + " 'numRounds': 1,\n", + " 'numTstates': 1,\n", + " 'numUnitsPerRound': [2],\n", + " 'physicalQubits': 6480,\n", + " 'physicalQubitsPerRound': [6480],\n", + " 'runtime': 46800.0,\n", + " 'runtimePerRound': [46800.0],\n", + " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", + "# result = qsharp.azure.output(\"...\")\n", + "result" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# The function that extracts the relevant resource information from the resource estimation job results and produces your absolute score.\n", + "def evaluate_results(res) : \n", + " width = res['physicalCounts']['breakdown']['algorithmicLogicalQubits']\n", + " depth = res['physicalCounts']['breakdown']['algorithmicLogicalDepth']\n", + " print(f\"Logical algorithmic qubits = {width}\")\n", + " print(f\"Algorithmic depth = {depth}\")\n", + " print(f\"Score = {width * depth}\")\n", + " return width * depth\n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Logical algorithmic qubits = 35\n", + "Algorithmic depth = 30\n", + "Score = 1050\n" + ] + }, + { + "data": { + "text/plain": [ + "1050" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "evaluate_results(result)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernel_info": { + "name": "python3" + }, + "kernelspec": { + "display_name": "Python 3 [Q#]", + "language": "python", + "name": "python3_qsharp_b54crn" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.10" + }, + "nteract": { + "version": "nteract-front-end@1.0.0" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/team_solutions/schrodingers-duck/.ipynb_checkpoints/iQuHack-challenge-2023-task7-checkpoint.ipynb b/team_solutions/schrodingers-duck/.ipynb_checkpoints/iQuHack-challenge-2023-task7-checkpoint.ipynb new file mode 100644 index 0000000..9d38b74 --- /dev/null +++ b/team_solutions/schrodingers-duck/.ipynb_checkpoints/iQuHack-challenge-2023-task7-checkpoint.ipynb @@ -0,0 +1,4993 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "# MIT iQuHack Microsoft Challenge: Optimizing Quantum Oracles, Task 7\n", + "\n", + "To work on this task,\n", + "1. Use the notebook for this task. Each of the notebooks in the repository has the code of the corresponding task.\n", + "2. Update your team name and Slack ID variables in the next code cell (you can use different Slack IDs for different tasks if different team members work on them, but make sure to use the same team name throughout the Hackathon). Do not change the task variable!\n", + "3. Work on your task in the cell that contains operation `Task7`! Your goal is to rewrite the code so that it maintains its correctness, but requires as few resources as possible. See `evaluate_results` function for details on how your absolute score for the task is calculated.\n", + "4. Submit your task using qBraid. Use the Share Notebook feature on qBraid (See File > Share Notebook) and enter the email rickyyoung@qbraid.com. Once you click submit, if the share notebook feature works correctly, it should show that you receive no errors and the email you entered will disappear. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "Log in to Azure (once per session, don't need to do it if running from Azure workspace)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "!az login" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 1. Write the code" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# Run this code cell to import the modules required to work with Q# and Azure\n", + "import qsharp\n", + "from qsharp import azure" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "teamname=\"schrodingers-duck\" # Update this field with your team name\n", + "task=[\"task7\"]\n", + "slack_id=\"U04L3SFUCQ2\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# You don't need to run this cell, it defines Q# operations as Python types to keep IntelliSense happy\n", + "Task7_DumpMachineWrapper : qsharp.QSharpCallable = None\n", + "Task7_ResourceEstimationWrapper : qsharp.QSharpCallable = None" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "**The complete code for Task 7 should be in this cell.** \n", + "This cell can include additional open statements and helper operations and functions if your solution needs them. \n", + "If you define helper operations in other cells, they will not be picked up by the grader!" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "open Microsoft.Quantum.Canon;\n", + "open Microsoft.Quantum.Diagnostics;\n", + "open Microsoft.Quantum.Arrays;\n", + "\n", + "// Task 7. \n", + "// (input will contain 7 qubits)\n", + "operation original(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " for i in [9,18,19,25,36,37,38,39,41,50,51,57,72,73,74,75,76,77,78,79,82,83,89,100,101,102,103,105,114,115,121] {\n", + " ControlledOnInt(i, X)(input, target);\n", + " }\n", + "}\n", + "\n", + "operation Task7(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " ControlledOnInt(9, X)([input[6], input[5], input[4], input[3]], target);\n", + " ControlledOnInt(9, X)([input[5], input[4], input[3], input[2]], target);\n", + " ControlledOnInt(9, X)([input[4], input[3], input[2], input[1]], target);\n", + " ControlledOnInt(9, X)([input[3], input[2], input[1], input[0]], target);\n", + " ControlledOnInt(73, X)(input, target);\n", + "}\n", + "\n", + "operation QubitArrayWrapperOperation (op : ((Qubit[], Qubit) => Unit is Adj), qs : Qubit[]) : Unit is Adj { \n", + " op(Most(qs), Tail(qs));\n", + "}\n", + "\n", + "operation TestCompoundGate () : Unit {\n", + " AssertOperationsEqualReferenced(7+1, QubitArrayWrapperOperation(Task7, _), QubitArrayWrapperOperation (original, _));\n", + "}\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "TestCompoundGate();" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "// Wrapper operation that allows you to observe the effects of the marking oracle by running it on a simulator.\n", + "operation Task7_DumpMachineWrapper() : Unit {\n", + " let N = 7;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " // Prepare an equal superposition of all input states in the input register.\n", + " ApplyToEach(H, input);\n", + " // Apply the oracle.\n", + " Task7(input, target);\n", + " // Print the state of the system after the oracle application.\n", + " DumpMachine();\n", + " ResetAll(input + [target]);\n", + "}\n", + "\n", + "// Wrapper operation that allows to run resource estimation for the task.\n", + "// This operation only allocates the qubits and applies the oracle once, not using any additional gates or measurements.\n", + "operation Task7_ResourceEstimationWrapper() : Unit {\n", + " let N = 7;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " Task7(input, target);\n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 2. Run the code on a simulator to see what it does\n", + "You can also write your own code to explore the effects of the oracle (for example, applying it to different basis states and measuring the results)." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "data": { + "application/x-qsharp-data": 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Qubit IDs0, 1, 2, 3, 4, 5, 6, 7
Basis state (bitstring)AmplitudeMeas. Pr.
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$\\left|00110110\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|01011010\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1001111100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10100000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10100010\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1010010100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1010011100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10101000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10101010\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10101100\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10101110\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10110000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1011001100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10110100\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10110110\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10111000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10111010\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|11000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|11000100\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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"output_type": "execute_result" + } + ], + "source": [ + "# Note that in the output of this cell the target qubit corresponds to the rightmost bit\n", + "qsharp.config[\"dump.basisStateLabelingConvention\"]=\"Bitstring\"\n", + "qsharp.config[\"dump.phaseDisplayStyle\"]=\"None\"\n", + "# Uncomment the following line if you want to see only the entries with non-zero amplitudes\n", + "qsharp.config[\"dump.truncateSmallAmplitudes\"]=True\n", + "Task7_DumpMachineWrapper.simulate()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 3. Evaluate the code using resource estimation" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "data": { + "application/x-qsharp-data": "\"Connecting to Azure Quantum...\"", + "text/plain": [ + "Connecting to Azure Quantum..." + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Connected to Azure Quantum workspace azure-q in location uksouth.\n" + ] + }, + { + "data": { + "text/plain": [ + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 179536},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 429485},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 2},\n", + " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 479},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 163},\n", + " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 479},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 163},\n", + " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.qpu.aspen-m-2', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", + "# If you're using this notebook in qBraid, keep it\n", + "qsharp.azure.connect(\n", + " resourceId=\"/subscriptions/7fc54e95-14cf-4a6f-b50e-d6155c241309/resourceGroups/AzureQuantum/providers/Microsoft.Quantum/Workspaces/azure-q\",\n", + " location=\"UK South\",\n", + " credential=\"CLI\")" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loading package Microsoft.Quantum.Providers.Core and dependencies...\n", + "Active target is now microsoft.estimator\n" + ] + }, + { + "data": { + "text/plain": [ + "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qsharp.azure.target(\"microsoft.estimator\")" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Submitting Task7_ResourceEstimationWrapper to target microsoft.estimator...\n", + "Job successfully submitted.\n", + " Job name: RE for the task 7\n", + " Job ID: 532dd603-96a9-42a3-a29f-91825cb1e61d\n", + "Waiting up to 30 seconds for Azure Quantum job to complete...\n", + "[2:14:25 PM] Current job status: Executing\n", + "[2:14:30 PM] Current job status: Succeeded\n" + ] + } + ], + "source": [ + "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", + "result = qsharp.azure.execute(Task7_ResourceEstimationWrapper, jobName=\"RE for the task 7\")" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "data": { + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":13,\"cczCount\":5,\"measurementCount\":13,\"numQubits\":13,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":67,\"algorithmicLogicalQubits\":38,\"cliffordErrorRate\":0.001,\"logicalDepth\":67,\"numTfactories\":12,\"numTfactoryRuns\":6,\"numTsPerRotation\":null,\"numTstates\":72,\"physicalQubitsForAlgorithm\":9196,\"physicalQubitsForTfactories\":77760,\"requiredLogicalQubitErrorRate\":1.9638648860958366E-07,\"requiredLogicalTstateErrorRate\":6.944444444444445E-06},\"physicalQubits\":86956,\"runtime\":294800},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"89.42 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"1.96e-7\",\"requiredLogicalTstateErrorRate\":\"6.94e-6\",\"runtime\":\"294us 800ns\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 9196 physical qubits to implement the algorithm logic, and 77760 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 67 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 13$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 38$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 13 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 5 CCZ and 13 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 67. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 5 CCZ and 13 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 72 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{72\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 294us 800ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 72 T states, the 12 copies of the T factory are repeatedly invoked 6 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 9196 are the product of the 38 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 12 in parallel, therefore we need $77760 = 6480 \\\\cdot 12$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 67.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 72.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000019638648860958366)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.94e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or ¬µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "text/html": [ + "\r\n", + "
\r\n", + " \r\n", + " Physical resource estimates\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits86956\r\n", + "

Number of physical qubits

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This value represents the total number of physical qubits, which is the sum of 9196 physical qubits to implement the algorithm logic, and 77760 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

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Runtime294us 800ns\r\n", + "

Total runtime

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This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 67 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

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Logical algorithmic qubits38\r\n", + "

Number of logical qubits for the algorithm after layout

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Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 13\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 38$ logical qubits.

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Algorithmic depth67\r\n", + "

Number of logical cycles for the algorithm

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To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 13 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 5 CCZ and 13 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

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Logical depth67\r\n", + "

Number of logical cycles performed

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This number is usually equal to the logical depth of the algorithm, which is 67. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

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Number of T states72\r\n", + "

Number of T states consumed by the algorithm

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To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 5 CCZ and 13 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

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Number of T factories12\r\n", + "

Number of T factories capable of producing the demanded 72 T states during the algorithm's runtime

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The total number of T factories 12 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{72\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 294us 800ns\\;\\text{algorithm runtime}}\\right\\rceil\\)

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Number of T factory invocations6\r\n", + "

Number of times all T factories are invoked

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In order to prepare the 72 T states, the 12 copies of the T factory are repeatedly invoked 6 times.

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Physical algorithmic qubits9196\r\n", + "

Number of physical qubits for the algorithm after layout

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The 9196 are the product of the 38 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.

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Physical T factory qubits77760\r\n", + "

Number of physical qubits for the T factories

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Each T factory requires 6480 physical qubits and we run 12 in parallel, therefore we need $77760 = 6480 \\cdot 12$ qubits.

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Required logical qubit error rate1.96e-7\r\n", + "

The minimum logical qubit error rate required to run the algorithm within the error budget

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The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 67.

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Required logical T state error rate6.94e-6\r\n", + "

The minimum T state error rate required for distilled T states

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The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 72.

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Number of T states per rotationNo rotations in algorithm\r\n", + "

Number of T states to implement a rotation with an arbitrary angle

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The number of T states to implement a rotation with an arbitrary angle is \\(\\lceil 0.53 \\log_2(0 / 0) + 5.3\\rceil\\) [arXiv:2203.10064]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.

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\r\n", + " \r\n", + " Logical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
QEC schemesurface_code\r\n", + "

Name of QEC scheme

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You can load pre-defined QEC schemes by using the name surface_code or floquet_code. The latter only works with Majorana qubits.

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Code distance11\r\n", + "

Required code distance for error correction

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The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000019638648860958366)}{\\log(0.01/0.001)} - 1\\)

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Physical qubits242\r\n", + "

Number of physical qubits per logical qubit

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The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.

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Logical cycle time4us 400ns\r\n", + "

Duration of a logical cycle in nanoseconds

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The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.

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Logical qubit error rate3.00e-8\r\n", + "

Logical qubit error rate

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The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{11 + 1}{2}$

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Crossing prefactor0.03\r\n", + "

Crossing prefactor used in QEC scheme

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The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.

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Error correction threshold0.01\r\n", + "

Error correction threshold used in QEC scheme

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The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.

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Logical cycle time formula(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\r\n", + "

QEC scheme formula used to compute logical cycle time

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This is the formula that is used to compute the logical cycle time 4us 400ns.

\n", + "\r\n", + "
Physical qubits formula2 * codeDistance * codeDistance\r\n", + "

QEC scheme formula used to compute number of physical qubits per logical qubit

\n", + "\r\n", + "
\r\n", + "

This is the formula that is used to compute the number of physical qubits per logical qubits 242.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " T factory parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits6480\r\n", + "

Number of physical qubits for a single T factory

\n", + "\r\n", + "
\r\n", + "

This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.

\n", + "\r\n", + "
Runtime46us 800ns\r\n", + "

Runtime of a single T factory

\n", + "\r\n", + "
\r\n", + "

The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.

\n", + "\r\n", + "
Number of output T states per run1\r\n", + "

Number of output T states produced in a single run of T factory

\n", + "\r\n", + "
\r\n", + "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.

\n", + "\r\n", + "
Number of input T states per run30\r\n", + "

Number of physical input T states consumed in a single run of a T factory

\n", + "\r\n", + "
\r\n", + "

This value includes the physical input T states of all copies of the distillation unit in the first round.

\n", + "\r\n", + "
Distillation rounds1\r\n", + "

The number of distillation rounds

\n", + "\r\n", + "
\r\n", + "

This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.

\n", + "\r\n", + "
Distillation units per round2\r\n", + "

The number of units in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the number of copies for the distillation units per round.

\n", + "\r\n", + "
Distillation units15-to-1 space efficient logical\r\n", + "

The types of distillation units

\n", + "\r\n", + "
\r\n", + "

These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.

\n", + "\r\n", + "
Distillation code distances9\r\n", + "

The code distance in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.

\n", + "\r\n", + "
Number of physical qubits per round6480\r\n", + "

The number of physical qubits used in each round of distillation

\n", + "\r\n", + "
\r\n", + "

The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.

\n", + "\r\n", + "
Runtime per round46us 800ns\r\n", + "

The runtime of each distillation round

\n", + "\r\n", + "
\r\n", + "

The runtime of the T factory is the sum of the runtimes in all rounds.

\n", + "\r\n", + "
Logical T state error rate2.17e-6\r\n", + "

Logical T state error rate

\n", + "\r\n", + "
\r\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.94e-6.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Pre-layout logical resources\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Logical qubits (pre-layout)13\r\n", + "

Number of logical qubits in the input quantum program

\n", + "\r\n", + "
\r\n", + "

We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", + "\r\n", + "
T gates0\r\n", + "

Number of T gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.

\n", + "\r\n", + "
Rotation gates0\r\n", + "

Number of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.

\n", + "\r\n", + "
Rotation depth0\r\n", + "

Depth of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.

\n", + "\r\n", + "
CCZ gates5\r\n", + "

Number of CCZ-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCZ gates.

\n", + "\r\n", + "
CCiX gates13\r\n", + "

Number of CCiX-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCiX gates, which applies \\(-iX\\) controlled on two control qubits [1212.5069].

\n", + "\r\n", + "
Measurement operations13\r\n", + "

Number of single qubit measurements in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Assumed error budget\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Total error budget1.00e-3\r\n", + "

Total error budget for the algorithm

\n", + "\r\n", + "
\r\n", + "

The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget \\(\\epsilon = \\epsilon_{\\log} + \\epsilon_{\\rm dis} + \\epsilon_{\\rm syn}\\) is uniformly distributed and applies to errors \\(\\epsilon_{\\log}\\) to implement logical qubits, an error budget \\(\\epsilon_{\\rm dis}\\) to produce T states through distillation, and an error budget \\(\\epsilon_{\\rm syn}\\) to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets \\(\\epsilon_{\\rm dis}\\) and \\(\\epsilon_{\\rm syn}\\) are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.

\n", + "\r\n", + "
Logical error probability5.00e-4\r\n", + "

Probability of at least one logical error

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
T distillation error probability5.00e-4\r\n", + "

Probability of at least one faulty T distillation

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
Rotation synthesis error probability0.00e0\r\n", + "

Probability of at least one failed rotation synthesis

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Physical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Qubit namequbit_gate_ns_e3\r\n", + "

Some descriptive name for the qubit model

\n", + "\r\n", + "
\r\n", + "

You can load pre-defined qubit parameters by using the names qubit_gate_ns_e3, qubit_gate_ns_e4, qubit_gate_us_e3, qubit_gate_us_e4, qubit_maj_ns_e4, or qubit_maj_ns_e6. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).

\n", + "\r\n", + "
Instruction setGateBased\r\n", + "

Underlying qubit technology (gate-based or Majorana)

\n", + "\r\n", + "
\r\n", + "

When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either gate-based or Majorana. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.

\n", + "\r\n", + "
Single-qubit measurement time100 ns\r\n", + "

Operation time for single-qubit measurement (t_meas) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.

\n", + "\r\n", + "
Single-qubit gate time50 ns\r\n", + "

Operation time for single-qubit gate (t_gate) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.

\n", + "\r\n", + "
Two-qubit gate time50 ns\r\n", + "

Operation time for two-qubit gate in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.

\n", + "\r\n", + "
T gate time50 ns\r\n", + "

Operation time for a T gate

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to execute a T gate.

\n", + "\r\n", + "
Single-qubit measurement error rate0.001\r\n", + "

Error rate for single-qubit measurement

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit measurement in the Pauli basis may fail.

\n", + "\r\n", + "
Single-qubit error rate0.001\r\n", + "

Error rate for single-qubit Clifford gate (p)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.

\n", + "\r\n", + "
Two-qubit error rate0.001\r\n", + "

Error rate for two-qubit Clifford gate

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.

\n", + "\r\n", + "
T gate error rate0.001\r\n", + "

Error rate to prepare single-qubit T state or apply a T gate (p_T)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which executing a single T gate may fail.

\n", + "\r\n", + "
\n", + "
\r\n", + " Assumptions\r\n", + "
    \n", + "

  • More details on the following lists of assumptions can be found in the paper Accessing requirements for scaling quantum computers and their applications.

    \n", + "
    • \n", + "

  • Uniform independent physical noise. We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.

    \n", + "
    • \n", + "

  • Efficient classical computation. We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.

    \n", + "
    • \n", + "

  • Extraction circuits for planar quantum ISA. We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).

    \n", + "
    • \n", + "

  • Uniform independent logical noise. We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.

    \n", + "
    • \n", + "

  • Negligible Clifford costs for synthesis. We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.

    \n", + "
    • \n", + "

  • Smooth magic state consumption rate. We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.

    \n", + "
    • \n", + "
\n" + ], + "text/plain": [ + "{'errorBudget': {'logical': 0.0005, 'rotations': 0.0, 'tstates': 0.0005},\n", + " 'jobParams': {'errorBudget': 0.001,\n", + " 'qecScheme': {'crossingPrefactor': 0.03,\n", + " 'errorCorrectionThreshold': 0.01,\n", + " 'logicalCycleTime': '(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance',\n", + " 'name': 'surface_code',\n", + " 'physicalQubitsPerLogicalQubit': '2 * codeDistance * codeDistance'},\n", + " 'qubitParams': {'instructionSet': 'GateBased',\n", + " 'name': 'qubit_gate_ns_e3',\n", + " 'oneQubitGateErrorRate': 0.001,\n", + " 'oneQubitGateTime': '50 ns',\n", + " 'oneQubitMeasurementErrorRate': 0.001,\n", + " 'oneQubitMeasurementTime': '100 ns',\n", + " 'tGateErrorRate': 0.001,\n", + " 'tGateTime': '50 ns',\n", + " 'twoQubitGateErrorRate': 0.001,\n", + " 'twoQubitGateTime': '50 ns'}},\n", + " 'logicalCounts': {'ccixCount': 13,\n", + " 'cczCount': 5,\n", + " 'measurementCount': 13,\n", + " 'numQubits': 13,\n", + " 'rotationCount': 0,\n", + " 'rotationDepth': 0,\n", + " 'tCount': 0},\n", + " 'logicalQubit': {'codeDistance': 11,\n", + " 'logicalCycleTime': 4400.0,\n", + " 'logicalErrorRate': 3.000000000000002e-08,\n", + " 'physicalQubits': 242},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 67,\n", + " 'algorithmicLogicalQubits': 38,\n", + " 'cliffordErrorRate': 0.001,\n", + " 'logicalDepth': 67,\n", + " 'numTfactories': 12,\n", + " 'numTfactoryRuns': 6,\n", + " 'numTsPerRotation': None,\n", + " 'numTstates': 72,\n", + " 'physicalQubitsForAlgorithm': 9196,\n", + " 'physicalQubitsForTfactories': 77760,\n", + " 'requiredLogicalQubitErrorRate': 1.9638648860958366e-07,\n", + " 'requiredLogicalTstateErrorRate': 6.944444444444445e-06},\n", + " 'physicalQubits': 86956,\n", + " 'runtime': 294800},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", + " 'errorBudget': '1.00e-3',\n", + " 'errorBudgetLogical': '5.00e-4',\n", + " 'errorBudgetRotations': '0.00e0',\n", + " 'errorBudgetTstates': '5.00e-4',\n", + " 'logicalCycleTime': '4us 400ns',\n", + " 'logicalErrorRate': '3.00e-8',\n", + " 'numTsPerRotation': 'No rotations in algorithm',\n", + " 'numUnitsPerRound': '2',\n", + " 'physicalQubitsForTfactoriesPercentage': '89.42 %',\n", + " 'physicalQubitsPerRound': '6480',\n", + " 'requiredLogicalQubitErrorRate': '1.96e-7',\n", + " 'requiredLogicalTstateErrorRate': '6.94e-6',\n", + " 'runtime': '294us 800ns',\n", + " 'tfactoryRuntime': '46us 800ns',\n", + " 'tfactoryRuntimePerRound': '46us 800ns',\n", + " 'tstateLogicalErrorRate': '2.17e-6',\n", + " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", + " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", + " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", + " '**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.',\n", + " '**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).',\n", + " '**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.',\n", + " '**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.',\n", + " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", + " 'groups': [{'alwaysVisible': True,\n", + " 'entries': [{'description': 'Number of physical qubits',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 9196 physical qubits to implement the algorithm logic, and 77760 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'physicalCounts/physicalQubits'},\n", + " {'description': 'Total runtime',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 67 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/runtime'}],\n", + " 'title': 'Physical resource estimates'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 13$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 38$ logical qubits.',\n", + " 'label': 'Logical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", + " {'description': 'Number of logical cycles for the algorithm',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 13 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 5 CCZ and 13 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'label': 'Algorithmic depth',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", + " {'description': 'Number of logical cycles performed',\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 67. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'label': 'Logical depth',\n", + " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", + " {'description': 'Number of T states consumed by the algorithm',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 5 CCZ and 13 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'label': 'Number of T states',\n", + " 'path': 'physicalCounts/breakdown/numTstates'},\n", + " {'description': \"Number of T factories capable of producing the demanded 72 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{72\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 294us 800ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " 'label': 'Number of T factories',\n", + " 'path': 'physicalCounts/breakdown/numTfactories'},\n", + " {'description': 'Number of times all T factories are invoked',\n", + " 'explanation': 'In order to prepare the 72 T states, the 12 copies of the T factory are repeatedly invoked 6 times.',\n", + " 'label': 'Number of T factory invocations',\n", + " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", + " {'description': 'Number of physical qubits for the algorithm after layout',\n", + " 'explanation': 'The 9196 are the product of the 38 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.',\n", + " 'label': 'Physical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", + " {'description': 'Number of physical qubits for the T factories',\n", + " 'explanation': 'Each T factory requires 6480 physical qubits and we run 12 in parallel, therefore we need $77760 = 6480 \\\\cdot 12$ qubits.',\n", + " 'label': 'Physical T factory qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", + " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 38 logical qubits and the total cycle count 67.',\n", + " 'label': 'Required logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", + " {'description': 'The minimum T state error rate required for distilled T states',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 72.',\n", + " 'label': 'Required logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", + " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", + " 'explanation': 'The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.',\n", + " 'label': 'Number of T states per rotation',\n", + " 'path': 'physicalCountsFormatted/numTsPerRotation'}],\n", + " 'title': 'Resource estimates breakdown'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Name of QEC scheme',\n", + " 'explanation': 'You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.',\n", + " 'label': 'QEC scheme',\n", + " 'path': 'jobParams/qecScheme/name'},\n", + " {'description': 'Required code distance for error correction',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000019638648860958366)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'label': 'Code distance',\n", + " 'path': 'logicalQubit/codeDistance'},\n", + " {'description': 'Number of physical qubits per logical qubit',\n", + " 'explanation': 'The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'logicalQubit/physicalQubits'},\n", + " {'description': 'Duration of a logical cycle in nanoseconds',\n", + " 'explanation': 'The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.',\n", + " 'label': 'Logical cycle time',\n", + " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", + " {'description': 'Logical qubit error rate',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$',\n", + " 'label': 'Logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", + " {'description': 'Crossing prefactor used in QEC scheme',\n", + " 'explanation': 'The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.',\n", + " 'label': 'Crossing prefactor',\n", + " 'path': 'jobParams/qecScheme/crossingPrefactor'},\n", + " {'description': 'Error correction threshold used in QEC scheme',\n", + " 'explanation': 'The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.',\n", + " 'label': 'Error correction threshold',\n", + " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", + " {'description': 'QEC scheme formula used to compute logical cycle time',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 4us 400ns.',\n", + " 'label': 'Logical cycle time formula',\n", + " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", + " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 242.',\n", + " 'label': 'Physical qubits formula',\n", + " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", + " 'title': 'Logical qubit parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of physical qubits for a single T factory',\n", + " 'explanation': 'This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'tfactory/physicalQubits'},\n", + " {'description': 'Runtime of a single T factory',\n", + " 'explanation': 'The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", + " {'description': 'Number of output T states produced in a single run of T factory',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.',\n", + " 'label': 'Number of output T states per run',\n", + " 'path': 'tfactory/numTstates'},\n", + " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", + " 'explanation': 'This value includes the physical input T states of all copies of the distillation unit in the first round.',\n", + " 'label': 'Number of input T states per run',\n", + " 'path': 'tfactory/numInputTstates'},\n", + " {'description': 'The number of distillation rounds',\n", + " 'explanation': 'This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.',\n", + " 'label': 'Distillation rounds',\n", + " 'path': 'tfactory/numRounds'},\n", + " {'description': 'The number of units in each round of distillation',\n", + " 'explanation': 'This is the number of copies for the distillation units per round.',\n", + " 'label': 'Distillation units per round',\n", + " 'path': 'physicalCountsFormatted/numUnitsPerRound'},\n", + " {'description': 'The types of distillation units',\n", + " 'explanation': 'These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.',\n", + " 'label': 'Distillation units',\n", + " 'path': 'physicalCountsFormatted/unitNamePerRound'},\n", + " {'description': 'The code distance in each round of distillation',\n", + " 'explanation': 'This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.',\n", + " 'label': 'Distillation code distances',\n", + " 'path': 'physicalCountsFormatted/codeDistancePerRound'},\n", + " {'description': 'The number of physical qubits used in each round of distillation',\n", + " 'explanation': 'The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.',\n", + " 'label': 'Number of physical qubits per round',\n", + " 'path': 'physicalCountsFormatted/physicalQubitsPerRound'},\n", + " {'description': 'The runtime of each distillation round',\n", + " 'explanation': 'The runtime of the T factory is the sum of the runtimes in all rounds.',\n", + " 'label': 'Runtime per round',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", + " {'description': 'Logical T state error rate',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 6.94e-6.',\n", + " 'label': 'Logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", + " 'title': 'T factory parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", + " 'explanation': 'We determine 38 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'label': 'Logical qubits (pre-layout)',\n", + " 'path': 'logicalCounts/numQubits'},\n", + " {'description': 'Number of T gates in the input quantum program',\n", + " 'explanation': 'This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.',\n", + " 'label': 'T gates',\n", + " 'path': 'logicalCounts/tCount'},\n", + " {'description': 'Number of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.',\n", + " 'label': 'Rotation gates',\n", + " 'path': 'logicalCounts/rotationCount'},\n", + " {'description': 'Depth of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.',\n", + " 'label': 'Rotation depth',\n", + " 'path': 'logicalCounts/rotationDepth'},\n", + " {'description': 'Number of CCZ-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCZ gates.',\n", + " 'label': 'CCZ gates',\n", + " 'path': 'logicalCounts/cczCount'},\n", + " {'description': 'Number of CCiX-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].',\n", + " 'label': 'CCiX gates',\n", + " 'path': 'logicalCounts/ccixCount'},\n", + " {'description': 'Number of single qubit measurements in the input quantum program',\n", + " 'explanation': 'This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.',\n", + " 'label': 'Measurement operations',\n", + " 'path': 'logicalCounts/measurementCount'}],\n", + " 'title': 'Pre-layout logical resources'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Total error budget for the algorithm',\n", + " 'explanation': \"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\n", + " 'label': 'Total error budget',\n", + " 'path': 'physicalCountsFormatted/errorBudget'},\n", + " {'description': 'Probability of at least one logical error',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'Logical error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetLogical'},\n", + " {'description': 'Probability of at least one faulty T distillation',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'T distillation error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetTstates'},\n", + " {'description': 'Probability of at least one failed rotation synthesis',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3.',\n", + " 'label': 'Rotation synthesis error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetRotations'}],\n", + " 'title': 'Assumed error budget'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Some descriptive name for the qubit model',\n", + " 'explanation': 'You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).',\n", + " 'label': 'Qubit name',\n", + " 'path': 'jobParams/qubitParams/name'},\n", + " {'description': 'Underlying qubit technology (gate-based or Majorana)',\n", + " 'explanation': 'When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.',\n", + " 'label': 'Instruction set',\n", + " 'path': 'jobParams/qubitParams/instructionSet'},\n", + " {'description': 'Operation time for single-qubit measurement (t_meas) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.',\n", + " 'label': 'Single-qubit measurement time',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementTime'},\n", + " {'description': 'Operation time for single-qubit gate (t_gate) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.',\n", + " 'label': 'Single-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateTime'},\n", + " {'description': 'Operation time for two-qubit gate in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.',\n", + " 'label': 'Two-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateTime'},\n", + " {'description': 'Operation time for a T gate',\n", + " 'explanation': 'This is the operation time in nanoseconds to execute a T gate.',\n", + " 'label': 'T gate time',\n", + " 'path': 'jobParams/qubitParams/tGateTime'},\n", + " {'description': 'Error rate for single-qubit measurement',\n", + " 'explanation': 'This is the probability in which a single-qubit measurement in the Pauli basis may fail.',\n", + " 'label': 'Single-qubit measurement error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementErrorRate'},\n", + " {'description': 'Error rate for single-qubit Clifford gate (p)',\n", + " 'explanation': 'This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.',\n", + " 'label': 'Single-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateErrorRate'},\n", + " {'description': 'Error rate for two-qubit Clifford gate',\n", + " 'explanation': 'This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.',\n", + " 'label': 'Two-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateErrorRate'},\n", + " {'description': 'Error rate to prepare single-qubit T state or apply a T gate (p_T)',\n", + " 'explanation': 'This is the probability in which executing a single T gate may fail.',\n", + " 'label': 'T gate error rate',\n", + " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", + " 'title': 'Physical qubit parameters'}]},\n", + " 'status': 'success',\n", + " 'tfactory': {'codeDistancePerRound': [9],\n", + " 'logicalErrorRate': 2.165000000000001e-06,\n", + " 'numInputTstates': 30,\n", + " 'numRounds': 1,\n", + " 'numTstates': 1,\n", + " 'numUnitsPerRound': [2],\n", + " 'physicalQubits': 6480,\n", + " 'physicalQubitsPerRound': [6480],\n", + " 'runtime': 46800.0,\n", + " 'runtimePerRound': [46800.0],\n", + " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", + "# result = qsharp.azure.output(\"...\")\n", + "result" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# The function that extracts the relevant resource information from the resource estimation job results and produces your absolute score.\n", + "def evaluate_results(res) : \n", + " width = res['physicalCounts']['breakdown']['algorithmicLogicalQubits']\n", + " depth = res['physicalCounts']['breakdown']['algorithmicLogicalDepth']\n", + " print(f\"Logical algorithmic qubits = {width}\")\n", + " print(f\"Algorithmic depth = {depth}\")\n", + " print(f\"Score = {width * depth}\")\n", + " return width * depth\n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Logical algorithmic qubits = 38\n", + "Algorithmic depth = 67\n", + "Score = 2546\n" + ] + }, + { + "data": { + "text/plain": [ + "2546" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "evaluate_results(result)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernel_info": { + "name": "python3" + }, + "kernelspec": { + "display_name": "Python 3 [Q#]", + "language": "python", + "name": "python3_qsharp_b54crn" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.10" + }, + "nteract": { + "version": "nteract-front-end@1.0.0" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/team_solutions/schrodingers-duck/.ipynb_checkpoints/iQuHack-challenge-2023-task8-checkpoint.ipynb b/team_solutions/schrodingers-duck/.ipynb_checkpoints/iQuHack-challenge-2023-task8-checkpoint.ipynb new file mode 100644 index 0000000..ecf01d4 --- /dev/null +++ b/team_solutions/schrodingers-duck/.ipynb_checkpoints/iQuHack-challenge-2023-task8-checkpoint.ipynb @@ -0,0 +1,5018 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "# MIT iQuHack Microsoft Challenge: Optimizing Quantum Oracles, Task 8\n", + "\n", + "To work on this task,\n", + "1. Use the notebook for this task. Each of the notebooks in the repository has the code of the corresponding task.\n", + "2. Update your team name and Slack ID variables in the next code cell (you can use different Slack IDs for different tasks if different team members work on them, but make sure to use the same team name throughout the Hackathon). Do not change the task variable!\n", + "3. Work on your task in the cell that contains operation `Task8`! Your goal is to rewrite the code so that it maintains its correctness, but requires as few resources as possible. See `evaluate_results` function for details on how your absolute score for the task is calculated.\n", + "4. Submit your task using qBraid. Use the Share Notebook feature on qBraid (See File > Share Notebook) and enter the email rickyyoung@qbraid.com. Once you click submit, if the share notebook feature works correctly, it should show that you receive no errors and the email you entered will disappear. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "Log in to Azure (once per session, don't need to do it if running from Azure workspace)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "!az login" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 1. Write the code" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Preparing Q# environment...\n" + ] + } + ], + "source": [ + "# Run this code cell to import the modules required to work with Q# and Azure\n", + "import qsharp\n", + "from qsharp import azure" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "teamname=\"schrodingers-duck\" # Update this field with your team name\n", + "task=[\"task8\"]\n", + "slack_id=\"U04L3SFUCQ2\" # Update this field with Slack ID of the person who worked on this task as the troubleshooting contact" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# You don't need to run this cell, it defines Q# operations as Python types to keep IntelliSense happy\n", + "Task8_DumpMachineWrapper : qsharp.QSharpCallable = None\n", + "Task8_ResourceEstimationWrapper : qsharp.QSharpCallable = None" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "**The complete code for Task 8 should be in this cell.** \n", + "This cell can include additional open statements and helper operations and functions if your solution needs them. \n", + "If you define helper operations in other cells, they will not be picked up by the grader!" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "open Microsoft.Quantum.Canon;\n", + "open Microsoft.Quantum.Diagnostics;\n", + "open Microsoft.Quantum.Arithmetic;\n", + "open Microsoft.Quantum.Math;\n", + "open Microsoft.Quantum.Synthesis;\n", + "open Microsoft.Quantum.Arrays;\n", + "\n", + "// Task 8. \n", + "// (input will contain 7 qubits)\n", + "operation original(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " for i in [15,23,27,29,30,31,39,43, 45,46,47,51,53,54,55,57, \n", + " 58,59,60,61,62,63,71,75, 77,78,79,83,85,86,87,89,\n", + " 90,91,92,93,94,95,99,101, 102,103,105,106,107,108,109,110,\n", + " 111,113,114,115,116,117,118,119, 120,121,122,123,124,125,126,127] {\n", + " ControlledOnInt(i, X)(input, target);\n", + " }\n", + "}\n", + "\n", + "operation Task8(input : Qubit[], target : Qubit) : Unit is Adj {\n", + " use sumWires = Qubit[7];\n", + " use zero = Qubit[1];\n", + " within{\n", + " //Ebene 1\n", + " CarryN(input[0], input[1], input[2], sumWires[0]);\n", + " CarryN(input[3], input[4], input[5], sumWires[1]);\n", + " //Ebene 2\n", + " CarryN(zero[0], input[2], input[5], sumWires[2]);\n", + " CarryN(sumWires[2], sumWires[0], sumWires[1], sumWires[3]);\n", + " //Ebene 3\n", + " CarryN(zero[0], input[6], input[5], sumWires[4]);\n", + " CarryN(sumWires[4], zero[0], sumWires[1], sumWires[5]);\n", + " CarryN(sumWires[5], zero[0], sumWires[3], sumWires[6]);\n", + " } apply{\n", + " //CNOT(sumWires[3], target);\n", + " CNOT(sumWires[3], target);\n", + " }\n", + "}\n", + "operation CarryN(carryIn: Qubit, summand1: Qubit, summand2: Qubit, carryOut: Qubit) : Unit is Adj + Ctl {\n", + " CCNOT (summand1, summand2, carryOut);\n", + " CNOT (summand1, summand2);\n", + " CCNOT (carryIn, summand2, carryOut);\n", + " CNOT(carryIn, summand2);\n", + "}\n", + "\n", + "operation QubitArrayWrapperOperation (op : ((Qubit[], Qubit) => Unit is Adj), qs : Qubit[]) : Unit is Adj { \n", + " op(Most(qs), Tail(qs));\n", + "}\n", + "\n", + "operation TestCompoundGate () : Unit {\n", + " AssertOperationsEqualReferenced(7+1, QubitArrayWrapperOperation(Task8, _), QubitArrayWrapperOperation (original, _));\n", + "}\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "TestCompoundGate();" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "microsoft": { + "language": "qsharp" + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "%%qsharp\n", + "// Wrapper operation that allows you to observe the effects of the marking oracle by running it on a simulator.\n", + "operation Task8_DumpMachineWrapper() : Unit {\n", + " let N = 7;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " // Prepare an equal superposition of all input states in the input register.\n", + " ApplyToEach(H, input);\n", + " // Apply the oracle.\n", + " Task8(input, target);\n", + " // Print the state of the system after the oracle application.\n", + " DumpMachine();\n", + " ResetAll(input + [target]);\n", + "}\n", + "\n", + "// Wrapper operation that allows to run resource estimation for the task.\n", + "// This operation only allocates the qubits and applies the oracle once, not using any additional gates or measurements.\n", + "operation Task8_ResourceEstimationWrapper() : Unit {\n", + " let N = 7;\n", + " use (input, target) = (Qubit[N], Qubit());\n", + " Task8(input, target);\n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 2. Run the code on a simulator to see what it does\n", + "You can also write your own code to explore the effects of the oracle (for example, applying it to different basis states and measuring the results)." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "data": { + "application/x-qsharp-data": 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Qubit IDs0, 1, 2, 3, 4, 5, 6, 7
Basis state (bitstring)AmplitudeMeas. Pr.
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$\\left|0011011100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|00111000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|0011101100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|01000110\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1010111100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|10110000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1011001100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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$\\left|1011010100000000\\right\\rangle$$0.0884 + 0.0000 i$\r\n", + " \r\n", + " \r\n", + "

