diff --git a/challenges/PIQUE challenge/QuantumVoyagers/README.md b/challenges/PIQUE challenge/QuantumVoyagers/README.md new file mode 100644 index 0000000..3c57f68 --- /dev/null +++ b/challenges/PIQUE challenge/QuantumVoyagers/README.md @@ -0,0 +1,56 @@ +# Quantum Algorithms for Tic Tac Toe + +This repository contains Python code and Jupyter Notebooks implementing quantum algorithms, specifically Grover's algorithm and Quantum Approximate Optimization Algorithm (QAOA), to solve the Tic Tac Toe game. + +## Table of Contents + +- [Grover's Algorithm](#grovers-algorithm) + + - [General Solution](./app/grover/general_solution.ipynb) + - [Grover Circuit Complete Image](./app/grover/grover_circuit_complete_image) + - [Solution Notebook](./app/grover/solution.ipynb) + +- [QAOA](./app/qaoa/qaoa.ipynb) + +- [Images](./app/Images) + + - [Best Play - Regular](./app/Images/best_play.png) + - [Best Play - Bonus](./app/Images/best_play_bonus.png) + - [Parts Oracle Grover](./app/Images/parts_oracle_grover.jpg) + - [Tic Tac Toe Image](./app/Images/tic-tac-toe-1777880_1280.jpg) + +- [Package](./pkg) + - [General Utilities](./pkg/general_utils.py) + - [Quantum Utilities](./pkg/quantum_utils.py) + +## Grover's Algorithm + +### General Solution + +The [General Solution](./app/grover/general_solution.ipynb) notebook contains the Python code for Grover's algorithm, focusing on solving Tic Tac Toe. + +### Grover Circuit Complete Image + +The [Grover Circuit Complete Image](./app/grover/grover_circuit_complete_image) directory includes the LaTeX file (`file.tex`) and the complete Grover circuit in PDF format (`grover_circuit.pdf`). + +### Solution Notebook + +The [Solution Notebook](./app/grover/solution.ipynb) provides detailed information on the solution implemented using Grover's algorithm. + +## QAOA + +The [QAOA Notebook](./app/qaoa/qaoa.ipynb) contains the Python code for Quantum Approximate Optimization Algorithm applied to Tic Tac Toe. + +## Images + +Various images related to Tic Tac Toe and the algorithms used, such as best plays and the Tic Tac Toe game itself. + +## Package + +### General Utilities + +The [General Utilities](./pkg/general_utils.py) module includes Python functions used for Tic Tac Toe and algorithm implementations. + +### Quantum Utilities + +The [Quantum Utilities](./pkg/quantum_utils.py) module contains Python functions specific to quantum operations in the Tic Tac Toe algorithms. diff --git a/challenges/PIQUE challenge/QuantumVoyagers/app/Images/best_play.png b/challenges/PIQUE challenge/QuantumVoyagers/app/Images/best_play.png new file mode 100644 index 0000000..7e4bac7 Binary files /dev/null and b/challenges/PIQUE challenge/QuantumVoyagers/app/Images/best_play.png differ diff --git a/challenges/PIQUE challenge/QuantumVoyagers/app/Images/best_play_bonus.png b/challenges/PIQUE challenge/QuantumVoyagers/app/Images/best_play_bonus.png new file mode 100644 index 0000000..6c62ae3 Binary files /dev/null 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challenge/QuantumVoyagers/app/Images/parts_oracle_grover.jpg b/challenges/PIQUE challenge/QuantumVoyagers/app/Images/parts_oracle_grover.jpg new file mode 100644 index 0000000..ae9c7e8 Binary files /dev/null and b/challenges/PIQUE challenge/QuantumVoyagers/app/Images/parts_oracle_grover.jpg differ diff --git a/challenges/PIQUE challenge/QuantumVoyagers/app/Images/tic-tac-toe-1777880_1280.jpg b/challenges/PIQUE challenge/QuantumVoyagers/app/Images/tic-tac-toe-1777880_1280.jpg new file mode 100644 index 0000000..edcf6ab Binary files /dev/null and b/challenges/PIQUE challenge/QuantumVoyagers/app/Images/tic-tac-toe-1777880_1280.jpg differ diff --git a/challenges/PIQUE challenge/QuantumVoyagers/app/grover/general_solution.ipynb b/challenges/PIQUE challenge/QuantumVoyagers/app/grover/general_solution.ipynb new file mode 100644 index 0000000..624ac9f --- /dev/null +++ b/challenges/PIQUE challenge/QuantumVoyagers/app/grover/general_solution.ipynb @@ -0,0 +1,234 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit.visualization import plot_histogram\n", + "\n", + "import sys\n", + "sys.path.append('../../')\n", + "from pkg.general_utils import display_board, generate_random_board, complete_lists_with_dictionary, filter_values_above_average\n", + "from pkg.quantum_utils import grover_algorithm, circuit_execute" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[['O', 'X', ' '], [' ', ' ', 'O'], [' ', ' ', 'X']]" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "challenge = generate_random_board(num_moves=4)\n", + "challenge" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "O | X | \n", + "---------\n", + " | | O\n", + "---------\n", + " | | X\n", + "---------\n" + ] + } + ], + "source": [ + "display_board(challenge)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = grover_algorithm(challenge, rep=1)\n", + "qc.draw('mpl')" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'01110': 389, '01101': 352, '01001': 333, '01000': 365, '00011': 4738, '11100': 342, '11000': 377, '11010': 351, '10111': 326, '11001': 360, '10100': 355, '10010': 344, '01011': 383, '10001': 332, '10110': 350, '00110': 379, '00010': 330, '10011': 334, '00000': 380, '00001': 345, '11111': 354, '11011': 355, '10101': 353, '00101': 4615, '11101': 341, '01100': 347, '10000': 380, '00111': 329, '11110': 372, '01010': 348, '00100': 329, '01111': 412}\n" + ] + } + ], + "source": [ + "\n", + "counts_without_qiskit_convention = circuit_execute(qc, shots=20000)\n", + "print(counts_without_qiskit_convention)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plot_histogram(counts_without_qiskit_convention, color='midnightblue')" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'00011': 4738, '00101': 4615}\n" + ] + } + ], + "source": [ + "possible_results = filter_values_above_average(counts_without_qiskit_convention)\n", + "\n", + "print(possible_results)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "List 1: [['O', 'X', 'O'], ['O', 'O', 'O'], ['X', 'X', 'X']]\n", + "List 2: [['O', 'X', 'O'], ['O', 'X', 'O'], ['O', 'X', 'X']]\n" + ] + } + ], + "source": [ + "completed_lists = complete_lists_with_dictionary(challenge, possible_results)\n", + "\n", + "for i, lst in enumerate(completed_lists, start=1):\n", + " print(f'List {i}: {lst}')" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Challenge:\n", + "O | X | \n", + "---------\n", + " | | O\n", + "---------\n", + " | | X\n", + "---------\n", + "\n", + "\n", + "Solution 1:\n", + "O | X | O\n", + "---------\n", + "O | O | O\n", + "---------\n", + "X | X | X\n", + "---------\n", + "\n", + "\n", + "Solution 2:\n", + "O | X | O\n", + "---------\n", + "O | X | O\n", + "---------\n", + "O | X | X\n", + "---------\n", + "\n", + "\n" + ] + } + ], + "source": [ + "print('Challenge:')\n", + "display_board(challenge)\n", + "print('\\n')\n", + "\n", + "for index, lst in enumerate(completed_lists):\n", + " print('Solution {}:'.format(index + 1))\n", + " display_board(lst)\n", + " print('\\n')" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "WOMANIUM", + "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": "3.11.4" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/challenges/PIQUE challenge/QuantumVoyagers/app/grover/grover_circuit_complete_image/file.tex b/challenges/PIQUE challenge/QuantumVoyagers/app/grover/grover_circuit_complete_image/file.tex new file mode 100644 index 0000000..1122f84 --- /dev/null +++ b/challenges/PIQUE challenge/QuantumVoyagers/app/grover/grover_circuit_complete_image/file.tex @@ -0,0 +1,33 @@ +\documentclass[border=2px]{standalone} + +\usepackage[braket, qm]{qcircuit} +\usepackage{graphicx} + +\begin{document} +\scalebox{1.0}{ +\Qcircuit @C=1.0em @R=0.2em @!R { \\ + \nghost{{q}_{0} : } & \lstick{{q}_{0} : } & \gate{\mathrm{X}} \barrier[0em]{21} & \qw \barrier[0em]{21} & \qw & \ctrl{3} & \ctrl{4} & \qw & \qw & \ctrl{1} & \qw & \qw & \qw \barrier[0em]{21} & \qw & \ctrl{9} \barrier[0em]{21} & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw \barrier[0em]{21} & \qw \barrier[0em]{21} & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw \barrier[0em]{21} & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw \barrier[0em]{21} & \qw & \ctrl{9} \barrier[0em]{21} & \qw & \qw & \qw & \qw & \ctrl{1} & \qw & \qw & \ctrl{4} & \ctrl{3} \barrier[0em]{21} & \qw \barrier[0em]{21} & \qw & \qw & \qw \barrier[0em]{8} & \qw & \qw & \qw & \qw \barrier[0em]{8} & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw\\ + \nghost{{q}_{1} : } & \lstick{{q}_{1} : } & \gate{\mathrm{I}} & \qw & \qw & \qw & \qw & \qw & \ctrl{3} & \ctrl{1} & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{8} & \ctrl{8} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{8} & \ctrl{8} & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{1} & \ctrl{3} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{2} : } & \lstick{{q}_{2} : } & \gate{\mathrm{I}} & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{15} & \ctrl{3} & \qw & \ctrl{2} & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{7} & \ctrl{7} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{7} & \ctrl{7} & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{2} & \qw & \ctrl{3} & \ctrl{15} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{3} : } & \lstick{{q}_{3} : } & \gate{\mathrm{X}} & \qw & \qw & \ctrl{3} & \qw & \ctrl{1} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{6} & \ctrl{6} & \ctrl{6} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{6} & \ctrl{6} & \ctrl{6} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{1} & \qw & \ctrl{3} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{4} : } & \lstick{{q}_{4} : } & \gate{\mathrm{H}} & \qw & \qw & \qw & \ctrl{4} & \ctrl{1} & \ctrl{3} & \qw & \qw & \qw & \ctrl{2} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{5} & \ctrl{5} & \ctrl{5} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{5} & \ctrl{5} & \ctrl{5} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{2} & \qw & \qw & \qw & \ctrl{3} & \ctrl{1} & \ctrl{4} & \qw & \qw & \qw & \gate{\mathrm{H}} & \gate{\mathrm{X}} & \qw & \qw & \ctrl{1} & \qw & \qw & \gate{\mathrm{X}} & \gate{\mathrm{H}} & \qw & \meter & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{5} : } & \lstick{{q}_{5} : } & \gate{\mathrm{H}} & \qw & \qw & \qw & \qw & \ctrl{10} & \qw & \qw & \ctrl{3} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{4} & \ctrl{4} & \ctrl{4} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{4} & \ctrl{4} & \ctrl{4} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{3} & \qw & \qw & \ctrl{10} & \qw & \qw & \qw & \qw & \gate{\mathrm{H}} & \gate{\mathrm{X}} & \qw & \qw & \ctrl{2} & \qw & \qw & \gate{\mathrm{X}} & \gate{\mathrm{H}} & \qw & \qw & \meter & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{6} : } & \lstick{{q}_{6} : } & \gate{\mathrm{I}} & \qw & \qw & \ctrl{7} & \qw & \qw & \qw & \qw & \qw & \ctrl{1} & \ctrl{14} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{3} & \ctrl{3} & \ctrl{3} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{3} & \ctrl{3} & \ctrl{3} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{14} & \ctrl{1} & \qw & \qw & \qw & \qw & \qw & \ctrl{7} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{7} : } & \lstick{{q}_{7} : } & \gate{\mathrm{H}} & \qw & \qw & \qw & \qw & \qw & \ctrl{9} & \qw & \qw & \ctrl{1} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{2} & \ctrl{2} & \ctrl{2} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{2} & \ctrl{2} & \ctrl{2} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{1} & \qw & \qw & \ctrl{9} & \qw & \qw & \qw & \qw & \qw & \gate{\mathrm{H}} & \gate{\mathrm{X}} & \qw & \qw & \ctrl{1} & \qw & \qw & \gate{\mathrm{X}} & \gate{\mathrm{H}} & \qw & \qw & \qw & \meter & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{8} : } & \lstick{{q}_{8} : } & \gate{\mathrm{H}} & \qw & \qw & \qw & \ctrl{6} & \qw & \qw & \qw & \ctrl{10} & \ctrl{11} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{1} & \ctrl{1} & \ctrl{1} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{1} & \ctrl{1} & \ctrl{1} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{11} & \ctrl{10} & \qw & \qw & \qw & \ctrl{6} & \qw & \qw & \qw & \gate{\mathrm{H}} & \gate{\mathrm{X}} & \qw & \gate{\mathrm{H}} & \targ & \gate{\mathrm{H}} & \qw & \gate{\mathrm{X}} & \gate{\mathrm{H}} & \qw & \qw & \qw & \qw & \meter & \qw & \qw & \qw\\ + \nghost{{q}_{9} : } & \lstick{{q}_{9} : } & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \ctrl{1} & \targ & \qw & \ctrl{1} & \targ & \qw & \ctrl{1} & \ctrl{1} & \targ & \qw & \ctrl{1} & \ctrl{1} & \targ & \qw & \ctrl{1} & \ctrl{1} & \targ & \qw & \ctrl{1} & \ctrl{1} & \targ & \qw & \ctrl{1} & \ctrl{1} & \targ & \qw & \ctrl{1} & \ctrl{1} & \targ & \qw & \gate{\mathrm{X}} & \ctrl{1} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{1} & \gate{\mathrm{X}} & \qw & \targ & \ctrl{1} & \ctrl{1} & \qw & \targ & \ctrl{1} & \ctrl{1} & \qw & \targ & \ctrl{1} & \ctrl{1} & \qw & \targ & \ctrl{1} & \ctrl{1} & \qw & \targ & \ctrl{1} & \ctrl{1} & \qw & \targ & \ctrl{1} & \ctrl{1} & \qw & \targ & \ctrl{1} & \qw & \targ & \ctrl{1} & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{10} : } & \lstick{{q}_{10} : } & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \targ & \qw & \qw & \ctrl{1} & \targ & \qw & \qw & \ctrl{1} & \targ & \qw & \qw & \ctrl{1} & \targ & \qw & \qw & \ctrl{1} & \targ & \qw & \qw & \ctrl{1} & \targ & \qw & \qw & \ctrl{1} & \targ & \qw & \qw & \gate{\mathrm{X}} & \ctrl{1} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{1} & \gate{\mathrm{X}} & \qw & \qw & \targ & \ctrl{1} & \qw & \qw & \targ & \ctrl{1} & \qw & \qw & \targ & \ctrl{1} & \qw & \qw & \targ & \ctrl{1} & \qw & \qw & \targ & \ctrl{1} & \qw & \qw & \targ & \ctrl{1} & \qw & \qw & \targ & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{11} : } & \lstick{{q}_{11} : } & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \ctrl{1} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{1} & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{12} : } & \lstick{{q}_{12} : } & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \ctrl{1} & \ctrl{2} & \ctrl{3} & \ctrl{4} & \ctrl{5} & \ctrl{6} & \ctrl{7} & \ctrl{8} & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{13} : } & \lstick{{q}_{13} : } & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{8} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{14} : } & \lstick{{q}_{14} : } & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{7} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{15} : } & \lstick{{q}_{15} : } & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{6} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{16} : } & \lstick{{q}_{16} : } & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{5} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{17} : } & \lstick{{q}_{17} : } & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{4} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{18} : } & \lstick{{q}_{18} : } & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{3} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{19} : } & \lstick{{q}_{19} : } & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{2} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{20} : } & \lstick{{q}_{20} : } & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{1} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{21} : } & \lstick{{q}_{21} : } & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \gate{\mathrm{X}} & \gate{\mathrm{H}} & \qw & \targ & \targ & \targ & \targ & \targ & \targ & \targ & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{\mathrm{{c} : }} & \lstick{\mathrm{{c} : }} & \lstick{/_{_{4}}} \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \dstick{_{_{\hspace{0.0em}0}}} \cw \ar @{<=} [-18,0] & \dstick{_{_{\hspace{0.0em}1}}} \cw \ar @{<=} [-17,0] & \dstick{_{_{\hspace{0.0em}2}}} \cw \ar @{<=} [-15,0] & \dstick{_{_{\hspace{0.0em}3}}} \cw \ar @{<=} [-14,0] & \cw & \cw & \cw\\ +\\ }} +\end{document} \ No newline at end of file diff --git a/challenges/PIQUE challenge/QuantumVoyagers/app/grover/grover_circuit_complete_image/grover_circuit.pdf b/challenges/PIQUE challenge/QuantumVoyagers/app/grover/grover_circuit_complete_image/grover_circuit.pdf new file mode 100644 index 0000000..01817bc Binary files /dev/null and b/challenges/PIQUE challenge/QuantumVoyagers/app/grover/grover_circuit_complete_image/grover_circuit.pdf differ diff --git a/challenges/PIQUE challenge/QuantumVoyagers/app/grover/solution.ipynb b/challenges/PIQUE challenge/QuantumVoyagers/app/grover/solution.ipynb new file mode 100644 index 0000000..6081169 --- /dev/null +++ b/challenges/PIQUE challenge/QuantumVoyagers/app/grover/solution.ipynb @@ -0,0 +1,834 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Solving Tic Tac Toe with Quantum Computing\n", + "In this notebook, we will explore how to apply quantum algorithms to solve the game of Tic Tac Toe. We will use two popular quantum algorithms: the Grover algorithm and the Quantum Approximate Optimization Algorithm (QAOA)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1. Introduction" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1.1 Overview of Tic Tac Toe\n", + "\n", + "Tic Tac Toe, also known as Noughts and Crosses, is a classic two-player game where players take turns marking spaces on a 3x3 grid. The grid is initially empty, and players alternate placing their symbols ('X' or 'O') in an attempt to form a horizontal, vertical, or diagonal line of three of their symbols. The game ends when one player achieves this goal, resulting in a win, or if the entire grid is filled without a winner, leading to a draw.\n", + "\n", + "#### Key Rules:\n", + "\n", + "1. **Players:** Two players, typically represented by 'X' and 'O'.\n", + "2. **Grid:** A 3x3 square grid.\n", + "3. **Objective:** Form a line of three of your symbols horizontally, vertically, or diagonally.\n", + "4. **Turns:** Players take turns to place their symbol in an empty grid space.\n", + "5. **Winning:** The game ends when a player forms a line of three symbols, declaring them the winner.\n", + "6. **Draw:** If the grid is fully occupied and no player has won, the game is a draw.\n", + "\n", + "Tic Tac Toe is a simple yet strategic game often used for educational purposes to teach basic game theory concepts. Now, let's explore how quantum algorithms can be applied to enhance the strategies involved in playing Tic Tac Toe.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "

\n", + "\"JuveYell\"\n", + "

\n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2. Grover's Algorithm" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 2.1 Explanation of Grover's Quantum Search Algorithm\n", + "\n", + "Grover's Quantum Search Algorithm, developed by Lov Grover in 1996, is a potent quantum algorithm designed to perform a quadratic speedup in searching an unsorted database compared to the best classical algorithms. This algorithm relies on the principles of amplitude amplification, enabling efficient solution discovery within a large solution space.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Key Concepts:\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "1. **Amplitude Amplification:**\n", + "In the quest for a marked element in a quantum list, we start in a uniform superposition:\n", + "\n", + " $$ \\ket{s} = \\frac{1}{\\sqrt{N}} \\sum_{x=0}^{N-1} \\ket{x} $$\n", + "\n", + " When measured in the standard basis, the probability of finding the correct element is $ \\frac{1}{N} = \\frac{1}{2^n} $. Amplitude amplification improves this probability by extending the amplitude of the marked element and reducing others. The algorithm's geometric interpretation involves two reflections generating a rotation in a two-dimensional plane. Introducing an additional state $ \\ket{s'} $, perpendicular to $ \\ket{w} $, achieves this by eliminating $ \\ket{w} $ from $ \\ket{s} $ and adjusting the scale." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Image obtained from the Qiskit Textbook