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+ 0𝑖\n", + "|1111110100000000⟩\t0.0883883476483185 + 0𝑖\n", + "|1111111100000000⟩\t0.0883883476483185 + 0𝑖" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "()" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Note that in the output of this cell the target qubit corresponds to the rightmost bit\n", + "qsharp.config[\"dump.basisStateLabelingConvention\"]=\"Bitstring\"\n", + "qsharp.config[\"dump.phaseDisplayStyle\"]=\"None\"\n", + "# Uncomment the following line if you want to see only the entries with non-zero amplitudes\n", + "qsharp.config[\"dump.truncateSmallAmplitudes\"]=True\n", + "Task8_DumpMachineWrapper.simulate()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nteract": { + "transient": { + "deleting": false + } + } + }, + "source": [ + "## Step 3. Evaluate the code using resource estimation" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "data": { + "application/x-qsharp-data": "\"Connecting to Azure Quantum...\"", + "text/plain": [ + "Connecting to Azure Quantum..." + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Connected to Azure Quantum workspace azure-q in location uksouth.\n" + ] + }, + { + "data": { + "text/plain": [ + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 296609},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 366858},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 3},\n", + " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 183},\n", + " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 183},\n", + " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", + " {'id': 'rigetti.qpu.aspen-m-2', 'current_availability': {}, 'average_queue_time': 5},\n", + " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# If you're using this notebook in Azure Quantum hosted notebooks, remove the credential=\"CLI\" parameter!\n", + "# If you're using this notebook in qBraid, keep it\n", + "qsharp.azure.connect(\n", + " resourceId=\"/subscriptions/7fc54e95-14cf-4a6f-b50e-d6155c241309/resourceGroups/AzureQuantum/providers/Microsoft.Quantum/Workspaces/azure-q\",\n", + " location=\"UK South\",\n", + " credential=\"CLI\")" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Loading package Microsoft.Quantum.Providers.Core and dependencies...\n", + "Active target is now microsoft.estimator\n" + ] + }, + { + "data": { + "text/plain": [ + "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qsharp.azure.target(\"microsoft.estimator\")" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Submitting Task8_ResourceEstimationWrapper to target microsoft.estimator...\n", + "Job successfully submitted.\n", + " Job name: RE for the task 8\n", + " Job ID: e310d987-293a-4420-8db8-d09b15c2f5ac\n", + "Waiting up to 30 seconds for Azure Quantum job to complete...\n", + "[8:04:56 AM] Current job status: Succeeded\n" + ] + } + ], + "source": [ + "# Update job name to a more descriptive string to make it easier to find it in Job Management tab later\n", + "result = qsharp.azure.execute(Task8_ResourceEstimationWrapper, jobName=\"RE for the task 8\")" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "data": { + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":0,\"cczCount\":28,\"measurementCount\":0,\"numQubits\":16,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":11,\"logicalCycleTime\":4400.0,\"logicalErrorRate\":3.000000000000002E-08,\"physicalQubits\":242},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":84,\"algorithmicLogicalQubits\":45,\"cliffordErrorRate\":0.001,\"logicalDepth\":84,\"numTfactories\":15,\"numTfactoryRuns\":8,\"numTsPerRotation\":null,\"numTstates\":112,\"physicalQubitsForAlgorithm\":10890,\"physicalQubitsForTfactories\":97200,\"requiredLogicalQubitErrorRate\":1.3227513227513228E-07,\"requiredLogicalTstateErrorRate\":4.464285714285715E-06},\"physicalQubits\":108090,\"runtime\":369600},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"4us 400ns\",\"logicalErrorRate\":\"3.00e-8\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"89.93 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"1.32e-7\",\"requiredLogicalTstateErrorRate\":\"4.46e-6\",\"runtime\":\"369us 600ns\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 10890 physical qubits to implement the algorithm logic, and 97200 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 84 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 16$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 45$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 0 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 28 CCZ and 0 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 84. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 28 CCZ and 0 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 112 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 15 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{112\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 369us 600ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 112 T states, the 15 copies of the T factory are repeatedly invoked 8 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 10890 are the product of the 45 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 15 in parallel, therefore we need $97200 = 6480 \\\\cdot 15$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 45 logical qubits and the total cycle count 84.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 112.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000013227513227513228)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 4us 400ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 242.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 4.46e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 45 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or ¬µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "text/html": [ + "\r\n", + "
\r\n", + " \r\n", + " Physical resource estimates\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits108090\r\n", + "

Number of physical qubits

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This value represents the total number of physical qubits, which is the sum of 10890 physical qubits to implement the algorithm logic, and 97200 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

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Runtime369us 600ns\r\n", + "

Total runtime

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This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 84 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

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Logical algorithmic qubits45\r\n", + "

Number of logical qubits for the algorithm after layout

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Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 16\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 45$ logical qubits.

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Algorithmic depth84\r\n", + "

Number of logical cycles for the algorithm

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To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 0 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 28 CCZ and 0 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

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Logical depth84\r\n", + "

Number of logical cycles performed

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This number is usually equal to the logical depth of the algorithm, which is 84. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

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Number of T states112\r\n", + "

Number of T states consumed by the algorithm

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To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 28 CCZ and 0 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

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Number of T factories15\r\n", + "

Number of T factories capable of producing the demanded 112 T states during the algorithm's runtime

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The total number of T factories 15 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{112\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 369us 600ns\\;\\text{algorithm runtime}}\\right\\rceil\\)

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Number of T factory invocations8\r\n", + "

Number of times all T factories are invoked

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In order to prepare the 112 T states, the 15 copies of the T factory are repeatedly invoked 8 times.

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Physical algorithmic qubits10890\r\n", + "

Number of physical qubits for the algorithm after layout

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The 10890 are the product of the 45 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.

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Physical T factory qubits97200\r\n", + "

Number of physical qubits for the T factories

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Each T factory requires 6480 physical qubits and we run 15 in parallel, therefore we need $97200 = 6480 \\cdot 15$ qubits.

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Required logical qubit error rate1.32e-7\r\n", + "

The minimum logical qubit error rate required to run the algorithm within the error budget

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The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 45 logical qubits and the total cycle count 84.

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Required logical T state error rate4.46e-6\r\n", + "

The minimum T state error rate required for distilled T states

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The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 112.

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Number of T states per rotationNo rotations in algorithm\r\n", + "

Number of T states to implement a rotation with an arbitrary angle

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The number of T states to implement a rotation with an arbitrary angle is \\(\\lceil 0.53 \\log_2(0 / 0) + 5.3\\rceil\\) [arXiv:2203.10064]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.

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\r\n", + " \r\n", + " Logical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
QEC schemesurface_code\r\n", + "

Name of QEC scheme

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You can load pre-defined QEC schemes by using the name surface_code or floquet_code. The latter only works with Majorana qubits.

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Code distance11\r\n", + "

Required code distance for error correction

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The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000013227513227513228)}{\\log(0.01/0.001)} - 1\\)

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Physical qubits242\r\n", + "

Number of physical qubits per logical qubit

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The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.

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Logical cycle time4us 400ns\r\n", + "

Duration of a logical cycle in nanoseconds

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The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.

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Logical qubit error rate3.00e-8\r\n", + "

Logical qubit error rate

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The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{11 + 1}{2}$

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Crossing prefactor0.03\r\n", + "

Crossing prefactor used in QEC scheme

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The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.

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Error correction threshold0.01\r\n", + "

Error correction threshold used in QEC scheme

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The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.

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Logical cycle time formula(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\r\n", + "

QEC scheme formula used to compute logical cycle time

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This is the formula that is used to compute the logical cycle time 4us 400ns.

\n", + "\r\n", + "
Physical qubits formula2 * codeDistance * codeDistance\r\n", + "

QEC scheme formula used to compute number of physical qubits per logical qubit

\n", + "\r\n", + "
\r\n", + "

This is the formula that is used to compute the number of physical qubits per logical qubits 242.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " T factory parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Physical qubits6480\r\n", + "

Number of physical qubits for a single T factory

\n", + "\r\n", + "
\r\n", + "

This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.

\n", + "\r\n", + "
Runtime46us 800ns\r\n", + "

Runtime of a single T factory

\n", + "\r\n", + "
\r\n", + "

The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.

\n", + "\r\n", + "
Number of output T states per run1\r\n", + "

Number of output T states produced in a single run of T factory

\n", + "\r\n", + "
\r\n", + "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.

\n", + "\r\n", + "
Number of input T states per run30\r\n", + "

Number of physical input T states consumed in a single run of a T factory

\n", + "\r\n", + "
\r\n", + "

This value includes the physical input T states of all copies of the distillation unit in the first round.

\n", + "\r\n", + "
Distillation rounds1\r\n", + "

The number of distillation rounds

\n", + "\r\n", + "
\r\n", + "

This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.

\n", + "\r\n", + "
Distillation units per round2\r\n", + "

The number of units in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the number of copies for the distillation units per round.

\n", + "\r\n", + "
Distillation units15-to-1 space efficient logical\r\n", + "

The types of distillation units

\n", + "\r\n", + "
\r\n", + "

These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.

\n", + "\r\n", + "
Distillation code distances9\r\n", + "

The code distance in each round of distillation

\n", + "\r\n", + "
\r\n", + "

This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.

\n", + "\r\n", + "
Number of physical qubits per round6480\r\n", + "

The number of physical qubits used in each round of distillation

\n", + "\r\n", + "
\r\n", + "

The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.

\n", + "\r\n", + "
Runtime per round46us 800ns\r\n", + "

The runtime of each distillation round

\n", + "\r\n", + "
\r\n", + "

The runtime of the T factory is the sum of the runtimes in all rounds.

\n", + "\r\n", + "
Logical T state error rate2.17e-6\r\n", + "

Logical T state error rate

\n", + "\r\n", + "
\r\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 4.46e-6.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Pre-layout logical resources\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Logical qubits (pre-layout)16\r\n", + "

Number of logical qubits in the input quantum program

\n", + "\r\n", + "
\r\n", + "

We determine 45 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", + "\r\n", + "
T gates0\r\n", + "

Number of T gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.

\n", + "\r\n", + "
Rotation gates0\r\n", + "

Number of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.

\n", + "\r\n", + "
Rotation depth0\r\n", + "

Depth of rotation gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.

\n", + "\r\n", + "
CCZ gates28\r\n", + "

Number of CCZ-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCZ gates.

\n", + "\r\n", + "
CCiX gates0\r\n", + "

Number of CCiX-gates in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of CCiX gates, which applies \\(-iX\\) controlled on two control qubits [1212.5069].

\n", + "\r\n", + "
Measurement operations0\r\n", + "

Number of single qubit measurements in the input quantum program

\n", + "\r\n", + "
\r\n", + "

This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Assumed error budget\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Total error budget1.00e-3\r\n", + "

Total error budget for the algorithm

\n", + "\r\n", + "
\r\n", + "

The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget \\(\\epsilon = \\epsilon_{\\log} + \\epsilon_{\\rm dis} + \\epsilon_{\\rm syn}\\) is uniformly distributed and applies to errors \\(\\epsilon_{\\log}\\) to implement logical qubits, an error budget \\(\\epsilon_{\\rm dis}\\) to produce T states through distillation, and an error budget \\(\\epsilon_{\\rm syn}\\) to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets \\(\\epsilon_{\\rm dis}\\) and \\(\\epsilon_{\\rm syn}\\) are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.

\n", + "\r\n", + "
Logical error probability5.00e-4\r\n", + "

Probability of at least one logical error

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
T distillation error probability5.00e-4\r\n", + "

Probability of at least one faulty T distillation

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.

\n", + "\r\n", + "
Rotation synthesis error probability0.00e0\r\n", + "

Probability of at least one failed rotation synthesis

\n", + "\r\n", + "
\r\n", + "

This is one third of the total error budget 1.00e-3.

\n", + "\r\n", + "
\n", + "\r\n", + "
\r\n", + " \r\n", + " Physical qubit parameters\r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "\r\n", + " \r\n", + " \r\n", + " \r\n", + " \r\n", + " \n", + "
Qubit namequbit_gate_ns_e3\r\n", + "

Some descriptive name for the qubit model

\n", + "\r\n", + "
\r\n", + "

You can load pre-defined qubit parameters by using the names qubit_gate_ns_e3, qubit_gate_ns_e4, qubit_gate_us_e3, qubit_gate_us_e4, qubit_maj_ns_e4, or qubit_maj_ns_e6. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).

\n", + "\r\n", + "
Instruction setGateBased\r\n", + "

Underlying qubit technology (gate-based or Majorana)

\n", + "\r\n", + "
\r\n", + "

When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either gate-based or Majorana. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.

\n", + "\r\n", + "
Single-qubit measurement time100 ns\r\n", + "

Operation time for single-qubit measurement (t_meas) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.

\n", + "\r\n", + "
Single-qubit gate time50 ns\r\n", + "

Operation time for single-qubit gate (t_gate) in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.

\n", + "\r\n", + "
Two-qubit gate time50 ns\r\n", + "

Operation time for two-qubit gate in ns

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.

\n", + "\r\n", + "
T gate time50 ns\r\n", + "

Operation time for a T gate

\n", + "\r\n", + "
\r\n", + "

This is the operation time in nanoseconds to execute a T gate.

\n", + "\r\n", + "
Single-qubit measurement error rate0.001\r\n", + "

Error rate for single-qubit measurement

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit measurement in the Pauli basis may fail.

\n", + "\r\n", + "
Single-qubit error rate0.001\r\n", + "

Error rate for single-qubit Clifford gate (p)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.

\n", + "\r\n", + "
Two-qubit error rate0.001\r\n", + "

Error rate for two-qubit Clifford gate

\n", + "\r\n", + "
\r\n", + "

This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.

\n", + "\r\n", + "
T gate error rate0.001\r\n", + "

Error rate to prepare single-qubit T state or apply a T gate (p_T)

\n", + "\r\n", + "
\r\n", + "

This is the probability in which executing a single T gate may fail.

\n", + "\r\n", + "
\n", + "
\r\n", + " Assumptions\r\n", + "
    \n", + "

  • More details on the following lists of assumptions can be found in the paper Accessing requirements for scaling quantum computers and their applications.

    \n", + "
    • \n", + "

  • Uniform independent physical noise. We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.

    \n", + "
    • \n", + "

  • Efficient classical computation. We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.

    \n", + "
    • \n", + "

  • Extraction circuits for planar quantum ISA. We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).

    \n", + "
    • \n", + "

  • Uniform independent logical noise. We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.

    \n", + "
    • \n", + "

  • Negligible Clifford costs for synthesis. We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.

    \n", + "
    • \n", + "

  • Smooth magic state consumption rate. We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.

    \n", + "
    • \n", + "
\n" + ], + "text/plain": [ + "{'errorBudget': {'logical': 0.0005, 'rotations': 0.0, 'tstates': 0.0005},\n", + " 'jobParams': {'errorBudget': 0.001,\n", + " 'qecScheme': {'crossingPrefactor': 0.03,\n", + " 'errorCorrectionThreshold': 0.01,\n", + " 'logicalCycleTime': '(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance',\n", + " 'name': 'surface_code',\n", + " 'physicalQubitsPerLogicalQubit': '2 * codeDistance * codeDistance'},\n", + " 'qubitParams': {'instructionSet': 'GateBased',\n", + " 'name': 'qubit_gate_ns_e3',\n", + " 'oneQubitGateErrorRate': 0.001,\n", + " 'oneQubitGateTime': '50 ns',\n", + " 'oneQubitMeasurementErrorRate': 0.001,\n", + " 'oneQubitMeasurementTime': '100 ns',\n", + " 'tGateErrorRate': 0.001,\n", + " 'tGateTime': '50 ns',\n", + " 'twoQubitGateErrorRate': 0.001,\n", + " 'twoQubitGateTime': '50 ns'}},\n", + " 'logicalCounts': {'ccixCount': 0,\n", + " 'cczCount': 28,\n", + " 'measurementCount': 0,\n", + " 'numQubits': 16,\n", + " 'rotationCount': 0,\n", + " 'rotationDepth': 0,\n", + " 'tCount': 0},\n", + " 'logicalQubit': {'codeDistance': 11,\n", + " 'logicalCycleTime': 4400.0,\n", + " 'logicalErrorRate': 3.000000000000002e-08,\n", + " 'physicalQubits': 242},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 84,\n", + " 'algorithmicLogicalQubits': 45,\n", + " 'cliffordErrorRate': 0.001,\n", + " 'logicalDepth': 84,\n", + " 'numTfactories': 15,\n", + " 'numTfactoryRuns': 8,\n", + " 'numTsPerRotation': None,\n", + " 'numTstates': 112,\n", + " 'physicalQubitsForAlgorithm': 10890,\n", + " 'physicalQubitsForTfactories': 97200,\n", + " 'requiredLogicalQubitErrorRate': 1.3227513227513228e-07,\n", + " 'requiredLogicalTstateErrorRate': 4.464285714285715e-06},\n", + " 'physicalQubits': 108090,\n", + " 'runtime': 369600},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", + " 'errorBudget': '1.00e-3',\n", + " 'errorBudgetLogical': '5.00e-4',\n", + " 'errorBudgetRotations': '0.00e0',\n", + " 'errorBudgetTstates': '5.00e-4',\n", + " 'logicalCycleTime': '4us 400ns',\n", + " 'logicalErrorRate': '3.00e-8',\n", + " 'numTsPerRotation': 'No rotations in algorithm',\n", + " 'numUnitsPerRound': '2',\n", + " 'physicalQubitsForTfactoriesPercentage': '89.93 %',\n", + " 'physicalQubitsPerRound': '6480',\n", + " 'requiredLogicalQubitErrorRate': '1.32e-7',\n", + " 'requiredLogicalTstateErrorRate': '4.46e-6',\n", + " 'runtime': '369us 600ns',\n", + " 'tfactoryRuntime': '46us 800ns',\n", + " 'tfactoryRuntimePerRound': '46us 800ns',\n", + " 'tstateLogicalErrorRate': '2.17e-6',\n", + " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", + " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", + " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", + " '**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.',\n", + " '**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).',\n", + " '**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.',\n", + " '**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.',\n", + " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", + " 'groups': [{'alwaysVisible': True,\n", + " 'entries': [{'description': 'Number of physical qubits',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 10890 physical qubits to implement the algorithm logic, and 97200 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'physicalCounts/physicalQubits'},\n", + " {'description': 'Total runtime',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (4us 400ns) multiplied by the 84 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/runtime'}],\n", + " 'title': 'Physical resource estimates'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 16$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 45$ logical qubits.',\n", + " 'label': 'Logical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", + " {'description': 'Number of logical cycles for the algorithm',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 0 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 28 CCZ and 0 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'label': 'Algorithmic depth',\n", + " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", + " {'description': 'Number of logical cycles performed',\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 84. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'label': 'Logical depth',\n", + " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", + " {'description': 'Number of T states consumed by the algorithm',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 28 CCZ and 0 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'label': 'Number of T states',\n", + " 'path': 'physicalCounts/breakdown/numTstates'},\n", + " {'description': \"Number of T factories capable of producing the demanded 112 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 15 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{112\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 369us 600ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " 'label': 'Number of T factories',\n", + " 'path': 'physicalCounts/breakdown/numTfactories'},\n", + " {'description': 'Number of times all T factories are invoked',\n", + " 'explanation': 'In order to prepare the 112 T states, the 15 copies of the T factory are repeatedly invoked 8 times.',\n", + " 'label': 'Number of T factory invocations',\n", + " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", + " {'description': 'Number of physical qubits for the algorithm after layout',\n", + " 'explanation': 'The 10890 are the product of the 45 logical qubits after layout and the 242 physical qubits that encode a single logical qubit.',\n", + " 'label': 'Physical algorithmic qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", + " {'description': 'Number of physical qubits for the T factories',\n", + " 'explanation': 'Each T factory requires 6480 physical qubits and we run 15 in parallel, therefore we need $97200 = 6480 \\\\cdot 15$ qubits.',\n", + " 'label': 'Physical T factory qubits',\n", + " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", + " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 45 logical qubits and the total cycle count 84.',\n", + " 'label': 'Required logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", + " {'description': 'The minimum T state error rate required for distilled T states',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 112.',\n", + " 'label': 'Required logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", + " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", + " 'explanation': 'The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.',\n", + " 'label': 'Number of T states per rotation',\n", + " 'path': 'physicalCountsFormatted/numTsPerRotation'}],\n", + " 'title': 'Resource estimates breakdown'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Name of QEC scheme',\n", + " 'explanation': 'You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.',\n", + " 'label': 'QEC scheme',\n", + " 'path': 'jobParams/qecScheme/name'},\n", + " {'description': 'Required code distance for error correction',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000013227513227513228)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'label': 'Code distance',\n", + " 'path': 'logicalQubit/codeDistance'},\n", + " {'description': 'Number of physical qubits per logical qubit',\n", + " 'explanation': 'The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'logicalQubit/physicalQubits'},\n", + " {'description': 'Duration of a logical cycle in nanoseconds',\n", + " 'explanation': 'The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.',\n", + " 'label': 'Logical cycle time',\n", + " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", + " {'description': 'Logical qubit error rate',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{11 + 1}{2}$',\n", + " 'label': 'Logical qubit error rate',\n", + " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", + " {'description': 'Crossing prefactor used in QEC scheme',\n", + " 'explanation': 'The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.',\n", + " 'label': 'Crossing prefactor',\n", + " 'path': 'jobParams/qecScheme/crossingPrefactor'},\n", + " {'description': 'Error correction threshold used in QEC scheme',\n", + " 'explanation': 'The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.',\n", + " 'label': 'Error correction threshold',\n", + " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", + " {'description': 'QEC scheme formula used to compute logical cycle time',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 4us 400ns.',\n", + " 'label': 'Logical cycle time formula',\n", + " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", + " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 242.',\n", + " 'label': 'Physical qubits formula',\n", + " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", + " 'title': 'Logical qubit parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of physical qubits for a single T factory',\n", + " 'explanation': 'This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.',\n", + " 'label': 'Physical qubits',\n", + " 'path': 'tfactory/physicalQubits'},\n", + " {'description': 'Runtime of a single T factory',\n", + " 'explanation': 'The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.',\n", + " 'label': 'Runtime',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", + " {'description': 'Number of output T states produced in a single run of T factory',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.',\n", + " 'label': 'Number of output T states per run',\n", + " 'path': 'tfactory/numTstates'},\n", + " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", + " 'explanation': 'This value includes the physical input T states of all copies of the distillation unit in the first round.',\n", + " 'label': 'Number of input T states per run',\n", + " 'path': 'tfactory/numInputTstates'},\n", + " {'description': 'The number of distillation rounds',\n", + " 'explanation': 'This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.',\n", + " 'label': 'Distillation rounds',\n", + " 'path': 'tfactory/numRounds'},\n", + " {'description': 'The number of units in each round of distillation',\n", + " 'explanation': 'This is the number of copies for the distillation units per round.',\n", + " 'label': 'Distillation units per round',\n", + " 'path': 'physicalCountsFormatted/numUnitsPerRound'},\n", + " {'description': 'The types of distillation units',\n", + " 'explanation': 'These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.',\n", + " 'label': 'Distillation units',\n", + " 'path': 'physicalCountsFormatted/unitNamePerRound'},\n", + " {'description': 'The code distance in each round of distillation',\n", + " 'explanation': 'This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.',\n", + " 'label': 'Distillation code distances',\n", + " 'path': 'physicalCountsFormatted/codeDistancePerRound'},\n", + " {'description': 'The number of physical qubits used in each round of distillation',\n", + " 'explanation': 'The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.',\n", + " 'label': 'Number of physical qubits per round',\n", + " 'path': 'physicalCountsFormatted/physicalQubitsPerRound'},\n", + " {'description': 'The runtime of each distillation round',\n", + " 'explanation': 'The runtime of the T factory is the sum of the runtimes in all rounds.',\n", + " 'label': 'Runtime per round',\n", + " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", + " {'description': 'Logical T state error rate',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 4.46e-6.',\n", + " 'label': 'Logical T state error rate',\n", + " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", + " 'title': 'T factory parameters'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", + " 'explanation': 'We determine 45 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'label': 'Logical qubits (pre-layout)',\n", + " 'path': 'logicalCounts/numQubits'},\n", + " {'description': 'Number of T gates in the input quantum program',\n", + " 'explanation': 'This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.',\n", + " 'label': 'T gates',\n", + " 'path': 'logicalCounts/tCount'},\n", + " {'description': 'Number of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.',\n", + " 'label': 'Rotation gates',\n", + " 'path': 'logicalCounts/rotationCount'},\n", + " {'description': 'Depth of rotation gates in the input quantum program',\n", + " 'explanation': 'This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.',\n", + " 'label': 'Rotation depth',\n", + " 'path': 'logicalCounts/rotationDepth'},\n", + " {'description': 'Number of CCZ-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCZ gates.',\n", + " 'label': 'CCZ gates',\n", + " 'path': 'logicalCounts/cczCount'},\n", + " {'description': 'Number of CCiX-gates in the input quantum program',\n", + " 'explanation': 'This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].',\n", + " 'label': 'CCiX gates',\n", + " 'path': 'logicalCounts/ccixCount'},\n", + " {'description': 'Number of single qubit measurements in the input quantum program',\n", + " 'explanation': 'This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.',\n", + " 'label': 'Measurement operations',\n", + " 'path': 'logicalCounts/measurementCount'}],\n", + " 'title': 'Pre-layout logical resources'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Total error budget for the algorithm',\n", + " 'explanation': \"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\n", + " 'label': 'Total error budget',\n", + " 'path': 'physicalCountsFormatted/errorBudget'},\n", + " {'description': 'Probability of at least one logical error',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'Logical error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetLogical'},\n", + " {'description': 'Probability of at least one faulty T distillation',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.',\n", + " 'label': 'T distillation error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetTstates'},\n", + " {'description': 'Probability of at least one failed rotation synthesis',\n", + " 'explanation': 'This is one third of the total error budget 1.00e-3.',\n", + " 'label': 'Rotation synthesis error probability',\n", + " 'path': 'physicalCountsFormatted/errorBudgetRotations'}],\n", + " 'title': 'Assumed error budget'},\n", + " {'alwaysVisible': False,\n", + " 'entries': [{'description': 'Some descriptive name for the qubit model',\n", + " 'explanation': 'You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).',\n", + " 'label': 'Qubit name',\n", + " 'path': 'jobParams/qubitParams/name'},\n", + " {'description': 'Underlying qubit technology (gate-based or Majorana)',\n", + " 'explanation': 'When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.',\n", + " 'label': 'Instruction set',\n", + " 'path': 'jobParams/qubitParams/instructionSet'},\n", + " {'description': 'Operation time for single-qubit measurement (t_meas) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.',\n", + " 'label': 'Single-qubit measurement time',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementTime'},\n", + " {'description': 'Operation time for single-qubit gate (t_gate) in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.',\n", + " 'label': 'Single-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateTime'},\n", + " {'description': 'Operation time for two-qubit gate in ns',\n", + " 'explanation': 'This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.',\n", + " 'label': 'Two-qubit gate time',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateTime'},\n", + " {'description': 'Operation time for a T gate',\n", + " 'explanation': 'This is the operation time in nanoseconds to execute a T gate.',\n", + " 'label': 'T gate time',\n", + " 'path': 'jobParams/qubitParams/tGateTime'},\n", + " {'description': 'Error rate for single-qubit measurement',\n", + " 'explanation': 'This is the probability in which a single-qubit measurement in the Pauli basis may fail.',\n", + " 'label': 'Single-qubit measurement error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitMeasurementErrorRate'},\n", + " {'description': 'Error rate for single-qubit Clifford gate (p)',\n", + " 'explanation': 'This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.',\n", + " 'label': 'Single-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/oneQubitGateErrorRate'},\n", + " {'description': 'Error rate for two-qubit Clifford gate',\n", + " 'explanation': 'This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.',\n", + " 'label': 'Two-qubit error rate',\n", + " 'path': 'jobParams/qubitParams/twoQubitGateErrorRate'},\n", + " {'description': 'Error rate to prepare single-qubit T state or apply a T gate (p_T)',\n", + " 'explanation': 'This is the probability in which executing a single T gate may fail.',\n", + " 'label': 'T gate error rate',\n", + " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", + " 'title': 'Physical qubit parameters'}]},\n", + " 'status': 'success',\n", + " 'tfactory': {'codeDistancePerRound': [9],\n", + " 'logicalErrorRate': 2.165000000000001e-06,\n", + " 'numInputTstates': 30,\n", + " 'numRounds': 1,\n", + " 'numTstates': 1,\n", + " 'numUnitsPerRound': [2],\n", + " 'physicalQubits': 6480,\n", + " 'physicalQubitsPerRound': [6480],\n", + " 'runtime': 46800.0,\n", + " 'runtimePerRound': [46800.0],\n", + " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# If you need to pull up the results of an old job, use its job ID with qsharp.azure.output command\n", + "# result = qsharp.azure.output(\"...\")\n", + "result" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [], + "source": [ + "# The function that extracts the relevant resource information from the resource estimation job results and produces your absolute score.\n", + "def evaluate_results(res) : \n", + " width = res['physicalCounts']['breakdown']['algorithmicLogicalQubits']\n", + " depth = res['physicalCounts']['breakdown']['algorithmicLogicalDepth']\n", + " print(f\"Logical algorithmic qubits = {width}\")\n", + " print(f\"Algorithmic depth = {depth}\")\n", + " print(f\"Score = {width * depth}\")\n", + " return width * depth\n" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false, + "source_hidden": false + }, + "nteract": { + "transient": { + "deleting": false + } + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Logical algorithmic qubits = 45\n", + "Algorithmic depth = 84\n", + "Score = 3780\n" + ] + }, + { + "data": { + "text/plain": [ + "3780" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "evaluate_results(result)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernel_info": { + "name": "python3" + }, + "kernelspec": { + "display_name": "Python 3 [Q#]", + "language": "python", + "name": "python3_qsharp_b54crn" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.10" + }, + "nteract": { + "version": "nteract-front-end@1.0.0" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/team_solutions/schrodingers-duck/iQuHack-challenge-2023-task5.ipynb b/team_solutions/schrodingers-duck/iQuHack-challenge-2023-task5.ipynb index 9d4c433..ab667c9 100644 --- a/team_solutions/schrodingers-duck/iQuHack-challenge-2023-task5.ipynb +++ b/team_solutions/schrodingers-duck/iQuHack-challenge-2023-task5.ipynb @@ -67,7 +67,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "collapsed": false, "jupyter": { @@ -89,7 +89,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": { "collapsed": false, "jupyter": { @@ -111,7 +111,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": { "collapsed": false, "jupyter": { @@ -148,7 +148,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": { "collapsed": false, "jupyter": { @@ -211,83 +211,16 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 5, "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\r\n", - "
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SourceCallable
(notebook)Task5
(notebook)QubitArrayWrapperOperation
/home/jovyan/2023_microsoft/D:\\a\\1\\s\\submodules\\qsharp-runtime\\src\\Simulation\\TargetDefinitions\\Decompositions\\AssertOperationsEqualReferenced.qs:0Microsoft.Quantum.Diagnostics.AssertOperationsEqualReferenced
(notebook)TestCompoundGate
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\r\n", "