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "2. **Oracle:**\n", + " In quantum algorithms like Grover's, an oracle designates specific states as solutions. In Tic Tac Toe, it flips the sign of the probability amplitude for correct states:\n", + " $$U_\\omega\\ket{x}=\\begin{cases}\n", + " \\ket{x},& \\text{si } x\\neq \\omega\\\\\n", + " -\\ket{x},& \\text{si } x= \\omega\n", + " \\end{cases}\n", + " $$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Image obtained from the Qiskit Textbook

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "3. **Grover Diffusion Operator:**\n", + " The Grover diffusion operator enhances the amplitudes of marked states and suppresses unmarked states. It involves a sequence of quantum gates:\n", + " $$U_s=2\\ket{s}\\bra{s}-\\mathbb{1}$$\n", + " This sequence concentrates probability amplitudes on marked states, contributing to the algorithm's efficiency." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Image obtained from the Qiskit Textbook

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, Grover's algorithm looks like:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Imagen obtenida del Qiskit Textbook

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "#### Application in Tic Tac Toe:\n", + "\n", + "For Tic Tac Toe, Grover's algorithm can be applied to search for optimal moves on the game board. By defining the oracle to identify winning board configurations and implementing the Grover diffusion operator, we can efficiently determine the optimal moves that lead to victory.\n", + "\n", + "
\n", + "

\n", + "\"JuveYell\"\n", + "

\n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The concept revolves around assigning a qubit to each box, such that when the qubit is in the state |1>, it represents 'X', and when in the state |0>, it represents 'O'. The empty spaces are filled with Hadamard gates, as these states are the ones sought by the Grover's algorithm.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For this case, our Oracle consists of two crucial components. First, there are the eight victory conditions detailed in the preceding figure. However, it is essential to filter only valid plays based on both logic and the rules established earlier. Therefore, the Oracle is composed of two parts:\n", + "\n", + "1. **Victory Conditions:**\n", + " - The eight specific conditions determining a win in the game.\n", + "\n", + "2. **X's Counter:**\n", + " - A mechanism to count the total number of 'X' on the board. Since in any game where 'O' starts, there must be a total of 5 'O' and 4 'X', our counter verifies the presence of exactly 4 'X'.\n", + "\n", + "Finally, it is imperative to mark the states that meet any of the eight winning conditions, always ensuring there are exactly 4 'X' throughout the game. For this reason, we implement eight controlled-NOT gates, one for each winning condition, targeting the oracle qubit. This approach ensures the validity of winning plays while adhering to the restriction of having 4 'X' in the game.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "

\n", + "\"JuveYell\"\n", + "

\n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the preceding image, we can identify the most crucial part of our circuit. Each number represents a component of the total circuit:\n", + "\n", + "1. **Tic Tac Toe Representation Circuit:**\n", + " - This circuit represents the Tic Tac Toe game, where 'H' denotes empty spaces, NOT gates represent 'X's, and 'I's represent 'O's.\n", + "\n", + "2. **Oracle Sub-Circuit:**\n", + " - This sub-circuit is part of the oracle and encompasses all possible winning scenarios (8 in total).\n", + "\n", + "3. **Counter:**\n", + " - The counter activates a Multi-Controlled NOT gate only if the number of 'X's is equal to 4.\n", + "\n", + "4. **State | - >:**\n", + " - This state, when the required conditions are met, changes sign, marking the desired state.\n", + "\n", + "5. **Toffoli Gates:**\n", + " - Toffoli gates determine the sought-after states, activating when the necessary conditions are fulfilled.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The remainder of the circuit corresponds to the inverse of circuits 2 and 3 from the preceding figure, followed by the application of the diffuser. Finally, the qubits in the 'H' states are measured, as these are the ones sought based on the established conditions.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we will see the results of implementing Grover's algorithm for our specific problem." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit.visualization import plot_histogram\n", + "\n", + "import sys\n", + "sys.path.append('../../')\n", + "from pkg.general_utils import display_board, complete_lists_with_dictionary, filter_values_above_average\n", + "from pkg.quantum_utils import grover_algorithm, circuit_execute" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Setting up the board the way it is asked to solve it" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "X | O | O\n", + "---------\n", + "X | | \n", + "---------\n", + "O | | \n", + "---------\n" + ] + } + ], + "source": [ + "challenge = [['X', 'O', 'O'], ['X', ' ', ' '], ['O', ' ', ' ']]\n", + "display_board(challenge)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Building the complete circuit and