\r\n", " \r\n", " \r\n", @@ -464,12 +397,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -489,12 +422,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -514,12 +447,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -539,12 +472,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -564,12 +497,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -589,12 +522,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -614,12 +547,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -639,12 +572,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -664,12 +597,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -689,12 +622,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -714,12 +647,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -739,12 +672,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -764,12 +697,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -789,12 +722,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -814,12 +747,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -839,12 +772,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -864,12 +797,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -889,12 +822,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -914,12 +847,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -939,12 +872,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -964,12 +897,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -989,12 +922,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1014,12 +947,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1039,12 +972,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1064,12 +997,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1089,12 +1022,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1114,12 +1047,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1139,12 +1072,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1164,12 +1097,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1189,12 +1122,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1214,12 +1147,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1239,12 +1172,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1264,12 +1197,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1289,12 +1222,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1314,12 +1247,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1339,12 +1272,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1364,12 +1297,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1389,12 +1322,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1414,12 +1347,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1439,12 +1372,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1464,12 +1397,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1489,12 +1422,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1514,12 +1447,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1539,12 +1472,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1564,12 +1497,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1589,12 +1522,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1614,12 +1547,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1639,12 +1572,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1664,12 +1597,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1689,12 +1622,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1714,12 +1647,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1739,12 +1672,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1764,12 +1697,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1789,12 +1722,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1814,12 +1747,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1839,12 +1772,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1864,12 +1797,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1889,12 +1822,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1914,12 +1847,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1939,12 +1872,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1964,12 +1897,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2056,7 +1989,7 @@ "()" ] }, - "execution_count": 6, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } @@ -2119,23 +2052,23 @@ { "data": { "text/plain": [ - "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 284985},\n", - " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 412930},\n", + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 180463},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 429377},\n", " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 2},\n", " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", - " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 257411},\n", + " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", - " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 4298},\n", - " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 137},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 412},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 164},\n", " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", - " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 257411},\n", + " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", - " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 4298},\n", - " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 137},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 412},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 164},\n", " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", @@ -2219,10 +2152,10 @@ "Submitting Task5_ResourceEstimationWrapper to target microsoft.estimator...\n", "Job successfully submitted.\n", " Job name: RE for the task 5\n", - " Job ID: ce9dd9e8-528c-46ec-94d2-289b8fed02a7\n", + " Job ID: ae64a7d8-db3c-4bf6-a371-91dc1499d013\n", "Waiting up to 30 seconds for Azure Quantum job to complete...\n", - "[11:30:22 PM] Current job status: Executing\n", - "[11:30:27 PM] Current job status: Succeeded\n" + "[2:09:44 PM] Current job status: Executing\n", + "[2:09:49 PM] Current job status: Succeeded\n" ] } ], diff --git a/team_solutions/schrodingers-duck/iQuHack-challenge-2023-task6.ipynb b/team_solutions/schrodingers-duck/iQuHack-challenge-2023-task6.ipynb index 330ddb9..f811e97 100644 --- a/team_solutions/schrodingers-duck/iQuHack-challenge-2023-task6.ipynb +++ b/team_solutions/schrodingers-duck/iQuHack-challenge-2023-task6.ipynb @@ -67,7 +67,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 1, "metadata": { "collapsed": false, "jupyter": { @@ -80,7 +80,15 @@ } } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Preparing Q# environment...\n" + ] + } + ], "source": [ "# Run this code cell to import the modules required to work with Q# and Azure\n", "import qsharp\n", @@ -89,7 +97,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 2, "metadata": { "collapsed": false, "jupyter": { @@ -111,7 +119,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 3, "metadata": { "collapsed": false, "jupyter": { @@ -148,7 +156,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 4, "metadata": { "collapsed": false, "jupyter": { @@ -196,7 +204,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ @@ -205,7 +213,7 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 6, "metadata": { "collapsed": false, "jupyter": { @@ -262,7 +270,7 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 7, "metadata": { "collapsed": false, "jupyter": { @@ -307,12 +315,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -332,12 +340,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -357,12 +365,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -382,12 +390,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -407,12 +415,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -432,12 +440,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -457,12 +465,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -482,12 +490,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -507,12 +515,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -532,12 +540,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -557,12 +565,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -582,12 +590,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -607,12 +615,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -632,12 +640,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -657,12 +665,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -682,12 +690,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -707,12 +715,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -732,12 +740,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -757,12 +765,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -782,12 +790,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -807,12 +815,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -832,12 +840,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -857,12 +865,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -882,12 +890,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -907,12 +915,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -932,12 +940,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -957,12 +965,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -982,12 +990,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1007,12 +1015,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1032,12 +1040,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1057,12 +1065,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1082,12 +1090,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1107,12 +1115,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1132,12 +1140,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1157,12 +1165,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1182,12 +1190,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1207,12 +1215,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1232,12 +1240,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1257,12 +1265,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1282,12 +1290,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1307,12 +1315,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1332,12 +1340,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1357,12 +1365,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1382,12 +1390,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1407,12 +1415,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1432,12 +1440,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1457,12 +1465,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1482,12 +1490,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1507,12 +1515,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1532,12 +1540,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1557,12 +1565,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1582,12 +1590,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1607,12 +1615,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1632,12 +1640,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1657,12 +1665,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1682,12 +1690,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1707,12 +1715,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1732,12 +1740,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1757,12 +1765,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1782,12 +1790,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1807,12 +1815,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1832,12 +1840,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1857,12 +1865,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1882,12 +1890,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1907,12 +1915,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1932,12 +1940,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1957,12 +1965,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1982,12 +1990,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2007,12 +2015,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2032,12 +2040,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2057,12 +2065,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2082,12 +2090,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2107,12 +2115,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2132,12 +2140,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2157,12 +2165,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2182,12 +2190,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2207,12 +2215,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2232,12 +2240,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2257,12 +2265,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2282,12 +2290,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2307,12 +2315,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2332,12 +2340,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2357,12 +2365,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2382,12 +2390,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2407,12 +2415,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2432,12 +2440,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2457,12 +2465,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2482,12 +2490,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2507,12 +2515,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2532,12 +2540,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2557,12 +2565,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2582,12 +2590,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2607,12 +2615,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2632,12 +2640,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2657,12 +2665,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2682,12 +2690,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2707,12 +2715,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2732,12 +2740,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2757,12 +2765,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2782,12 +2790,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2807,12 +2815,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2832,12 +2840,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2857,12 +2865,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2882,12 +2890,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2907,12 +2915,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2932,12 +2940,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2957,12 +2965,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2982,12 +2990,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3007,12 +3015,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3032,12 +3040,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3057,12 +3065,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3082,12 +3090,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3107,12 +3115,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3132,12 +3140,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3157,12 +3165,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3182,12 +3190,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3207,12 +3215,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3232,12 +3240,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3257,12 +3265,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3282,12 +3290,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3307,12 +3315,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3332,12 +3340,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3357,12 +3365,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3382,12 +3390,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3407,12 +3415,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3432,12 +3440,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3457,12 +3465,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3482,12 +3490,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3507,12 +3515,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3532,12 +3540,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3557,12 +3565,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3582,12 +3590,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3607,12 +3615,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3632,12 +3640,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3657,12 +3665,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3682,12 +3690,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3707,12 +3715,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3732,12 +3740,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3757,12 +3765,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3782,12 +3790,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3807,12 +3815,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3832,12 +3840,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3857,12 +3865,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3882,12 +3890,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3907,12 +3915,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3932,12 +3940,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3957,12 +3965,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3982,12 +3990,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4007,12 +4015,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4032,12 +4040,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4057,12 +4065,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4082,12 +4090,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4107,12 +4115,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4132,12 +4140,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4157,12 +4165,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4182,12 +4190,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4207,12 +4215,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4232,12 +4240,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4257,12 +4265,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4282,12 +4290,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4307,12 +4315,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4332,12 +4340,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4357,12 +4365,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4382,12 +4390,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4407,12 +4415,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4432,12 +4440,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4457,12 +4465,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4482,12 +4490,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4507,12 +4515,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4532,12 +4540,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4557,12 +4565,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4582,12 +4590,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4607,12 +4615,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4632,12 +4640,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4657,12 +4665,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4682,12 +4690,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4707,12 +4715,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4732,12 +4740,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4757,12 +4765,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4782,12 +4790,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4807,12 +4815,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4832,12 +4840,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4857,12 +4865,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4882,12 +4890,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4907,12 +4915,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4932,12 +4940,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4957,12 +4965,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -4982,12 +4990,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5007,12 +5015,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5032,12 +5040,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5057,12 +5065,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5082,12 +5090,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5107,12 +5115,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5132,12 +5140,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5157,12 +5165,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5182,12 +5190,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5207,12 +5215,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5232,12 +5240,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5257,12 +5265,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5282,12 +5290,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5307,12 +5315,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5332,12 +5340,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5357,12 +5365,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5382,12 +5390,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5407,12 +5415,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5432,12 +5440,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5457,12 +5465,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5482,12 +5490,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5507,12 +5515,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5532,12 +5540,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5557,12 +5565,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5582,12 +5590,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5607,12 +5615,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5632,12 +5640,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5657,12 +5665,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5682,12 +5690,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5707,12 +5715,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5732,12 +5740,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5757,12 +5765,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5782,12 +5790,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5807,12 +5815,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5832,12 +5840,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5857,12 +5865,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5882,12 +5890,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5907,12 +5915,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5932,12 +5940,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5957,12 +5965,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -5982,12 +5990,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6007,12 +6015,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6032,12 +6040,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6057,12 +6065,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6082,12 +6090,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6107,12 +6115,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6132,12 +6140,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6157,12 +6165,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6182,12 +6190,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6207,12 +6215,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -6232,12 +6240,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -6257,12 +6265,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -6282,12 +6290,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -6307,12 +6315,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -6332,12 +6340,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -6357,12 +6365,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -6382,12 +6390,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -6407,12 +6415,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -6432,12 +6440,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -6457,12 +6465,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -6482,12 +6490,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -6507,12 +6515,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -6532,12 +6540,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -6557,12 +6565,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -6582,12 +6590,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -6607,12 +6615,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -6632,12 +6640,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -6657,12 +6665,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -6682,12 +6690,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", " \r\n", " \r\n", @@ -6966,7 +6974,7 @@ "()" ] }, - "execution_count": 30, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } @@ -6995,7 +7003,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 8, "metadata": { "collapsed": false, "jupyter": { @@ -7029,23 +7037,23 @@ { "data": { "text/plain": [ - "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 178621},\n", - " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 409767},\n", - " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 4},\n", + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 180106},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 429377},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 2},\n", " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", - " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 70},\n", - " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 168},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 445},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 163},\n", " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", - " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 70},\n", - " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 168},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 445},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 163},\n", " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", @@ -7053,7 +7061,7 @@ " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" ] }, - "execution_count": 31, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -7069,7 +7077,7 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 9, "metadata": { "collapsed": false, "jupyter": { @@ -7097,7 +7105,7 @@ "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" ] }, - "execution_count": 32, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } @@ -7108,7 +7116,7 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 10, "metadata": { "collapsed": false, "jupyter": { @@ -7129,10 +7137,10 @@ "Submitting Task6_ResourceEstimationWrapper to target microsoft.estimator...\n", "Job successfully submitted.\n", " Job name: RE for the task 6\n", - " Job ID: 51c97eab-212e-45b6-9f03-7489fad62c36\n", + " Job ID: 9acb26ad-ff11-4b7d-8502-bc6a6f2ca438\n", "Waiting up to 30 seconds for Azure Quantum job to complete...\n", - "[1:15:38 PM] Current job status: Executing\n", - "[1:15:43 PM] Current job status: Succeeded\n" + "[2:12:45 PM] Current job status: Executing\n", + "[2:12:50 PM] Current job status: Succeeded\n" ] } ], @@ -7143,7 +7151,7 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 11, "metadata": { "collapsed": false, "jupyter": { @@ -7159,7 +7167,7 @@ "outputs": [ { "data": { - "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":96,\"cczCount\":16,\"measurementCount\":96,\"numQubits\":15,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":13,\"logicalCycleTime\":5200.0,\"logicalErrorRate\":3.000000000000002E-09,\"physicalQubits\":338},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":432,\"algorithmicLogicalQubits\":42,\"cliffordErrorRate\":0.001,\"logicalDepth\":432,\"numTfactories\":12,\"numTfactoryRuns\":38,\"numTsPerRotation\":null,\"numTstates\":448,\"physicalQubitsForAlgorithm\":14196,\"physicalQubitsForTfactories\":116160,\"requiredLogicalQubitErrorRate\":2.755731922398589E-08,\"requiredLogicalTstateErrorRate\":1.1160714285714287E-06},\"physicalQubits\":130356,\"runtime\":2246400},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"11\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"5us 200ns\",\"logicalErrorRate\":\"3.00e-9\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"89.11 %\",\"physicalQubitsPerRound\":\"9680\",\"requiredLogicalQubitErrorRate\":\"2.76e-8\",\"requiredLogicalTstateErrorRate\":\"1.12e-6\",\"runtime\":\"2ms 246us 400ns\",\"tfactoryRuntime\":\"57us 200ns\",\"tfactoryRuntimePerRound\":\"57us 200ns\",\"tstateLogicalErrorRate\":\"2.48e-7\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 14196 physical qubits to implement the algorithm logic, and 116160 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (5us 200ns) multiplied by the 432 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 15$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 42$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 96 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 16 CCZ and 96 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 432. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 16 CCZ and 96 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 448 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{448\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 2ms 246us 400ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 448 T states, the 12 copies of the T factory are repeatedly invoked 38 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 14196 are the product of the 42 logical qubits after layout and the 338 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 9680 physical qubits and we run 12 in parallel, therefore we need $116160 = 9680 \\\\cdot 12$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 42 logical qubits and the total cycle count 432.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 448.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000002755731922398589)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{13 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 5us 200ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 338.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.12e-6.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 42 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[11],\"logicalErrorRate\":2.480000000000001E-07,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":9680,\"physicalQubitsPerRound\":[9680],\"runtime\":57200.0,\"runtimePerRound\":[57200.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", + "application/x-qsharp-data": "{\"errorBudget\":{\"logical\":0.0005,\"rotations\":0.0,\"tstates\":0.0005},\"jobParams\":{\"errorBudget\":0.001,\"qecScheme\":{\"crossingPrefactor\":0.03,\"errorCorrectionThreshold\":0.01,\"logicalCycleTime\":\"(4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance\",\"name\":\"surface_code\",\"physicalQubitsPerLogicalQubit\":\"2 * codeDistance * codeDistance\"},\"qubitParams\":{\"instructionSet\":\"GateBased\",\"name\":\"qubit_gate_ns_e3\",\"oneQubitGateErrorRate\":0.001,\"oneQubitGateTime\":\"50 ns\",\"oneQubitMeasurementErrorRate\":0.001,\"oneQubitMeasurementTime\":\"100 ns\",\"tGateErrorRate\":0.001,\"tGateTime\":\"50 ns\",\"twoQubitGateErrorRate\":0.001,\"twoQubitGateTime\":\"50 ns\"}},\"logicalCounts\":{\"ccixCount\":6,\"cczCount\":2,\"measurementCount\":6,\"numQubits\":12,\"rotationCount\":0,\"rotationDepth\":0,\"tCount\":0},\"logicalQubit\":{\"codeDistance\":9,\"logicalCycleTime\":3600.0,\"logicalErrorRate\":3.0000000000000015E-07,\"physicalQubits\":162},\"physicalCounts\":{\"breakdown\":{\"algorithmicLogicalDepth\":30,\"algorithmicLogicalQubits\":35,\"cliffordErrorRate\":0.001,\"logicalDepth\":30,\"numTfactories\":14,\"numTfactoryRuns\":3,\"numTsPerRotation\":null,\"numTstates\":32,\"physicalQubitsForAlgorithm\":5670,\"physicalQubitsForTfactories\":90720,\"requiredLogicalQubitErrorRate\":4.761904761904762E-07,\"requiredLogicalTstateErrorRate\":1.5625E-05},\"physicalQubits\":96390,\"runtime\":108000},\"physicalCountsFormatted\":{\"codeDistancePerRound\":\"9\",\"errorBudget\":\"1.00e-3\",\"errorBudgetLogical\":\"5.00e-4\",\"errorBudgetRotations\":\"0.00e0\",\"errorBudgetTstates\":\"5.00e-4\",\"logicalCycleTime\":\"3us 600ns\",\"logicalErrorRate\":\"3.00e-7\",\"numTsPerRotation\":\"No rotations in algorithm\",\"numUnitsPerRound\":\"2\",\"physicalQubitsForTfactoriesPercentage\":\"94.12 %\",\"physicalQubitsPerRound\":\"6480\",\"requiredLogicalQubitErrorRate\":\"4.76e-7\",\"requiredLogicalTstateErrorRate\":\"1.56e-5\",\"runtime\":\"108us\",\"tfactoryRuntime\":\"46us 800ns\",\"tfactoryRuntimePerRound\":\"46us 800ns\",\"tstateLogicalErrorRate\":\"2.17e-6\",\"unitNamePerRound\":\"15-to-1 space efficient logical\"},\"reportData\":{\"assumptions\":[\"_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._\",\"**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.\",\"**Efficient classical computation.** We assume that classical overhead (compilation, control, feedback, readout, decoding, etc.) does not dominate the overall cost of implementing the full quantum algorithm.\",\"**Extraction circuits for planar quantum ISA.** We assume that stabilizer extraction circuits with similar depth and error correction performance to those for standard surface and Hastings-Haah code patches can be constructed to implement all operations of the planar quantum ISA (instruction set architecture).\",\"**Uniform independent logical noise.** We assume that the error rate of a logical operation is approximately equal to its space-time volume (the number of tiles multiplied by the number of logical time steps) multiplied by the error rate of a logical qubit in a standard one-tile patch in one logical time step.\",\"**Negligible Clifford costs for synthesis.** We assume that the space overhead for synthesis and space and time overhead for transport of magic states within magic state factories and to synthesis qubits are all negligible.\",\"**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.\"],\"groups\":[{\"alwaysVisible\":true,\"entries\":[{\"description\":\"Number of physical qubits\",\"explanation\":\"This value represents the total number of physical qubits, which is the sum of 5670 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.\",\"label\":\"Physical qubits\",\"path\":\"physicalCounts/physicalQubits\"},{\"description\":\"Total runtime\",\"explanation\":\"This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 30 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/runtime\"}],\"title\":\"Physical resource estimates\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits for the algorithm after layout\",\"explanation\":\"Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 12$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 35$ logical qubits.\",\"label\":\"Logical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalQubits\"},{\"description\":\"Number of logical cycles for the algorithm\",\"explanation\":\"To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 6 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 2 CCZ and 6 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.\",\"label\":\"Algorithmic depth\",\"path\":\"physicalCounts/breakdown/algorithmicLogicalDepth\"},{\"description\":\"Number of logical cycles performed\",\"explanation\":\"This number is usually equal to the logical depth of the algorithm, which is 30. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\"label\":\"Logical depth\",\"path\":\"physicalCounts/breakdown/logicalDepth\"},{\"description\":\"Number of T states consumed by the algorithm\",\"explanation\":\"To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 2 CCZ and 6 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.\",\"label\":\"Number of T states\",\"path\":\"physicalCounts/breakdown/numTstates\"},{\"description\":\"Number of T factories capable of producing the demanded 32 T states during the algorithm's runtime\",\"explanation\":\"The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{32\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 108us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$\",\"label\":\"Number of T factories\",\"path\":\"physicalCounts/breakdown/numTfactories\"},{\"description\":\"Number of times all T factories are invoked\",\"explanation\":\"In order to prepare the 32 T states, the 14 copies of the T factory are repeatedly invoked 3 times.\",\"label\":\"Number of T factory invocations\",\"path\":\"physicalCounts/breakdown/numTfactoryRuns\"},{\"description\":\"Number of physical qubits for the algorithm after layout\",\"explanation\":\"The 5670 are the product of the 35 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.\",\"label\":\"Physical algorithmic qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForAlgorithm\"},{\"description\":\"Number of physical qubits for the T factories\",\"explanation\":\"Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\\\cdot 14$ qubits.\",\"label\":\"Physical T factory qubits\",\"path\":\"physicalCounts/breakdown/physicalQubitsForTfactories\"},{\"description\":\"The minimum logical qubit error rate required to run the algorithm within the error budget\",\"explanation\":\"The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 35 logical qubits and the total cycle count 30.\",\"label\":\"Required logical qubit error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalQubitErrorRate\"},{\"description\":\"The minimum T state error rate required for distilled T states\",\"explanation\":\"The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 32.\",\"label\":\"Required logical T state error rate\",\"path\":\"physicalCountsFormatted/requiredLogicalTstateErrorRate\"},{\"description\":\"Number of T states to implement a rotation with an arbitrary angle\",\"explanation\":\"The number of T states to implement a rotation with an arbitrary angle is $\\\\lceil 0.53 \\\\log_2(0 / 0) + 5.3\\\\rceil$ [[arXiv:2203.10064](https://arxiv.org/abs/2203.10064)]. For simplicity, we use this formula for all single-qubit arbitrary angle rotations, and do not distinguish between best, worst, and average cases.\",\"label\":\"Number of T states per rotation\",\"path\":\"physicalCountsFormatted/numTsPerRotation\"}],\"title\":\"Resource estimates breakdown\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Name of QEC scheme\",\"explanation\":\"You can load pre-defined QEC schemes by using the name `surface_code` or `floquet_code`. The latter only works with Majorana qubits.\",\"label\":\"QEC scheme\",\"path\":\"jobParams/qecScheme/name\"},{\"description\":\"Required code distance for error correction\",\"explanation\":\"The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.0000004761904761904762)}{\\\\log(0.01/0.001)} - 1$\",\"label\":\"Code distance\",\"path\":\"logicalQubit/codeDistance\"},{\"description\":\"Number of physical qubits per logical qubit\",\"explanation\":\"The number of physical qubits per logical qubit are evaluated using the formula 2 * codeDistance * codeDistance that can be user-specified.\",\"label\":\"Physical qubits\",\"path\":\"logicalQubit/physicalQubits\"},{\"description\":\"Duration of a logical cycle in nanoseconds\",\"explanation\":\"The runtime of one logical cycle in nanoseconds is evaluated using the formula (4 * twoQubitGateTime + 2 * oneQubitMeasurementTime) * codeDistance that can be user-specified.\",\"label\":\"Logical cycle time\",\"path\":\"physicalCountsFormatted/logicalCycleTime\"},{\"description\":\"Logical qubit error rate\",\"explanation\":\"The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{9 + 1}{2}$\",\"label\":\"Logical qubit error rate\",\"path\":\"physicalCountsFormatted/logicalErrorRate\"},{\"description\":\"Crossing prefactor used in QEC scheme\",\"explanation\":\"The crossing prefactor is usually extracted numerically from simulations when fitting an exponential curve to model the relationship between logical and physical error rate.\",\"label\":\"Crossing prefactor\",\"path\":\"jobParams/qecScheme/crossingPrefactor\"},{\"description\":\"Error correction threshold used in QEC scheme\",\"explanation\":\"The error correction threshold is the physical error rate below which the error rate of the logical qubit is less than the error rate of the physical qubit that constitute it. This value is usually extracted numerically from simulations of the logical error rate.\",\"label\":\"Error correction threshold\",\"path\":\"jobParams/qecScheme/errorCorrectionThreshold\"},{\"description\":\"QEC scheme formula used to compute logical cycle time\",\"explanation\":\"This is the formula that is used to compute the logical cycle time 3us 600ns.\",\"label\":\"Logical cycle time formula\",\"path\":\"jobParams/qecScheme/logicalCycleTime\"},{\"description\":\"QEC scheme formula used to compute number of physical qubits per logical qubit\",\"explanation\":\"This is the formula that is used to compute the number of physical qubits per logical qubits 162.\",\"label\":\"Physical qubits formula\",\"path\":\"jobParams/qecScheme/physicalQubitsPerLogicalQubit\"}],\"title\":\"Logical qubit parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of physical qubits for a single T factory\",\"explanation\":\"This corresponds to the maximum number of physical qubits over all rounds of T distillation units in a T factory. A round of distillation contains of multiple copies of distillation units to achieve the required success probability of producing a T state with the expected logical T state error rate.\",\"label\":\"Physical qubits\",\"path\":\"tfactory/physicalQubits\"},{\"description\":\"Runtime of a single T factory\",\"explanation\":\"The runtime of a single T factory is the accumulated runtime of executing each round in a T factory.\",\"label\":\"Runtime\",\"path\":\"physicalCountsFormatted/tfactoryRuntime\"},{\"description\":\"Number of output T states produced in a single run of T factory\",\"explanation\":\"The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.\",\"label\":\"Number of output T states per run\",\"path\":\"tfactory/numTstates\"},{\"description\":\"Number of physical input T states consumed in a single run of a T factory\",\"explanation\":\"This value includes the physical input T states of all copies of the distillation unit in the first round.\",\"label\":\"Number of input T states per run\",\"path\":\"tfactory/numInputTstates\"},{\"description\":\"The number of distillation rounds\",\"explanation\":\"This is the number of distillation rounds. In each round one or multiple copies of some distillation unit is executed.\",\"label\":\"Distillation rounds\",\"path\":\"tfactory/numRounds\"},{\"description\":\"The number of units in each round of distillation\",\"explanation\":\"This is the number of copies for the distillation units per round.\",\"label\":\"Distillation units per round\",\"path\":\"physicalCountsFormatted/numUnitsPerRound\"},{\"description\":\"The types of distillation units\",\"explanation\":\"These are the types of distillation units that are executed in each round. The units can be either physical or logical, depending on what type of qubit they are operating. Space-efficient units require fewer qubits for the cost of longer runtime compared to Reed-Muller preparation units.\",\"label\":\"Distillation units\",\"path\":\"physicalCountsFormatted/unitNamePerRound\"},{\"description\":\"The code distance in each round of distillation\",\"explanation\":\"This is the code distance used for the units in each round. If the code distance is 1, then the distillation unit operates on physical qubits instead of error-corrected logical qubits.\",\"label\":\"Distillation code distances\",\"path\":\"physicalCountsFormatted/codeDistancePerRound\"},{\"description\":\"The number of physical qubits used in each round of distillation\",\"explanation\":\"The maximum number of physical qubits over all rounds is the number of physical qubits for the T factory, since qubits are reused by different rounds.\",\"label\":\"Number of physical qubits per round\",\"path\":\"physicalCountsFormatted/physicalQubitsPerRound\"},{\"description\":\"The runtime of each distillation round\",\"explanation\":\"The runtime of the T factory is the sum of the runtimes in all rounds.\",\"label\":\"Runtime per round\",\"path\":\"physicalCountsFormatted/tfactoryRuntimePerRound\"},{\"description\":\"Logical T state error rate\",\"explanation\":\"This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.56e-5.\",\"label\":\"Logical T state error rate\",\"path\":\"physicalCountsFormatted/tstateLogicalErrorRate\"}],\"title\":\"T factory parameters\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Number of logical qubits in the input quantum program\",\"explanation\":\"We determine 35 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.\",\"label\":\"Logical qubits (pre-layout)\",\"path\":\"logicalCounts/numQubits\"},{\"description\":\"Number of T gates in the input quantum program\",\"explanation\":\"This includes all T gates and adjoint T gates, but not T gates used to implement rotation gates with arbitrary angle, CCZ gates, or CCiX gates.\",\"label\":\"T gates\",\"path\":\"logicalCounts/tCount\"},{\"description\":\"Number of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all rotation gates. If an angle corresponds to a Pauli, Clifford, or T gate, it is not accounted for in this number.\",\"label\":\"Rotation gates\",\"path\":\"logicalCounts/rotationCount\"},{\"description\":\"Depth of rotation gates in the input quantum program\",\"explanation\":\"This is the number of all non-Clifford layers that include at least one single-qubit rotation gate with an arbitrary angle.\",\"label\":\"Rotation depth\",\"path\":\"logicalCounts/rotationDepth\"},{\"description\":\"Number of CCZ-gates in the input quantum program\",\"explanation\":\"This is the number of CCZ gates.\",\"label\":\"CCZ gates\",\"path\":\"logicalCounts/cczCount\"},{\"description\":\"Number of CCiX-gates in the input quantum program\",\"explanation\":\"This is the number of CCiX gates, which applies $-iX$ controlled on two control qubits [[1212.5069](https://arxiv.org/abs/1212.5069)].\",\"label\":\"CCiX gates\",\"path\":\"logicalCounts/ccixCount\"},{\"description\":\"Number of single qubit measurements in the input quantum program\",\"explanation\":\"This is the number of single qubit measurements in Pauli basis that are used in the input program. Note that all measurements are counted, however, the measurement result is is determined randomly (with a fixed seed) to be 0 or 1 with a probability of 50%.\",\"label\":\"Measurement operations\",\"path\":\"logicalCounts/measurementCount\"}],\"title\":\"Pre-layout logical resources\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Total error budget for the algorithm\",\"explanation\":\"The total error budget sets the overall allowed error for the algorithm, i.e., the number of times it is allowed to fail. Its value must be between 0 and 1 and the default value is 0.001, which corresponds to 0.1%, and means that the algorithm is allowed to fail once in 1000 executions. This parameter is highly application specific. For example, if one is running Shor's algorithm for factoring integers, a large value for the error budget may be tolerated as one can check that the output are indeed the prime factors of the input. On the other hand, a much smaller error budget may be needed for an algorithm solving a problem with a solution which cannot be efficiently verified. This budget $\\\\epsilon = \\\\epsilon_{\\\\log} + \\\\epsilon_{\\\\rm dis} + \\\\epsilon_{\\\\rm syn}$ is uniformly distributed and applies to errors $\\\\epsilon_{\\\\log}$ to implement logical qubits, an error budget $\\\\epsilon_{\\\\rm dis}$ to produce T states through distillation, and an error budget $\\\\epsilon_{\\\\rm syn}$ to synthesize rotation gates with arbitrary angles. Note that for distillation and rotation synthesis, the respective error budgets $\\\\epsilon_{\\\\rm dis}$ and $\\\\epsilon_{\\\\rm syn}$ are uniformly distributed among all T states and all rotation gates, respectively. If there are no rotation gates in the input algorithm, the error budget is uniformly distributed to logical errors and T state errors.\",\"label\":\"Total error budget\",\"path\":\"physicalCountsFormatted/errorBudget\"},{\"description\":\"Probability of at least one logical error\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"Logical error probability\",\"path\":\"physicalCountsFormatted/errorBudgetLogical\"},{\"description\":\"Probability of at least one faulty T distillation\",\"explanation\":\"This is one third of the total error budget 1.00e-3 if the input algorithm contains rotation with gates with arbitrary angles, or one half of it, otherwise.\",\"label\":\"T distillation error probability\",\"path\":\"physicalCountsFormatted/errorBudgetTstates\"},{\"description\":\"Probability of at least one failed rotation synthesis\",\"explanation\":\"This is one third of the total error budget 1.00e-3.\",\"label\":\"Rotation synthesis error probability\",\"path\":\"physicalCountsFormatted/errorBudgetRotations\"}],\"title\":\"Assumed error budget\"},{\"alwaysVisible\":false,\"entries\":[{\"description\":\"Some descriptive name for the qubit model\",\"explanation\":\"You can load pre-defined qubit parameters by using the names `qubit_gate_ns_e3`, `qubit_gate_ns_e4`, `qubit_gate_us_e3`, `qubit_gate_us_e4`, `qubit_maj_ns_e4`, or `qubit_maj_ns_e6`. The names of these pre-defined qubit parameters indicate the instruction set (gate-based or Majorana), the operation speed (ns or µs regime), as well as the fidelity (e.g., e3 for $10^{-3}$ gate error rates).\",\"label\":\"Qubit name\",\"path\":\"jobParams/qubitParams/name\"},{\"description\":\"Underlying qubit technology (gate-based or Majorana)\",\"explanation\":\"When modeling the physical qubit abstractions, we distinguish between two different physical instruction sets that are used to operate the qubits. The physical instruction set can be either *gate-based* or *Majorana*. A gate-based instruction set provides single-qubit measurement, single-qubit gates (incl. T gates), and two-qubit gates. A Majorana instruction set provides a physical T gate, single-qubit measurement and two-qubit joint measurement operations.\",\"label\":\"Instruction set\",\"path\":\"jobParams/qubitParams/instructionSet\"},{\"description\":\"Operation time for single-qubit measurement (t_meas) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit measurement in the Pauli basis.\",\"label\":\"Single-qubit measurement time\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementTime\"},{\"description\":\"Operation time for single-qubit gate (t_gate) in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a single-qubit Clifford operation, e.g., Hadamard or Phase gates.\",\"label\":\"Single-qubit gate time\",\"path\":\"jobParams/qubitParams/oneQubitGateTime\"},{\"description\":\"Operation time for two-qubit gate in ns\",\"explanation\":\"This is the operation time in nanoseconds to perform a two-qubit Clifford operation, e.g., a CNOT or CZ gate.\",\"label\":\"Two-qubit gate time\",\"path\":\"jobParams/qubitParams/twoQubitGateTime\"},{\"description\":\"Operation time for a T gate\",\"explanation\":\"This is the operation time in nanoseconds to execute a T gate.\",\"label\":\"T gate time\",\"path\":\"jobParams/qubitParams/tGateTime\"},{\"description\":\"Error rate for single-qubit measurement\",\"explanation\":\"This is the probability in which a single-qubit measurement in the Pauli basis may fail.\",\"label\":\"Single-qubit measurement error rate\",\"path\":\"jobParams/qubitParams/oneQubitMeasurementErrorRate\"},{\"description\":\"Error rate for single-qubit Clifford gate (p)\",\"explanation\":\"This is the probability in which a single-qubit Clifford operation, e.g., Hadamard or Phase gates, may fail.\",\"label\":\"Single-qubit error rate\",\"path\":\"jobParams/qubitParams/oneQubitGateErrorRate\"},{\"description\":\"Error rate for two-qubit Clifford gate\",\"explanation\":\"This is the probability in which a two-qubit Clifford operation, e.g., CNOT or CZ gates, may fail.\",\"label\":\"Two-qubit error rate\",\"path\":\"jobParams/qubitParams/twoQubitGateErrorRate\"},{\"description\":\"Error rate to prepare single-qubit T state or apply a T gate (p_T)\",\"explanation\":\"This is the probability in which executing a single T gate may fail.\",\"label\":\"T gate error rate\",\"path\":\"jobParams/qubitParams/tGateErrorRate\"}],\"title\":\"Physical qubit parameters\"}]},\"status\":\"success\",\"tfactory\":{\"codeDistancePerRound\":[9],\"logicalErrorRate\":2.165000000000001E-06,\"numInputTstates\":30,\"numRounds\":1,\"numTstates\":1,\"numUnitsPerRound\":[2],\"physicalQubits\":6480,\"physicalQubitsPerRound\":[6480],\"runtime\":46800.0,\"runtimePerRound\":[46800.0],\"unitNamePerRound\":[\"15-to-1 space efficient logical\"]}}", "text/html": [ "\r\n", "
\r\n", @@ -7171,24 +7179,24 @@ "\r\n", " \r\n", " Physical qubits\r\n", - " 130356\r\n", + " 96390\r\n", " \r\n", "

Number of physical qubits

\n", "\r\n", "
\r\n", - "

This value represents the total number of physical qubits, which is the sum of 14196 physical qubits to implement the algorithm logic, and 116160 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

\n", + "

This value represents the total number of physical qubits, which is the sum of 5670 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Runtime\r\n", - " 2ms 246us 400ns\r\n", + " 108us\r\n", " \r\n", "

Total runtime

\n", "\r\n", "
\r\n", - "

This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (5us 200ns) multiplied by the 432 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

\n", + "

This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 30 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.

\n", "\r\n", " \r\n", " \n", @@ -7203,120 +7211,120 @@ "\r\n", " \r\n", " Logical algorithmic qubits\r\n", - " 42\r\n", + " 35\r\n", " \r\n", "

Number of logical qubits for the algorithm after layout

\n", "\r\n", "
\r\n", - "

Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 15\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 42$ logical qubits.

\n", + "

Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the \\(Q_{\\rm alg} = 12\\) logical qubits in the input algorithm, we require in total $2 \\cdot Q_{\\rm alg} + \\lceil \\sqrt{8 \\cdot Q_{\\rm alg}}\\rceil + 1 = 35$ logical qubits.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Algorithmic depth\r\n", - " 432\r\n", + " 30\r\n", " \r\n", "

Number of logical cycles for the algorithm

\n", "\r\n", "
\r\n", - "

To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 96 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 16 CCZ and 96 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

\n", + "

To execute the algorithm using Parallel Synthesis Sequential Pauli Computation (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 6 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 2 CCZ and 6 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Logical depth\r\n", - " 432\r\n", + " 30\r\n", " \r\n", "

Number of logical cycles performed

\n", "\r\n", "
\r\n", - "

This number is usually equal to the logical depth of the algorithm, which is 432. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", + "

This number is usually equal to the logical depth of the algorithm, which is 30. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Number of T states\r\n", - " 448\r\n", + " 32\r\n", " \r\n", "

Number of T states consumed by the algorithm

\n", "\r\n", "
\r\n", - "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 16 CCZ and 96 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", + "

To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 2 CCZ and 6 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Number of T factories\r\n", - " 12\r\n", + " 14\r\n", " \r\n", - "

Number of T factories capable of producing the demanded 448 T states during the algorithm's runtime

\n", + "

Number of T factories capable of producing the demanded 32 T states during the algorithm's runtime

\n", "\r\n", "
\r\n", - "

The total number of T factories 12 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{448\\;\\text{T states} \\cdot 57us 200ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 2ms 246us 400ns\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", + "

The total number of T factories 14 that are executed in parallel is computed as \\(\\left\\lceil\\dfrac{32\\;\\text{T states} \\cdot 46us 800ns\\;\\text{T factory duration}}{1\\;\\text{T states per T factory} \\cdot 108us\\;\\text{algorithm runtime}}\\right\\rceil\\)

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Number of T factory invocations\r\n", - " 38\r\n", + " 3\r\n", " \r\n", "

Number of times all T factories are invoked

\n", "\r\n", "
\r\n", - "

In order to prepare the 448 T states, the 12 copies of the T factory are repeatedly invoked 38 times.

\n", + "

In order to prepare the 32 T states, the 14 copies of the T factory are repeatedly invoked 3 times.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Physical algorithmic qubits\r\n", - " 14196\r\n", + " 5670\r\n", " \r\n", "

Number of physical qubits for the algorithm after layout

\n", "\r\n", "
\r\n", - "

The 14196 are the product of the 42 logical qubits after layout and the 338 physical qubits that encode a single logical qubit.

\n", + "

The 5670 are the product of the 35 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Physical T factory qubits\r\n", - " 116160\r\n", + " 90720\r\n", " \r\n", "

Number of physical qubits for the T factories

\n", "\r\n", "
\r\n", - "

Each T factory requires 9680 physical qubits and we run 12 in parallel, therefore we need $116160 = 9680 \\cdot 12$ qubits.

\n", + "

Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\cdot 14$ qubits.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Required logical qubit error rate\r\n", - " 2.76e-8\r\n", + " 4.76e-7\r\n", " \r\n", "

The minimum logical qubit error rate required to run the algorithm within the error budget

\n", "\r\n", "
\r\n", - "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 42 logical qubits and the total cycle count 432.

\n", + "

The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 35 logical qubits and the total cycle count 30.

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Required logical T state error rate\r\n", - " 1.12e-6\r\n", + " 1.56e-5\r\n", " \r\n", "

The minimum T state error rate required for distilled T states

\n", "\r\n", "
\r\n", - "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 448.

\n", + "

The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 32.

\n", "\r\n", " \r\n", " \n", @@ -7355,19 +7363,19 @@ "\r\n", " \r\n", " Code distance\r\n", - " 13\r\n", + " 9\r\n", " \r\n", "

Required code distance for error correction

\n", "\r\n", "
\r\n", - "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.00000002755731922398589)}{\\log(0.01/0.001)} - 1\\)

\n", + "

The code distance is the smallest odd integer greater or equal to \\(\\dfrac{2\\log(0.03 / 0.0000004761904761904762)}{\\log(0.01/0.001)} - 1\\)

\n", "\r\n", " \r\n", " \n", "\r\n", " \r\n", " Physical qubits\r\n", - " 338\r\n", + " 162\r\n", " \r\n", "

Number of physical qubits per logical qubit

\n", "\r\n", @@ -7379,7 +7387,7 @@ "\r\n", " \r\n", " Logical cycle time\r\n", - " 5us 200ns\r\n", + " 3us 600ns\r\n", " \r\n", "

Duration of a logical cycle in nanoseconds

\n", "\r\n", @@ -7391,12 +7399,12 @@ "\r\n", " \r\n", " Logical qubit error rate\r\n", - " 3.00e-9\r\n", + " 3.00e-7\r\n", " \r\n", "

Logical qubit error rate

\n", "\r\n", "
\r\n", - "

The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{13 + 1}{2}$

\n", + "

The logical qubit error rate is computed as $0.03 \\cdot \\left(\\dfrac{0.001}{0.01}\\right)^\\frac{9 + 1}{2}$

\n", "\r\n", " \r\n", " \n", @@ -7432,7 +7440,7 @@ "

QEC scheme formula used to compute logical cycle time

\n", "\r\n", "
\r\n", - "

This is the formula that is used to compute the logical cycle time 5us 200ns.

\n", + "

This is the formula that is used to compute the logical cycle time 3us 600ns.

\n", "\r\n", " \r\n", " \n", @@ -7444,7 +7452,7 @@ "

QEC scheme formula used to compute number of physical qubits per logical qubit

\n", "\r\n", "
\r\n", - "

This is the formula that is used to compute the number of physical qubits per logical qubits 338.

\n", + "

This is the formula that is used to compute the number of physical qubits per logical qubits 162.

\n", "\r\n", " \r\n", " \n", @@ -7459,7 +7467,7 @@ "\r\n", " \r\n", " Physical qubits\r\n", - " 9680\r\n", + " 6480\r\n", " \r\n", "

Number of physical qubits for a single T factory

\n", "\r\n", @@ -7471,7 +7479,7 @@ "\r\n", " \r\n", " Runtime\r\n", - " 57us 200ns\r\n", + " 46us 800ns\r\n", " \r\n", "

Runtime of a single T factory

\n", "\r\n", @@ -7488,7 +7496,7 @@ "

Number of output T states produced in a single run of T factory

\n", "\r\n", "
\r\n", - "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.

\n", + "

The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.

\n", "\r\n", " \r\n", " \n", @@ -7543,7 +7551,7 @@ "\r\n", " \r\n", " Distillation code distances\r\n", - " 11\r\n", + " 9\r\n", " \r\n", "

The code distance in each round of distillation

\n", "\r\n", @@ -7555,7 +7563,7 @@ "\r\n", " \r\n", " Number of physical qubits per round\r\n", - " 9680\r\n", + " 6480\r\n", " \r\n", "

The number of physical qubits used in each round of distillation

\n", "\r\n", @@ -7567,7 +7575,7 @@ "\r\n", " \r\n", " Runtime per round\r\n", - " 57us 200ns\r\n", + " 46us 800ns\r\n", " \r\n", "

The runtime of each distillation round

\n", "\r\n", @@ -7579,12 +7587,12 @@ "\r\n", " \r\n", " Logical T state error rate\r\n", - " 2.48e-7\r\n", + " 2.17e-6\r\n", " \r\n", "

Logical T state error rate

\n", "\r\n", "
\r\n", - "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.12e-6.

\n", + "

This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.56e-5.

\n", "\r\n", " \r\n", " \n", @@ -7599,12 +7607,12 @@ "\r\n", " \r\n", " Logical qubits (pre-layout)\r\n", - " 15\r\n", + " 12\r\n", " \r\n", "

Number of logical qubits in the input quantum program

\n", "\r\n", "
\r\n", - "

We determine 42 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", + "

We determine 35 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.

\n", "\r\n", " \r\n", " \n", @@ -7647,7 +7655,7 @@ "\r\n", " \r\n", " CCZ gates\r\n", - " 16\r\n", + " 2\r\n", " \r\n", "

Number of CCZ-gates in the input quantum program

\n", "\r\n", @@ -7659,7 +7667,7 @@ "\r\n", " \r\n", " CCiX gates\r\n", - " 96\r\n", + " 6\r\n", " \r\n", "

Number of CCiX-gates in the input quantum program

\n", "\r\n", @@ -7671,7 +7679,7 @@ "\r\n", " \r\n", " Measurement operations\r\n", - " 96\r\n", + " 6\r\n", " \r\n", "

Number of single qubit measurements in the input quantum program

\n", "\r\n", @@ -7902,48 +7910,48 @@ " 'tGateTime': '50 ns',\n", " 'twoQubitGateErrorRate': 0.001,\n", " 'twoQubitGateTime': '50 ns'}},\n", - " 'logicalCounts': {'ccixCount': 96,\n", - " 'cczCount': 16,\n", - " 'measurementCount': 96,\n", - " 'numQubits': 15,\n", + " 'logicalCounts': {'ccixCount': 6,\n", + " 'cczCount': 2,\n", + " 'measurementCount': 6,\n", + " 'numQubits': 12,\n", " 'rotationCount': 0,\n", " 'rotationDepth': 0,\n", " 'tCount': 0},\n", - " 'logicalQubit': {'codeDistance': 13,\n", - " 'logicalCycleTime': 5200.0,\n", - " 'logicalErrorRate': 3.000000000000002e-09,\n", - " 'physicalQubits': 338},\n", - " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 432,\n", - " 'algorithmicLogicalQubits': 42,\n", + " 'logicalQubit': {'codeDistance': 9,\n", + " 'logicalCycleTime': 3600.0,\n", + " 'logicalErrorRate': 3.0000000000000015e-07,\n", + " 'physicalQubits': 162},\n", + " 'physicalCounts': {'breakdown': {'algorithmicLogicalDepth': 30,\n", + " 'algorithmicLogicalQubits': 35,\n", " 'cliffordErrorRate': 0.001,\n", - " 'logicalDepth': 432,\n", - " 'numTfactories': 12,\n", - " 'numTfactoryRuns': 38,\n", + " 'logicalDepth': 30,\n", + " 'numTfactories': 14,\n", + " 'numTfactoryRuns': 3,\n", " 'numTsPerRotation': None,\n", - " 'numTstates': 448,\n", - " 'physicalQubitsForAlgorithm': 14196,\n", - " 'physicalQubitsForTfactories': 116160,\n", - " 'requiredLogicalQubitErrorRate': 2.755731922398589e-08,\n", - " 'requiredLogicalTstateErrorRate': 1.1160714285714287e-06},\n", - " 'physicalQubits': 130356,\n", - " 'runtime': 2246400},\n", - " 'physicalCountsFormatted': {'codeDistancePerRound': '11',\n", + " 'numTstates': 32,\n", + " 'physicalQubitsForAlgorithm': 5670,\n", + " 'physicalQubitsForTfactories': 90720,\n", + " 'requiredLogicalQubitErrorRate': 4.761904761904762e-07,\n", + " 'requiredLogicalTstateErrorRate': 1.5625e-05},\n", + " 'physicalQubits': 96390,\n", + " 'runtime': 108000},\n", + " 'physicalCountsFormatted': {'codeDistancePerRound': '9',\n", " 'errorBudget': '1.00e-3',\n", " 'errorBudgetLogical': '5.00e-4',\n", " 'errorBudgetRotations': '0.00e0',\n", " 'errorBudgetTstates': '5.00e-4',\n", - " 'logicalCycleTime': '5us 200ns',\n", - " 'logicalErrorRate': '3.00e-9',\n", + " 'logicalCycleTime': '3us 600ns',\n", + " 'logicalErrorRate': '3.00e-7',\n", " 'numTsPerRotation': 'No rotations in algorithm',\n", " 'numUnitsPerRound': '2',\n", - " 'physicalQubitsForTfactoriesPercentage': '89.11 %',\n", - " 'physicalQubitsPerRound': '9680',\n", - " 'requiredLogicalQubitErrorRate': '2.76e-8',\n", - " 'requiredLogicalTstateErrorRate': '1.12e-6',\n", - " 'runtime': '2ms 246us 400ns',\n", - " 'tfactoryRuntime': '57us 200ns',\n", - " 'tfactoryRuntimePerRound': '57us 200ns',\n", - " 'tstateLogicalErrorRate': '2.48e-7',\n", + " 'physicalQubitsForTfactoriesPercentage': '94.12 %',\n", + " 'physicalQubitsPerRound': '6480',\n", + " 'requiredLogicalQubitErrorRate': '4.76e-7',\n", + " 'requiredLogicalTstateErrorRate': '1.56e-5',\n", + " 'runtime': '108us',\n", + " 'tfactoryRuntime': '46us 800ns',\n", + " 'tfactoryRuntimePerRound': '46us 800ns',\n", + " 'tstateLogicalErrorRate': '2.17e-6',\n", " 'unitNamePerRound': '15-to-1 space efficient logical'},\n", " 'reportData': {'assumptions': ['_More details on the following lists of assumptions can be found in the paper [Accessing requirements for scaling quantum computers and their applications](https://aka.ms/AQ/RE/Paper)._',\n", " '**Uniform independent physical noise.** We assume that the noise on physical qubits and physical qubit operations is the standard circuit noise model. In particular we assume error events at different space-time locations are independent and that error rates are uniform across the system in time and space.',\n", @@ -7954,53 +7962,53 @@ " '**Smooth magic state consumption rate.** We assume that the rate of T state consumption throughout the compiled algorithm is almost constant, or can be made almost constant without significantly increasing the number of logical time steps for the algorithm.'],\n", " 'groups': [{'alwaysVisible': True,\n", " 'entries': [{'description': 'Number of physical qubits',\n", - " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 14196 physical qubits to implement the algorithm logic, and 116160 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", + " 'explanation': 'This value represents the total number of physical qubits, which is the sum of 5670 physical qubits to implement the algorithm logic, and 90720 physical qubits to execute the T factories that are responsible to produce the T states that are consumed by the algorithm.',\n", " 'label': 'Physical qubits',\n", " 'path': 'physicalCounts/physicalQubits'},\n", " {'description': 'Total runtime',\n", - " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (5us 200ns) multiplied by the 432 logical cycles to run the algorithm. If however the duration of a single T factory (here: 57us 200ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", + " 'explanation': 'This is a runtime estimate (in nanosecond precision) for the execution time of the algorithm. In general, the execution time corresponds to the duration of one logical cycle (3us 600ns) multiplied by the 30 logical cycles to run the algorithm. If however the duration of a single T factory (here: 46us 800ns) is larger than the algorithm runtime, we extend the number of logical cycles artificially in order to exceed the runtime of a single T factory.',\n", " 'label': 'Runtime',\n", " 'path': 'physicalCountsFormatted/runtime'}],\n", " 'title': 'Physical resource estimates'},\n", " {'alwaysVisible': False,\n", " 'entries': [{'description': 'Number of logical qubits for the algorithm after layout',\n", - " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 15$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 42$ logical qubits.',\n", + " 'explanation': 'Laying out the logical qubits in the presence of nearest-neighbor constraints requires additional logical qubits. In particular, to layout the $Q_{\\\\rm alg} = 12$ logical qubits in the input algorithm, we require in total $2 \\\\cdot Q_{\\\\rm alg} + \\\\lceil \\\\sqrt{8 \\\\cdot Q_{\\\\rm alg}}\\\\rceil + 1 = 35$ logical qubits.',\n", " 'label': 'Logical algorithmic qubits',\n", " 'path': 'physicalCounts/breakdown/algorithmicLogicalQubits'},\n", " {'description': 'Number of logical cycles for the algorithm',\n", - " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 96 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 16 CCZ and 96 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", + " 'explanation': 'To execute the algorithm using _Parallel Synthesis Sequential Pauli Computation_ (PSSPC), operations are scheduled in terms of multi-qubit Pauli measurements, for which assume an execution time of one logical cycle. Based on the input algorithm, we require one multi-qubit measurement for the 6 single-qubit measurements, the 0 arbitrary single-qubit rotations, and the 0 T gates, three multi-qubit measurements for each of the 2 CCZ and 6 CCiX gates in the input program, as well as No rotations in algorithm multi-qubit measurements for each of the 0 non-Clifford layers in which there is at least one single-qubit rotation with an arbitrary angle rotation.',\n", " 'label': 'Algorithmic depth',\n", " 'path': 'physicalCounts/breakdown/algorithmicLogicalDepth'},\n", " {'description': 'Number of logical cycles performed',\n", - " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 432. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", + " 'explanation': \"This number is usually equal to the logical depth of the algorithm, which is 30. However, in the case in which a single T factory is slower than the execution time of the algorithm, we adjust the logical cycle depth to exceed the T factory's execution time.\",\n", " 'label': 'Logical depth',\n", " 'path': 'physicalCounts/breakdown/logicalDepth'},\n", " {'description': 'Number of T states consumed by the algorithm',\n", - " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 16 CCZ and 96 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", + " 'explanation': 'To execute the algorithm, we require one T state for each of the 0 T gates, four T states for each of the 2 CCZ and 6 CCiX gates, as well as No rotations in algorithm for each of the 0 single-qubit rotation gates with arbitrary angle rotation.',\n", " 'label': 'Number of T states',\n", " 'path': 'physicalCounts/breakdown/numTstates'},\n", - " {'description': \"Number of T factories capable of producing the demanded 448 T states during the algorithm's runtime\",\n", - " 'explanation': 'The total number of T factories 12 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{448\\\\;\\\\text{T states} \\\\cdot 57us 200ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 2ms 246us 400ns\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", + " {'description': \"Number of T factories capable of producing the demanded 32 T states during the algorithm's runtime\",\n", + " 'explanation': 'The total number of T factories 14 that are executed in parallel is computed as $\\\\left\\\\lceil\\\\dfrac{32\\\\;\\\\text{T states} \\\\cdot 46us 800ns\\\\;\\\\text{T factory duration}}{1\\\\;\\\\text{T states per T factory} \\\\cdot 108us\\\\;\\\\text{algorithm runtime}}\\\\right\\\\rceil$',\n", " 'label': 'Number of T factories',\n", " 'path': 'physicalCounts/breakdown/numTfactories'},\n", " {'description': 'Number of times all T factories are invoked',\n", - " 'explanation': 'In order to prepare the 448 T states, the 12 copies of the T factory are repeatedly invoked 38 times.',\n", + " 'explanation': 'In order to prepare the 32 T states, the 14 copies of the T factory are repeatedly invoked 3 times.',\n", " 'label': 'Number of T factory invocations',\n", " 'path': 'physicalCounts/breakdown/numTfactoryRuns'},\n", " {'description': 'Number of physical qubits for the algorithm after layout',\n", - " 'explanation': 'The 14196 are the product of the 42 logical qubits after layout and the 338 physical qubits that encode a single logical qubit.',\n", + " 'explanation': 'The 5670 are the product of the 35 logical qubits after layout and the 162 physical qubits that encode a single logical qubit.',\n", " 'label': 'Physical algorithmic qubits',\n", " 'path': 'physicalCounts/breakdown/physicalQubitsForAlgorithm'},\n", " {'description': 'Number of physical qubits for the T factories',\n", - " 'explanation': 'Each T factory requires 9680 physical qubits and we run 12 in parallel, therefore we need $116160 = 9680 \\\\cdot 12$ qubits.',\n", + " 'explanation': 'Each T factory requires 6480 physical qubits and we run 14 in parallel, therefore we need $90720 = 6480 \\\\cdot 14$ qubits.',\n", " 'label': 'Physical T factory qubits',\n", " 'path': 'physicalCounts/breakdown/physicalQubitsForTfactories'},\n", " {'description': 'The minimum logical qubit error rate required to run the algorithm within the error budget',\n", - " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 42 logical qubits and the total cycle count 432.',\n", + " 'explanation': 'The minimum logical qubit error rate is obtained by dividing the logical error probability 5.00e-4 by the product of 35 logical qubits and the total cycle count 30.',\n", " 'label': 'Required logical qubit error rate',\n", " 'path': 'physicalCountsFormatted/requiredLogicalQubitErrorRate'},\n", " {'description': 'The minimum T state error rate required for distilled T states',\n", - " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 448.',\n", + " 'explanation': 'The minimum T state error rate is obtained by dividing the T distillation error probability 5.00e-4 by the total number of T states 32.',\n", " 'label': 'Required logical T state error rate',\n", " 'path': 'physicalCountsFormatted/requiredLogicalTstateErrorRate'},\n", " {'description': 'Number of T states to implement a rotation with an arbitrary angle',\n", @@ -8014,7 +8022,7 @@ " 'label': 'QEC scheme',\n", " 'path': 'jobParams/qecScheme/name'},\n", " {'description': 'Required code distance for error correction',\n", - " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.00000002755731922398589)}{\\\\log(0.01/0.001)} - 1$',\n", + " 'explanation': 'The code distance is the smallest odd integer greater or equal to $\\\\dfrac{2\\\\log(0.03 / 0.0000004761904761904762)}{\\\\log(0.01/0.001)} - 1$',\n", " 'label': 'Code distance',\n", " 'path': 'logicalQubit/codeDistance'},\n", " {'description': 'Number of physical qubits per logical qubit',\n", @@ -8026,7 +8034,7 @@ " 'label': 'Logical cycle time',\n", " 'path': 'physicalCountsFormatted/logicalCycleTime'},\n", " {'description': 'Logical qubit error rate',\n", - " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{13 + 1}{2}$',\n", + " 'explanation': 'The logical qubit error rate is computed as $0.03 \\\\cdot \\\\left(\\\\dfrac{0.001}{0.01}\\\\right)^\\\\frac{9 + 1}{2}$',\n", " 'label': 'Logical qubit error rate',\n", " 'path': 'physicalCountsFormatted/logicalErrorRate'},\n", " {'description': 'Crossing prefactor used in QEC scheme',\n", @@ -8038,11 +8046,11 @@ " 'label': 'Error correction threshold',\n", " 'path': 'jobParams/qecScheme/errorCorrectionThreshold'},\n", " {'description': 'QEC scheme formula used to compute logical cycle time',\n", - " 'explanation': 'This is the formula that is used to compute the logical cycle time 5us 200ns.',\n", + " 'explanation': 'This is the formula that is used to compute the logical cycle time 3us 600ns.',\n", " 'label': 'Logical cycle time formula',\n", " 'path': 'jobParams/qecScheme/logicalCycleTime'},\n", " {'description': 'QEC scheme formula used to compute number of physical qubits per logical qubit',\n", - " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 338.',\n", + " 'explanation': 'This is the formula that is used to compute the number of physical qubits per logical qubits 162.',\n", " 'label': 'Physical qubits formula',\n", " 'path': 'jobParams/qecScheme/physicalQubitsPerLogicalQubit'}],\n", " 'title': 'Logical qubit parameters'},\n", @@ -8056,7 +8064,7 @@ " 'label': 'Runtime',\n", " 'path': 'physicalCountsFormatted/tfactoryRuntime'},\n", " {'description': 'Number of output T states produced in a single run of T factory',\n", - " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.48e-7.',\n", + " 'explanation': 'The T factory takes as input 30 noisy physical T states with an error rate of 0.001 and produces 1 T states with an error rate of 2.17e-6.',\n", " 'label': 'Number of output T states per run',\n", " 'path': 'tfactory/numTstates'},\n", " {'description': 'Number of physical input T states consumed in a single run of a T factory',\n", @@ -8088,13 +8096,13 @@ " 'label': 'Runtime per round',\n", " 'path': 'physicalCountsFormatted/tfactoryRuntimePerRound'},\n", " {'description': 'Logical T state error rate',\n", - " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.12e-6.',\n", + " 'explanation': 'This is the logical T state error rate achieved by the T factory which is equal or smaller than the required error rate 1.56e-5.',\n", " 'label': 'Logical T state error rate',\n", " 'path': 'physicalCountsFormatted/tstateLogicalErrorRate'}],\n", " 'title': 'T factory parameters'},\n", " {'alwaysVisible': False,\n", " 'entries': [{'description': 'Number of logical qubits in the input quantum program',\n", - " 'explanation': 'We determine 42 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", + " 'explanation': 'We determine 35 from this number by assuming to align them in a 2D grid. Auxiliary qubits are added to allow for sufficient space to execute multi-qubit Pauli measurements on all or a subset of the logical qubits.',\n", " 'label': 'Logical qubits (pre-layout)',\n", " 'path': 'logicalCounts/numQubits'},\n", " {'description': 'Number of T gates in the input quantum program',\n", @@ -8183,20 +8191,20 @@ " 'path': 'jobParams/qubitParams/tGateErrorRate'}],\n", " 'title': 'Physical qubit parameters'}]},\n", " 'status': 'success',\n", - " 'tfactory': {'codeDistancePerRound': [11],\n", - " 'logicalErrorRate': 2.480000000000001e-07,\n", + " 'tfactory': {'codeDistancePerRound': [9],\n", + " 'logicalErrorRate': 2.165000000000001e-06,\n", " 'numInputTstates': 30,\n", " 'numRounds': 1,\n", " 'numTstates': 1,\n", " 'numUnitsPerRound': [2],\n", - " 'physicalQubits': 9680,\n", - " 'physicalQubitsPerRound': [9680],\n", - " 'runtime': 57200.0,\n", - " 'runtimePerRound': [57200.0],\n", + " 'physicalQubits': 6480,\n", + " 'physicalQubitsPerRound': [6480],\n", + " 'runtime': 46800.0,\n", + " 'runtimePerRound': [46800.0],\n", " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" ] }, - "execution_count": 34, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" } @@ -8209,7 +8217,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 12, "metadata": { "collapsed": false, "jupyter": { @@ -8236,7 +8244,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 13, "metadata": { "collapsed": false, "jupyter": { @@ -8254,18 +8262,18 @@ "name": "stdout", "output_type": "stream", "text": [ - "Logical algorithmic qubits = 42\n", - "Algorithmic depth = 432\n", - "Score = 18144\n" + "Logical algorithmic qubits = 35\n", + "Algorithmic depth = 30\n", + "Score = 1050\n" ] }, { "data": { "text/plain": [ - "18144" + "1050" ] }, - "execution_count": 36, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" } diff --git a/team_solutions/schrodingers-duck/iQuHack-challenge-2023-task7.ipynb b/team_solutions/schrodingers-duck/iQuHack-challenge-2023-task7.ipynb index 029dfd4..9d38b74 100644 --- a/team_solutions/schrodingers-duck/iQuHack-challenge-2023-task7.ipynb +++ b/team_solutions/schrodingers-duck/iQuHack-challenge-2023-task7.ipynb @@ -67,7 +67,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 1, "metadata": { "collapsed": false, "jupyter": { @@ -89,7 +89,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 2, "metadata": { "collapsed": false, "jupyter": { @@ -111,7 +111,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 3, "metadata": { "collapsed": false, "jupyter": { @@ -148,7 +148,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 4, "metadata": { "collapsed": false, "jupyter": { @@ -198,7 +198,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ @@ -207,7 +207,7 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 6, "metadata": { "collapsed": false, "jupyter": { @@ -264,7 +264,7 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 7, "metadata": { "collapsed": false, "jupyter": { @@ -309,12 +309,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

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\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1509,12 +1509,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1534,12 +1534,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1559,12 +1559,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1584,12 +1584,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1609,12 +1609,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1634,12 +1634,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1659,12 +1659,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1684,12 +1684,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1709,12 +1709,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1734,12 +1734,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1759,12 +1759,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1784,12 +1784,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1809,12 +1809,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1834,12 +1834,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1859,12 +1859,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1884,12 +1884,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1909,12 +1909,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1934,12 +1934,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1959,12 +1959,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -1984,12 +1984,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2009,12 +2009,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2034,12 +2034,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2059,12 +2059,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2084,12 +2084,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2109,12 +2109,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2134,12 +2134,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2159,12 +2159,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2184,12 +2184,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2209,12 +2209,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2234,12 +2234,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2259,12 +2259,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2284,12 +2284,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2309,12 +2309,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2334,12 +2334,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2359,12 +2359,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2384,12 +2384,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2409,12 +2409,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2434,12 +2434,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2459,12 +2459,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2484,12 +2484,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2509,12 +2509,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2534,12 +2534,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2559,12 +2559,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2584,12 +2584,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2609,12 +2609,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2634,12 +2634,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2659,12 +2659,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2684,12 +2684,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2709,12 +2709,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2734,12 +2734,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2759,12 +2759,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2784,12 +2784,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2809,12 +2809,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2834,12 +2834,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2859,12 +2859,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2884,12 +2884,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2909,12 +2909,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2934,12 +2934,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2959,12 +2959,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -2984,12 +2984,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3009,12 +3009,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3034,12 +3034,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3059,12 +3059,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3084,12 +3084,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3109,12 +3109,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3134,12 +3134,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3159,12 +3159,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3184,12 +3184,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3209,12 +3209,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3234,12 +3234,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3259,12 +3259,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3284,12 +3284,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3309,12 +3309,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3334,12 +3334,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3359,12 +3359,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3384,12 +3384,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3409,12 +3409,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3434,12 +3434,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3459,12 +3459,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3484,12 +3484,12 @@ " style=\"width: 100%;\"\r\n", " > \r\n", " \r\n", - "

\r\n", + "

\r\n", "

\r\n", " \r\n", " \r\n", @@ -3640,7 +3640,7 @@ "()" ] }, - "execution_count": 30, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } @@ -3669,7 +3669,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 8, "metadata": { "collapsed": false, "jupyter": { @@ -3703,23 +3703,23 @@ { "data": { "text/plain": [ - "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 178643},\n", - " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 426101},\n", - " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 4},\n", + "[{'id': 'ionq.qpu', 'current_availability': {}, 'average_queue_time': 179536},\n", + " {'id': 'ionq.qpu.aria-1', 'current_availability': {}, 'average_queue_time': 429485},\n", + " {'id': 'ionq.simulator', 'current_availability': {}, 'average_queue_time': 2},\n", " {'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s1-apival', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.hqs-lt-s2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.hqs-lt-s2-apival', 'current_availability': {}, 'average_queue_time': 1},\n", - " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 69},\n", - " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 168},\n", + " {'id': 'quantinuum.hqs-lt-s1-sim', 'current_availability': {}, 'average_queue_time': 479},\n", + " {'id': 'quantinuum.hqs-lt-s2-sim', 'current_availability': {}, 'average_queue_time': 163},\n", " {'id': 'quantinuum.hqs-lt', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.qpu.h1-1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-1sc', 'current_availability': {}, 'average_queue_time': 1},\n", " {'id': 'quantinuum.qpu.h1-2', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'quantinuum.sim.h1-2sc', 'current_availability': {}, 'average_queue_time': 1},\n", - " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 69},\n", - " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 168},\n", + " {'id': 'quantinuum.sim.h1-1e', 'current_availability': {}, 'average_queue_time': 479},\n", + " {'id': 'quantinuum.sim.h1-2e', 'current_availability': {}, 'average_queue_time': 163},\n", " {'id': 'quantinuum.qpu.h1', 'current_availability': {}, 'average_queue_time': 0},\n", " {'id': 'rigetti.sim.qvm', 'current_availability': {}, 'average_queue_time': 5},\n", " {'id': 'rigetti.qpu.aspen-11', 'current_availability': {}, 'average_queue_time': 0},\n", @@ -3727,7 +3727,7 @@ " {'id': 'rigetti.qpu.aspen-m-3', 'current_availability': {}, 'average_queue_time': 5}]" ] }, - "execution_count": 31, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -3743,7 +3743,7 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 9, "metadata": { "collapsed": false, "jupyter": { @@ -3771,7 +3771,7 @@ "{'id': 'microsoft.estimator', 'current_availability': {}, 'average_queue_time': 0}" ] }, - "execution_count": 32, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } @@ -3782,7 +3782,7 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 10, "metadata": { "collapsed": false, "jupyter": { @@ -3803,10 +3803,10 @@ "Submitting Task7_ResourceEstimationWrapper to target microsoft.estimator...\n", "Job successfully submitted.\n", " Job name: RE for the task 7\n", - " Job ID: a7d42efd-1393-44bf-bf4d-7e90bcc2df62\n", + " Job ID: 532dd603-96a9-42a3-a29f-91825cb1e61d\n", "Waiting up to 30 seconds for Azure Quantum job to complete...\n", - "[1:17:00 PM] Current job status: Executing\n", - "[1:17:05 PM] Current job status: Succeeded\n" + "[2:14:25 PM] Current job status: Executing\n", + "[2:14:30 PM] Current job status: Succeeded\n" ] } ], @@ -3817,7 +3817,7 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 11, "metadata": { "collapsed": false, "jupyter": { @@ -4870,7 +4870,7 @@ " 'unitNamePerRound': ['15-to-1 space efficient logical']}}" ] }, - "execution_count": 34, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" } @@ -4883,7 +4883,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 12, "metadata": { "collapsed": false, "jupyter": { @@ -4910,7 +4910,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 13, "metadata": { "collapsed": false, "jupyter": { @@ -4939,7 +4939,7 @@ "2546" ] }, - "execution_count": 36, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" } diff --git a/team_solutions/schrodingers-duck/obj/__entrypoint__.dll 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z(7du3BbK^|KCS{5OhzbmY);}ZLcNo6z4Ue`*m?hsS`3%4r84g?x#Ttvm|9 z?0rp1w5ToGq2NUA{oy__Q4X9~Zx61@8(m=JJKXW8)|BQ@4}_8Bgb@ z=kc33a$?wmtCHK^C-954G=K1x%nVMX_;H9_LH{n!t>}OJj1SxA)7e6LS~Evf^DwD8 z;i1w`?}V@)nM#evGsyzPCNtwXsE~8-S!;Z$_dZcfLCajWFnB0gJS(jE23sX-n}SD} zl@yTqI8MWa%`RUetB1^oYLDh~)2Tusmme(YBRu?{&L77w8FRBj`F3m*csifU(g%dwI%FyvU($WhV~3jb9!08rcve*KH;eN=y3qK0ru%)F z>SQO*XYs?)LfZB7TYMWmmQNSY&ftkvV)W$fK|5@a}(*TYyr}GoKJldHSqHr_?0$o5*AiCDU0oTbRbMNDa=I zFYdg&9z2%ICqm?8a)n{XW-!o!8Dwj=!6~XcOnRqDhfTW8q@yO4Ex2qu?>F!VOnT6y zhfI3dq(@A8+@vQ=`g)Vjm{f+aEQ@53nl^Y@I*RGf8+bEWU<>>>rf=~t3@tF Date: Mon, 27 Feb 2023 18:02:11 +0100 Subject: [PATCH 7/7] Update README.md --- README.md | 9 +++++++++ 1 file changed, 9 insertions(+) diff --git a/README.md b/README.md index 58743d7..ccb4356 100644 --- a/README.md +++ b/README.md @@ -1,3 +1,12 @@ +# Project Submission for Microsoft Challenge @ MIT iQuHACK 2023 by +- Hamish Hall +- Vadym Kuzyak +- Alexander Doye +- Olivia Xuan Zhu +- Ivan Rojas + + +_____________ # Welcome to the Microsoft Challenge @ MIT iQuHACK 2023! ## Challenge overview