graphing" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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xilddddVxf/+Zz3wmDz744LE/P3jwYFauXJnf+I3f8DxeAAAAAABg0Bg5JjljdvKjVwbumEOHJ1MXDNzx6mFAlpMPyHp6emraT3Nzc/bs2dNfZQEAAAAAAPSbcz6WdPwg6T4yMMf7uQuTYSMH5lj18ojFnHxABgAAAAAAcLob/Z7eIdlAGD8tef+HB+ZYfeEOsiSrV6+uuoRBb/LkybnjjjsyefLkqksBKiADADkAZZMBlE4PUDo9gDUAjWXGh3vvItu9tfZt3ux6+9eTGTYyWXBZ0jSIb9MyIKMmkyZNynXXXVd1GUBFZAAgB6BsMoDS6QFKpwewBqCxNDUlC389WfvN5I322rb57l/Uvv+hw5PFv9V7t9pgNohndwwme/fuzVNPPZW9e/dWXQpQARkAyAEomwygdHqA0ukBrAFoPMNGJB++Kpl4Vv/ud/io5MO/nUx4X//u91QwIKMmbW1tufXWW9PW1lZ1KUAFZAAgB6BsMoDS6QFKpwewBqAxDRuRfOi3ktkfT4b0w/MGz5yTXPC7yfip735fA8EjFgEAAAAAAArUNCQ56yPJGbOS1n9IdrUmPT317WPMGcnZFyST55yaGk8VAzIAAAAAAICCjX5P7+eSHexMtv9zsuvVpKsj6ek+/vubxyXvmZ5MW5SMf1/v55qdbgzIAAAAAAAASPPYZNaFvb+OHkn27UoOvpF0H0mahibDm5OxZyYjRldd6btnQEZNmpubM2/evDQ3N1ddClABGQDIASibDKB0eoDS6QGsASjT0GG9nyd2unymWL0MyKjJrFmz8uijj1ZdBlARGQDIASibDKB0eoDS6QGsAaARDam6AAAAAAAAABhIBmTUZMOGDVm4cGE2bNhQdSlABWQAIAegbDKA0ukBSqcHsAaARmRARk16enpy+PDh9PT0VF0KUAEZAMgBKJsMoHR6gNLpAawBoBEZkAEAAAAAAFAUAzIAAAAAAACKYkAGAAAAAABAUYZVXQCnh1mzZuWxxx7LjBkzqi4FqIAMAOQAlE0GUDo9QOn0ANYA0IgMyKhJc3NzZs+eXXUZQEVkACAHoGwygNLpAUqnB7AGgEbkEYvUZPv27fnSl76U7du3V10KUAEZAMgBKJsMoHR6gNLpAawBoBEZkFGTPXv2ZNWqVdmzZ0/VpQAVkAGAHICyyQBKpwconR7AGgAakQEZAAAAAAAARTEgAwAAAAAAoCgGZAAAAAAAABTFgIyaTJo0KTfccEMmTZpUdSlABWQAIAegbDKA0ukBSqcHsAaARmRARk2ampoyYsSINDU1VV0KUAEZAMgBKJsMoHR6gNLpAawBoBEZkFGTXbt25Wtf+1p27dpVdSlABWQAIAegbDKA0ukBSqcHsAaARmRABgAAAAAAQFEMyAAAAAAAACiKARkAAAAAAABFMSCjJuPHj8+yZcsyfvz4qksBKiADADkAZZMBlE4PUDo9gDUANKKmnp6enqqL4O26uroyZsyYJMm+ffvS0tLS78fYtGlTv+/zfzV37txTfgyg7+QAlE0GAHKA0ukBSqcHsAbq8+yfJIf2JSPHJB/7fNXVDDznX/b5Dzb9NUNxBxk1OXToULZu3ZpDhw5VXQpQARkAyAEomwygdHqA0ukBrAGgERmQUZPW1tZcdtllaW1trboUoAIyAJADUDYZQOn0AKXTA1gDQCMyIAMAAAAAAKAoBmQAAAAAAAAUxYAMAAAAAACAohiQAQAAAAAAUJRhVRfA6WHBggXZuHFj1WUAFZEBgByAsskASqcHKJ0ewBoAGpE7yAAAAAAAACiKARk12bx5c66++ups3ry56lKACsgAQA5A2WQApdMDlE4PYA1QqiNvJnteS44e6f1995Gka3fS01NtXfQPj1ikJvv3789LL72U/fv3V10KUAEZAMgBKJsMoHR6gNLpAawBSvLGzmT7Pyd7ftg7DPtphw8m//hnydARydgzkzNnJ1MXJMObq6mVd8eADAAAAAAAKNquV5PN/zN5o/3k7z36ZrKnrfdX67PJlHnJrAuTkWNOfZ30HwMyAAAAAACgSG8eSF5ZnezY2Lftu48kr72c/OiV5AO/lEyZnzQ19W+NnBoGZAAAAAAAQHHe2JGs+6vkza53v68jh5L130o6fpAsWJoMMX0Z9IZUXQCnh2nTpmXFihWZNm1a1aUAFZABgByAsskASqcHKJ0ewBqgEe1tT/7pL/tnOPbTdn4veemve+8sY3Azw6QmEyZMyBVXXFF1GUBFZAAgB6BsMoDS6QFKpwewBmg0XbuTF1f1fpbYqfDjLcn6p5JzL/e4xcHMHWTUZPfu3XnooYeye/fuqksBKiADADkAZZMBlE4PUDo9gDVAI+npTjY8lRw5WPs25386uehzvV9rtXNTsmND/fUxcIobkHV0dGT58uU555xz0tzcnBkzZuSWW25JV1dXrr/++jQ1NeW+++6rusxBp729PXfddVfa29urLgWogAwA5ACUTQZQOj1A6fQA1gCNZNs/JXtfq2+bES1J89jer/X43urk0L76tmHgFPWIxXXr1mXp0qXZsWNHWlpaMn/+/Lz22mu599578+qrrx77CYjFixdXWygAAAAAANCvDh9MXn1u4I535FDv8eb/6sAdk9oVcwdZR0dHli1blh07duS2225Le3t71q5dmx07dmTFihV54oknsmbNmjQ1NWXhwoVVlwsAAAAAAPSj1/4l6T4ysMfcsbF3MMfgU8yA7Oabb05bW1tuuumm3HPPPRk7duyx15YvX55FixblyJEjmTlzZsaNG1dhpQAAAAAAQH/q6Um2vzTwx+0+krSvH/jjcnJFDMg2btyYRx55JJMmTcrdd9993Pecd955SZJFixYd+7O3Bmrnn39+Ro4cmaamphMe49lnn80v//IvZ9KkSZkwYUI++tGP5tFHH+3fE6lQS0tLLrzwwrS01PmQVaAhyABADkDZZACl0wOUTg9gDdAIujqS/a9Xc+wffb+a4/LOivgMsocffjjd3d255pprMmbMmOO+Z9SoUUnePiBrbW3NqlWrsmTJkowYMSLPPXf8h5O+9NJL+cQnPpGLL744Dz74YIYPH54HHnggV155ZR577LF88pOf7P+TGmAzZ87MAw88UHUZQEVkACAHoGwygNLpAUqnB7AGaARv7Kzu2J0/6r2D7R3uwaECRdxBtnr16iTJJZdccsL3tLW1JXn7gOziiy9Oe3t7HnvssVx66aUn3PaRRx5JU1NT/vqv/zqf/OQn86u/+qv5L//lv2TGjBl56KGH+uksqnX06NHs27cvR48erboUoAIyAJADUDYZQOn0AKXTA1gDNIIqB2RH36zu7jVOrIgB2datW5MkZ5111nFfP3LkyLG7w356QDZkSG3fnjfffDMjRow4dhdakgwdOjRjx45Nd3d3X8seVDZt2pQlS5Zk06ZNVZcCVEAGAHIAyiYDKJ0eoHR6AGuARnBgT9nH52cV8YjFrq6uJMmBAweO+/ojjzySjo6OjB07NmeffXbd+7/22mvzta99LbfddlvuuOOODBs2LPfff3++//3v54//+I/fVe2zZ8+ueVBXj+uuu66u97e3tydJnnzyybz44os1bfPggw/WWRUwkOrJgb5kQCIHYDBzLQC4FqB0eoDS6QGsgfr8wfVrMnHs1LS3t2f69CVVlzPgGuH8l//mf8n891903NfO/3Qy4h0+Ym9ky0++XvS5dz7Om13Jd//iZ//8+t+9If/06rdqrJZ38tM3Jl100UV15dJPK2JANmXKlLz++utZu3ZtLrjggre91t7enttvvz1JsnDhwjT14SGgixYtyt/+7d/mN3/zN/OHf/iHSXo/uPKb3/xmLr744ndV+1t/+fS3/fv31/X+gwcPHvta67bbt2+vuy5g4NSTA33JgEQOwGDmWgBwLUDp9ACl0wNYA/V56/GSR48ebajzqlUjnP/+A10nfG1ES9I89uT7aBpS2/uO50e7dpy237vBbOfOvj87s4gB2aWXXpqNGzdmxYoV+cQnPpE5c+YkSdasWZNrr702HR0dSZLFixf3af/f//7386lPfSpLlizJjTfemKFDh+ahhx7K1Vdfnccffzy/9Eu/1Ofap06dekruIBs9enRd729ubj72tdZtp02bVnddwMCpJwf6kgGJHIDBzLUA4FqA0ukBSqcHsAbqM3To0GNfG+m8atUI538kx3/CXNJ719c7GdnSOxzr6U4OneS9J9rXyJbT93s32HR3dx+7uWjy5Ml93k9TT09PT38VNVi1tbVl8eLF+fGPf5xhw4Zl7ty5OXjwYFpbW7N06dJ0d3fn6aefzte//vXccMMNx93HnXfemS9/+cs53rfrqquuyj//8z9n/fr1GTbsJzPHSy65JHv27Kn79r6urq6MGTMmSbJv3760tLzDvZ19VO/zgtevX58rr7wyK1euzIIFC2raZu7cuX0pDRgg9eRAXzIgkQMwmLkWAFwLUDo9QOn0ANZAfZ79k+TQvmTkmORjn6+6moHXCOe/5btJ6z/0bduLPtd759jBzuQ79/dtHx+/ORk2om/b8nb9NUPp/1uTBqHp06fn2WefzeWXX57m5uZs2bIlEydOzP33358nnngir7zySpLeRyX2xcsvv5xFixa9bTiWJB/5yEeycePGd13/YDBnzpw899xzx+6+A8oiAwA5AGWTAZROD1A6PYA1QCMY1/cbjd610RMNxwajIh6xmCTz5s3L448//jN/vm/fvmzZsiVDhgzJueee26d9T5kyJevWrcuRI0feNiRbs2ZNw9wyOXz48EycOLHqMoCKyABADkDZZACl0wOUTg9gDdAIxk1JhgxLuo8M/LHfM33gj8nJFXEH2TtZv359enp6Mnv27OM+P3flypVZuXJlNmzY8Lbfv/DCC8fe84UvfCHf//7382/+zb/J448/nm9961u59tpr8/d///e55ZZbBuxcTqVt27blxhtvzLZt26ouBaiADADkAJRNBlA6PUDp9ADWAI1g2Mhk8geqOfa0hdUcl3dW/IDs5ZdfTnLixyteddVVueqqq/LNb37zbb+/77773vae//bf/lv27NmTz3zmM/md3/mdfO9738tDDz2Um2+++dSfxADo7OzMM888k87OzqpLASogAwA5AGWTAZROD1A6PYA1QKOYvnjgjzluSu8vBp9iHrF4IicbkPX09NS0n09+8pP55Cc/2W91AQAAAAAA/Wf81GTiWcnurQN3zJkfHbhjUR93kJ1kQAYAAAAAADSGeb+SDB0+MMeaPDc585yBORb1K/4OstWrV1ddAgAAAAAAMABGjU9m/2Ky6du1b/Nm19u/1mLE6OQDv1RfbQys4gdk1Gby5Mm54447Mnny5KpLASogAwA5AGWTAZROD1A6PYA1QKOZtijp+nHywxdre/93/6K+/Q8dkSz+zd4hGYOXARk1mTRpUq677rqqywAqIgMAOQBlkwGUTg9QOj2ANUCjaWpK5vzr3V21DslqNWxksvi3knFT+ne/9L/iP4OM2uzduzdPPfVU9u7dW3UpQAVkACAHoGwygNLpAUqnB7AGaERvDcnmfqL/PpNs3NRkyTXJhPf1z/44tQzIqElbW1tuvfXWtLW1VV0KUAEZAMgBKJsMoHR6gNLpAawBGlVTUzJ9UfLR65KJZ/V9P0OGJedcnCz5naRlYr+VxynmEYsAAAAAAECxRo1PPnRl8saOpG1dsnNT0n20hu0m9A7Ypp6bjBh1qqukvxmQAQAAAAAARWtqSsZP7f31gV/qHZa9sTPp3JkcPpj0dPfeKTZqfDJucjJ2SjJmUu92nJ4MyAAAAAAAAP7VsJG9j1x8N49dZPDzGWTUpLm5OfPmzUtzc3PVpQAVkAGAHICyyQBKpwconR7AGgAakTvIqMmsWbPy6KOPVl0GUBEZAMgBKJsMoHR6gNLpAawBoBG5gwwAAAAAAICiGJBRkw0bNmThwoXZsGFD1aUAFZABgByAsskASqcHKJ0ewBoAGpEBGTXp6enJ4cOH09PTU3UpQAVkACAHoGwygNLpAUqnB7AGgEZkQAYAAAAAAEBRDMgAAAAAAAAoigEZAAAAAAAARRlWdQGcHmbNmpXHHnssM2bMqLoUoAIyAJADUDYZQOn0AKXTA1gDQCMyIKMmzc3NmT17dtVlABWRAYAcgLLJAEqnByidHsAaABqRRyxSk+3bt+dLX/pStm/fXnUpQAVkACAHoGwygNLpAUqnB7AGgEZkQEZN9uzZk1WrVmXPnj1VlwJUQAYAcgDKJgMonR6gdHoAawBoRAZkAAAAAAAAFMWADAAAAAAAgKIYkAEAAAAAAFAUAzJqMmTIkCxZsiRDhlgyUCIZAMgBKJsMoHR6gNLpAawBoBFJNGrS3d2dNWvWpLu7u+pSgArIAEAOQNlkAKXTA5ROD2ANAI3IgAwAAAAAAICiGJABAAAAAABQFAMyAAAAAAAAimJARk3Gjx+fZcuWZfz48VWXAlRABgByAMomAyidHqB0egBrAGhETT09PT1VF8HbdXV1ZcyYMUmSffv2paWlpd+PsWnTpn7f5/9q7ty5p/wYQN/JASibDADkAKXTA5ROD2AN1OfZP0kO7UtGjkk+9vmqqxl4pZ8/g0t/zVDcQUZNDh06lK1bt+bQoUNVlwJUQAYAcgDKJgMonR6gdHoAawBoRAZk1KS1tTWXXXZZWltbqy4FqIAMAOQAlE0GUDo9QOn0ANYA0IgMyAAAAAAAACiKARkAAAAAAABFMSADAAAAAACgKAZkAAAAAAAAFGVY1QVweliwYEE2btxYdRlARWQAIAegbDKA0ukBSqcHsAaARuQOMgAAAAAAAIpiQEZNNm/enKuvvjqbN2+uuhSgAjIAkANQNhlA6fQApdMDWANAI/KIRWqyf//+vPTSS9m/f3/VpQAVkAGAHICyyQBKpwconR7AGijL0cNJx+bkjR1J586k68fJoX29rx3qStb9VTJucjL+fcl73p8McRsOpykDMgAAAAAAKFzX7qTtpaT9X5Ijh07wpp6k49XeX0kycmwybWHvr5EtA1Yq9AsDMgAAAAAAKFT3keQH/5hs/W7S01Pftoc6kx88l2xdk8z5ePK+DyZNTaekTOh3BmQAAAAAAFCgfbuSl59Iujre3X6Ovpls/O/JzleSBUvdTcbpwdNBqcm0adOyYsWKTJs2repSgArIAEAOQNlkAKXTA5ROD2ANNKY9ryUv/Jd3Pxz7abu3JC88nBzY23/7hFPFHWTUZMKECbniiiuqLgOoiAwA5ACUTQZQOj1A6fQA1kDjeWNn8uLK3ju/+tuBPcnabyYf+R13kjG4uYOMmuzevTsPPfRQdu/eXXUpQAVkACAHoGwygNLpAUqnB7AGGsuRN5OXHzs1w7G3HNiTrH+y/s80g4FkQEZN2tvbc9ddd6W9vb3qUoAKyABADkDZZACl0wOUTg9gDTSW1n+o/xGI5386uehzvV9rtXtr8trL9R0HBlKRA7KOjo4sX74855xzTpqbmzNjxozccsst6erqyvXXX5+mpqbcd999VZcJAAAAAAD9Zs9rSdu6+rcb0ZI0j+39Wo9X/i451FX/8WAgFPcZZOvWrcvSpUuzY8eOtLS0ZP78+Xnttddy77335tVXXz12m/DixYurLRQAAAAAAPrRthcG9nhH3+y9i+zsjw7scaEWRd1B1tHRkWXLlmXHjh257bbb0t7enrVr12bHjh1ZsWJFnnjiiaxZsyZNTU1ZuHBh1eUCAAAAAEC/OLQv2dU68Mdteynp7h7448LJFDUgu/nmm9PW1pabbrop99xzT8aOHXvsteXLl2fRokU5cuRIZs6cmXHjxlVY6eDT0tKSCy+8MC0tdd5DCzQEGQDIASibDKB0eoDS6QGsgcbQviHpqWBQdagzeX3rwB8XTqaYAdnGjRvzyCOPZNKkSbn77ruP+57zzjsvSbJo0aJjf/bWQO3888/PyJEj09TUdMJjfPvb385HP/rRNDc358wzz8znP//57N1b56cdDlIzZ87MAw88kJkzZ1ZdClABGQDIASibDKB0eoDS6QGsgcawt73MY8OJFDMge/jhh9Pd3Z1rrrkmY8aMOe57Ro0aleTtA7LW1tasWrUqU6ZMyZIlS064/7//+7/PZZddlmnTpuWv/uqv8n//3/93Vq5cmd/4jd9Iz/+fvb8Ps6uu74X/90yehswkgQgmMQkEQ9KEYELF0CJUpTe2oKDtEZQefKClYCv84OZ4CL+71Us95a5iaXtXsUeoWm5bpWigFgNiq0ltzKkY5EHMgxjMAxMmSMgDM5MHksy+/5hDJJCQmWFm1mR/X6/ryjVk9lp7f76T9XnvTT5Za9Vq/buYCuzbty8dHR3Zt29f1aUAFZABgByAsskASqcHKJ0ewDFQH9o3Vffazz5V3WvDoRQzIFu8eHGS5Oyzzz7kNq2trUkOHJC96U1vSltbW+6+++6cc845h9z3f/yP/5EZM2bk61//es4777xcfvnlufXWW/Pv//7vueeee/ppFdVZvXp15s+fn9WrV1ddClABGQDIASibDKB0eoDS6QEcA0e+vbuTXe3VvX7H09W9NhzK8KoLGCzr13df5PSEE0446ON79+7NsmXLkhw4IGts7NkM8f7778/v//7vH7D9b/3WbyVJvvGNb+T888/vU90zZszocQ29cemll/Zq+7a27nNg77333jz00EM92ue2227rZVXAYOpNDvQlAxI5AEOZzwKAzwKUTg9QOj2AY6B3/uqy5Rk/ZlLa2toyZcqhrzQ2VB3TMil//YfLD/n46e9NRr7MLeZGNf/y61kfPPR2z3UmP/zHl35/81NbM2XK63pYLby8rq5f3kzvrLPO6lUuvVAxA7LOzs4kyc6dOw/6+B133JHNmzdnzJgxOfHEE3v9/MOGDcvIkSMP+N6IESPS0NCQFStW9L7g/+35N5/+tmPHjl5tv2vXrv1fe7rvxo0be10XMHh6kwN9yYBEDsBQ5rMA4LMApdMDlE4P4BjonecvL7lv374jcl3PjWt42cdHNidNYw7/PA2NPdvuxWq1+joeGDqeeqrv1+8sZkA2ceLEbN26NQ8++GDOOOOMAx5ra2vLddddlySZO3duGhpePiwOZubMmbn//vsP+N7y5ctTq9WyZcuWPtc9adKkATmDbPTo0b3avqmpaf/Xnu47efLkXtcFDJ7e5EBfMiCRAzCU+SwA+CxA6fQApdMDOAZ6Z9iwYfu/Honram4a97KPP9f58vuPau4ejtW6kt0vs+2hnmdv1+4j8ufG0NTV1bX/5KIJEyb0+XkaarVarb+KGsquvvrqfPazn83UqVPzne98JzNnzkzSPcR63/vel5///OfZs2dPrrzyytx8880HfY6Pf/zj+cQnPpGD/cj+4R/+Ie9///vzZ3/2Z/mjP/qjtLa25v3vf39WrlyZGTNmZNWqVT2utbOzMy0tLUmSjo6ONDe/zLmtfdTb6wWvWLEiF154YRYuXJg5c+b0aJ9Zs2b1pTRgkPQmB/qSAYkcgKHMZwHAZwFKpwconR7AMdA7Sz+f7O5IRrUkv/FHVVfTe7Va8h9/m+w5+AXWDuusD3afObarPfn+Lb3ff/zxyevf3bfXhhfrrxlKMWeQLViwIF/96lfzxBNPZM6cOZk1a1Z27dqVNWvW5Lzzzsu0adPy7W9/+4D7j/XGe9/73qxYsSJ/9md/lo9+9KMZNmxYrrzyyowcOTJjx47t59UMvpkzZ2bZsmUZM6YP588CRzwZAMgBKJsMoHR6gNLpARwDR76GhmTshOSZddW8/pi+n+QDA6b/r903RE2ZMiVLly7N29/+9jQ1NWXdunUZP358brnlltxzzz157LHHkqTPA7KGhoZ86lOfyubNm/PII4/kqaeeyl/+5V/mZz/7Wd74xjf251IqMWLEiIwfPz4jRoyouhSgAjIAkANQNhlA6fQApdMDOAbqw9iJZb42HEoxA7IkmT17dhYtWpT29va0t7fn/vvvzxVXXJHOzs6sW7c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+ "text/plain": [ + "
" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = grover_algorithm(challenge, rep=1)\n", + "\n", + "qc.draw('mpl')" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'\\\\documentclass[border=2px]{standalone}\\n\\n\\\\usepackage[braket, qm]{qcircuit}\\n\\\\usepackage{graphicx}\\n\\n\\\\begin{document}\\n\\\\scalebox{1.0}{\\n\\\\Qcircuit @C=1.0em @R=0.2em @!R { \\\\\\\\\\n\\t \\t\\\\nghost{{q}_{0} : } & \\\\lstick{{q}_{0} : } & \\\\gate{\\\\mathrm{X}} \\\\barrier[0em]{21} & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\ctrl{3} & \\\\ctrl{4} & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\ctrl{9} \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\ctrl{9} \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\ctrl{4} & \\\\ctrl{3} \\\\barrier[0em]{21} & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{8} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{8} & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{1} : } & \\\\lstick{{q}_{1} : } & \\\\gate{\\\\mathrm{I}} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{3} & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{8} & \\\\ctrl{8} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{8} & \\\\ctrl{8} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\ctrl{3} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{2} : } & \\\\lstick{{q}_{2} : } & \\\\gate{\\\\mathrm{I}} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{15} & \\\\ctrl{3} & \\\\qw & \\\\ctrl{2} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{7} & \\\\ctrl{7} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{7} & \\\\ctrl{7} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{2} & \\\\qw & \\\\ctrl{3} & \\\\ctrl{15} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{3} : } & \\\\lstick{{q}_{3} : } & \\\\gate{\\\\mathrm{X}} & \\\\qw & \\\\qw & \\\\ctrl{3} & \\\\qw & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{6} & \\\\ctrl{6} & \\\\ctrl{6} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{6} & \\\\ctrl{6} & \\\\ctrl{6} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\qw & \\\\ctrl{3} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{4} : } & \\\\lstick{{q}_{4} : } & \\\\gate{\\\\mathrm{H}} & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{4} & \\\\ctrl{1} & \\\\ctrl{3} & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{2} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{5} & \\\\ctrl{5} & \\\\ctrl{5} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{5} & \\\\ctrl{5} & \\\\ctrl{5} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{2} & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{3} & \\\\ctrl{1} & \\\\ctrl{4} & \\\\qw & \\\\qw & \\\\qw & \\\\gate{\\\\mathrm{H}} & \\\\gate{\\\\mathrm{X}} & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\gate{\\\\mathrm{X}} & \\\\gate{\\\\mathrm{H}} & \\\\qw & \\\\meter & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{5} : } & \\\\lstick{{q}_{5} : } & \\\\gate{\\\\mathrm{H}} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{10} & \\\\qw & \\\\qw & \\\\ctrl{3} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{4} & \\\\ctrl{4} & \\\\ctrl{4} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{4} & \\\\ctrl{4} & \\\\ctrl{4} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{3} & \\\\qw & \\\\qw & \\\\ctrl{10} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\gate{\\\\mathrm{H}} & \\\\gate{\\\\mathrm{X}} & \\\\qw & \\\\qw & \\\\ctrl{2} & \\\\qw & \\\\qw & \\\\gate{\\\\mathrm{X}} & \\\\gate{\\\\mathrm{H}} & \\\\qw & \\\\qw & \\\\meter & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{6} : } & \\\\lstick{{q}_{6} : } & \\\\gate{\\\\mathrm{I}} & \\\\qw & \\\\qw & \\\\ctrl{7} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\ctrl{14} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{3} & \\\\ctrl{3} & \\\\ctrl{3} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{3} & \\\\ctrl{3} & \\\\ctrl{3} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{14} & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{7} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{7} : } & \\\\lstick{{q}_{7} : } & \\\\gate{\\\\mathrm{H}} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{9} & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{2} & \\\\ctrl{2} & \\\\ctrl{2} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{2} & \\\\ctrl{2} & \\\\ctrl{2} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\ctrl{9} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\gate{\\\\mathrm{H}} & \\\\gate{\\\\mathrm{X}} & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\gate{\\\\mathrm{X}} & \\\\gate{\\\\mathrm{H}} & \\\\qw & \\\\qw & \\\\qw & \\\\meter & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{8} : } & \\\\lstick{{q}_{8} : } & \\\\gate{\\\\mathrm{H}} & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{6} & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{10} & \\\\ctrl{11} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\ctrl{1} & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\ctrl{1} & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{11} & \\\\ctrl{10} & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{6} & \\\\qw & \\\\qw & \\\\qw & \\\\gate{\\\\mathrm{H}} & \\\\gate{\\\\mathrm{X}} & \\\\qw & \\\\gate{\\\\mathrm{H}} & \\\\targ & \\\\gate{\\\\mathrm{H}} & \\\\qw & \\\\gate{\\\\mathrm{X}} & \\\\gate{\\\\mathrm{H}} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\meter & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{9} : } & \\\\lstick{{q}_{9} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\ctrl{1} & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\ctrl{1} & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\ctrl{1} & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\ctrl{1} & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\ctrl{1} & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\ctrl{1} & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\gate{\\\\mathrm{X}} & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\gate{\\\\mathrm{X}} & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\ctrl{1} & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\ctrl{1} & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\ctrl{1} & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\ctrl{1} & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\ctrl{1} & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\ctrl{1} & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{10} : } & \\\\lstick{{q}_{10} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\qw & \\\\gate{\\\\mathrm{X}} & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\gate{\\\\mathrm{X}} & \\\\qw & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{11} : } & \\\\lstick{{q}_{11} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{12} : } & \\\\lstick{{q}_{12} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\ctrl{2} & \\\\ctrl{3} & \\\\ctrl{4} & \\\\ctrl{5} & \\\\ctrl{6} & \\\\ctrl{7} & \\\\ctrl{8} & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{13} : } & \\\\lstick{{q}_{13} : } & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{8} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{14} : } & \\\\lstick{{q}_{14} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{7} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{15} : } & \\\\lstick{{q}_{15} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{6} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{16} : } & \\\\lstick{{q}_{16} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{5} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{17} : } & \\\\lstick{{q}_{17} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{4} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{18} : } & \\\\lstick{{q}_{18} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{3} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{19} : } & \\\\lstick{{q}_{19} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{2} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{20} : } & \\\\lstick{{q}_{20} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{21} : } & \\\\lstick{{q}_{21} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\gate{\\\\mathrm{X}} & \\\\gate{\\\\mathrm{H}} & \\\\qw & \\\\targ & \\\\targ & \\\\targ & \\\\targ & \\\\targ & \\\\targ & \\\\targ & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{\\\\mathrm{{c} : }} & \\\\lstick{\\\\mathrm{{c} : }} & \\\\lstick{/_{_{4}}} \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\dstick{_{_{\\\\hspace{0.0em}0}}} \\\\cw \\\\ar @{<=} [-18,0] & \\\\dstick{_{_{\\\\hspace{0.0em}1}}} \\\\cw \\\\ar @{<=} [-17,0] & \\\\dstick{_{_{\\\\hspace{0.0em}2}}} \\\\cw \\\\ar @{<=} [-15,0] & \\\\dstick{_{_{\\\\hspace{0.0em}3}}} \\\\cw \\\\ar @{<=} [-14,0] & \\\\cw & \\\\cw & \\\\cw\\\\\\\\\\n\\\\\\\\ }}\\n\\\\end{document}'" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc.draw('latex_source', filename='./grover_circuit_complete_image/file.tex')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Running the complete circuit and graphing the results" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'1011': 288, '0000': 293, '1000': 296, '0011': 317, '1101': 293, '1100': 7852, '1110': 315, '0111': 323, '1001': 7791, '1010': 319, '0010': 286, '1111': 329, '0101': 323, '0001': 298, '0110': 348, '0100': 329}\n" + ] + } + ], + "source": [ + "counts_without_qiskit_convention = circuit_execute(qc, shots=20000)\n", + "print(counts_without_qiskit_convention)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plot_histogram(counts_without_qiskit_convention, color='midnightblue')" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'1100': 7852, '1001': 7791}\n" + ] + } + ], + "source": [ + "possible_results = filter_values_above_average(counts_without_qiskit_convention)\n", + "\n", + "print(possible_results)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "List 1: [['X', 'O', 'O'], ['X', 'X', 'X'], ['O', 'O', 'O']]\n", + "List 2: [['X', 'O', 'O'], ['X', 'X', 'O'], ['O', 'O', 'X']]\n" + ] + } + ], + "source": [ + "completed_lists = complete_lists_with_dictionary(challenge, possible_results)\n", + "\n", + "for i, lst in enumerate(completed_lists, start=1):\n", + " print(f'List {i}: {lst}')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Printing all possible valid results" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Challenge:\n", + "X | O | O\n", + "---------\n", + "X | | \n", + "---------\n", + "O | | \n", + "---------\n", + "\n", + "\n", + "Solution 1:\n", + "X | O | O\n", + "---------\n", + "X | X | X\n", + "---------\n", + "O | O | O\n", + "---------\n", + "\n", + "\n", + "Solution 2:\n", + "X | O | O\n", + "---------\n", + "X | X | O\n", + "---------\n", + "O | O | X\n", + "---------\n", + "\n", + "\n" + ] + } + ], + "source": [ + "print('Challenge:')\n", + "display_board(challenge)\n", + "print('\\n')\n", + "\n", + "for index, lst in enumerate(completed_lists):\n", + " print('Solution {}:'.format(index + 1))\n", + " display_board(lst)\n", + " print('\\n')\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Post quantum analysis" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is evident for us that there are only two ways to win if we play as 'X'. The first is with the move |1100>, and the second is with the move |1001>, as shown in the results obtained by the implemented Grover's algorithm. Furthermore, we observe that for both winning plays, the 'X's played in the first available position. This implies that making this move increases the probability of winning, which makes sense since having this move with the 'X's provides two winning options in the next turn. However, if we analyze the 'O' move, meaning if 'O' plays in the third available position, then a guaranteed win is ensured, as the subsequent moves of 'X' become irrelevant.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "

\n", + "\"JuveYell\"\n", + "

\n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Bonus" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "X | O | O\n", + "---------\n", + "X | | \n", + "---------\n", + " | | \n", + "---------\n" + ] + } + ], + "source": [ + "challenge_bonus = [['X', 'O', 'O'], ['X', ' ', ' '], [' ', ' ', ' ']]\n", + "display_board(challenge_bonus)" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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Zjh079NBDD8l/zj8WP/vZz0qSXn/9dd17770xxVNYWHjec8bLggULbG1fWxu58PKmTZu0e/fuqPZ5+eWXbUYFAADgDCd6Ial/90N23gMv5t+Xr9z2lP7sE4ts7xc6HVZ+foGsfvDRaWvAAGnVC/F7PstS9z99T+rqlK7LV/inP5P/07fJd+2IuL3GuMJx8p11/vQb09ZAevZozVz6mz4f++uZ0pBBl95/SOBP37/1hYtvd6ZN+ufNF/68vLJaeXm3RBmtO9JSAvrhf4vtRkkrvv0DrXtnRZwjct43Zq3ULdffZ3u/yg+P6768G+MfUAKZ2Avc9OXvqeDGL/X52OXqQLQ1QLp4HXjsieWq2LE6ymjd8cVpf6M5n/wr2/udDUljR49TR2dyX3d52JDr9N2/fCemff9m8d/rzb3/FueIEsu046OBIcN179+9d9HH41UHLlYDjh1vUF5ecZTRusMnn360pFJ+v/177f7gn36kn779VAKictZDd31Xn570Fdv7nahuUV5eUQIi6lv4nOv2zpgxw9bfzediQNZLKBS50HZbW1ufj69du1b19fXKyMjQqFGjen6ekpKiAQMGnLdtWlqafD6f9u/fH3M8HxfeeGtttfcXdnt7e8/3aPetqamxHRcAAIATnOiFpP7dD9nJw4v596WtNbbTa/w+v+pq69TV3RnniGIQGKi0OD5d+PX1svZ+IP9DX5N/2i3qevS/qfufvqeU51bI5/PF5TWO1R6T2mP4uP4VMm0NXGVlXPSxIYOkoYOjex6/P/ptzxW2+tf70ZdBA/u+zUI02lrb+31+0Tgb4w2q/EpNuvxN7AUmtl3877lo60CsNUCSzpxp7lfvR19Cob6PB0bjxPGTamlrjF8wbuiI8Q9XUktLqN//+fZm2vHRjPZLn4SR6Dpgydev3o+++P0pMQ3HJKmj/Wy/zy8aHTH25Sk+93qB48ePx7wvA7Jehg8frtOnT2vXrl2aNm3aeY/V1tZq6dKlkqTi4uLz/kE4btw47dix47ztd+7cKcuy1NAQ+wVWR4wYkZAzyAYPtlfFAoFAz/do983NzbUdFwAAgBOc6IWk/t0P2cnDi/n3JeyPbUAWam9UzvBr4hxNbKwBAxSv+59bNTUK//hl+a4fJ/+X75cvJUX+B+cp/G//V+HX1yvlC5+Py+tcO+JaV84gM20NDL4q86KPnYniePCQQOSAWDgsnbnEUrnoc3Wf7Vfvx8V0dLZpYNplTqfrg5XSkRT5XU6nFdu1t5rbTyVd/ib2AgPTLn586XJ1INoacKnnSh88sF+9H32xUmI7MNzZ1aGhV2co0wrGOSJnBQcOuPxGF+FL6+r3f769mXZ8dEBw6CUfj1cduNjzWN3J8XflmdZTGjL4atv7dfvakiK/y+lSbB8UaG5zthcIh8M9Jxfl5OTE/Dw+y/LCFXLjZ8mSJfrBD36g/Px8vfnmmxo3bpykyLBr/vz5Onz4sDo7O/Xoo49q5cqVPfv95Cc/0Ve/+lV9+9vf1je+8Q1VV1frq1/9qg4cOKDCwkKVlpZGHUMoFFJ6euSTay0tLQoG4/+Xq91r5e7fv1/333+/XnnlFU2cODGqfYqKnDulEgAAwA4neiGpf/dDdt4DL+bfl1CD9Lsf298vr0Qqujv+8cQi1N2lq7b81xU/jxUOq/uvl8r6qFyp/+cH8l13XeTn3d3qfuyvZR2pUuqqf4nLpRZP33m3ginOf3bTtDXQHZb++39Ind2x7f+tL0Q+Ld7YKn3rNfv7T7hWevjit/ruN/b/MnLvDbumL5IGXXwGmTROV0vv/8z+fqOnS6OnXX67/sTEXmDLAWl9bFeguuIaIEmPfVYaNSy2fZ3Sfkb67Q8l2TxaOnyCNOlzCQnJcbtfkU5V2tvHnyrd9v9JqQMTElLCmHZ81LKkv3tFao3xc0lXWgfG5kiL74rttZ1U9mupOoZaOe0hKWh/rtbvnDku/f4n9vcbOVUq/HT847mYeM1QzLu78mUsW7ZMV199tY4ePaqJEydq8uTJKiws1M0336zRo0frzjvvlHT+/cck6cEHH9Ty5cv17W9/W8OGDdNNN92kO+64Q1OmTNGIEfG7Pr9bxo0bp+3bt/cMDAEAAExiei9kSv7BLCmr71sRX1LelLiH4rrwK6/KOlAq/9ce7BmOSZIvJUUpf/PXUrhb3f/0PZnyeUsvrIEUv5R7lXuvn58kB4xiWc/ZY7wxHJOkobn2D+75/FLu5MTE0594oQ7kZ7n32j6fuzUoWoEh0rAx9vfLnxL3UFwTSx0cMSH5hmOxSPY64PNJeS7WATdrkB15JZffprer8r0xHJOkITnSkBjGGbkxvG/9AQOyXvLy8rRt2zbdc889CgQCqqysVFZWllatWqWNGzfq4MGDki4ckPl8Pn3nO99RfX299u7dq+PHj+uf/umf9NFHH+lTn/qUG6nEVVpamrKyspSWFs87GgAAACQH03shk/IfM0Oyc9uBEROl9H7+aXi7rKoqhf/vT+QbXyT/n3/xgsd9BSPlf3CerH1/UPj19S5E6DyvrAE3h1TJclAsc4SUY+PD/v5Uacz0xMXjNJ/vj5/+tnGLwZE3SVdw+7ak4YU6kJdl6482roZnSgOS5EYvoz8lpdj4Y75mXGwHk/ur7NHSVdddfruPpQ2SCm5OXDz9iRfqgJt/HydLL5CeLV1r44Mf/hRpzK2Ji8cNY2+NfAAmWvk3SIOHJiychGJA1ofx48drw4YNam5uVnNzs3bs2KGHH35YoVBIlZWV8vv9mjRpUp/7ZmRkqLi4WFdffbX+7d/+TW1tbXrooYccziD+qqqq9Mgjj6iqqsrtUAAAABxnei9kUv6ZI6TiOZGD3pczrFAa/9nEx+Q033XXKW3jfyr1f/+zfCl9TwtTvvKA0n61KW73IevvvLIGbrBxwDOeBg+Qxg1357VjMWFm5ADx5aSkSSX3SRn94xaEcZM9WprwZ4pqkpJb7L2DghfjhTowaIBUdK07r31DDGdouyXjmsjajmZIdvUoaeKsyHDZK3z+SC+UGcXvStogacoXpUFDEx5Wv+CFOuDWWhyYKk1IottzFd0VGX5fjj9FmjxbGupSbU2UrOukSfdIvig+ODh8gjQuCS6jfTEMyGzYv3+/LMtSYWHhBTdifO+99/TMM8/ojTfe0MaNG/X444/rG9/4hlasWKExY2I4N7ufaW5u1tatW9Xc3Ox2KAAAAI4zvRcyLf/sMdLUv5Byru/7k5ODs6TrPyMVz7Z3thmSl1fWwKhh0rVDnX/dT45JnjNHJCklVSq+L3KwZ3Afl4TzpUjDx0fqxNUFTkfnjGsnSTfNjdTDvmRcI02YFbn/opcGA5filToww4Urw6X4pVuS7NBY1khp6rzIgd++DhAPGioV3i6VfMHe2WbJIi0gfeJLkTPrB2Zc+Lg/NXKGzdR5kQ8XmcILdSAvSxqV7fzr3jRKCiTRWvl48HX9ZyKXYe/N548M0G76C2nYWOfjc0LO9ZFeYFih+vzQTHp25MOCE2fZO9usv0miFtV9+/btk3Th5RUlaeDAgfrFL36hZ555Rl1dXZo8ebLWrl2r+++/3+kwAQAAAFyhjGsi/yjuCEn1h6WDW6Xus5EDRtMeMueAMLzF55NuvV5au8O51/T7pOmFzr1evPj90nU3SvmfkE5XSXv/M1IDUgdKn/pLaUBs94FPKkNzpSlfkNqapFOV0kdv/7EODpJunk8dTFbjR0jZ6VJ9i3OvOeU6acgg514vXtKzpUmfk8bdLtUfkj48pxf41ELvr4GUNGnULdLIm6WGCmnfxj/VwemLIu8DktOM66WKeudezyd3hvNXyueLXDowb4rUWC3tfU3q+uMamPaQGZcXzhwhlXxeam+WTlVIB9/6Uy/wya95ow4m8WzPeZcakE2ePFnvvPOOzpw5o9bWVu3YsYPhGAAAAJDkBgal3MlS6oDI//tTvfEPQZjrk6OlkQ7ei+wzE6TsPs4+SBY+X+RMko9rQEqaGcOxcw3KlPJKzqmDKdTBZOb3S/c7eL+oQJo0+wbnXi8RBgyOnC1lai/g90fOJj23DjIcS243jJQKc5x7vVuvl0YMde714s3nk67Kl1LOWQMmDMfOFciIXFbZi70AAzIbLjUgAwAAAACgv/P7pb+YJqU6cDRgeKb0ZzZucg/AGUUjnLvk4RdulIYOvvx2AJzj90lzb3Hm8sfZ6dI9UxL/OkCsGJDZsGXLFlmWpXvuucftUByXk5Oj5cuXKyfHwY8XAAAA9BOm90Km5w94bQ3kZEp/PtXePmfapMbWyPdoBNKk+dOlVO7TB4/wWh2470Z7Z3TYrQGSdGOBdPNou5EB/ZeX6sDV6dKXbZ5NarcODEiRHpwuDeQmT+jH+PVEVLKzs7VgwQK3wwAAAHCF6b2Q6fkDXlwD08ZKbWel9buj2/6fN0f/3ANTpUW3S7lXxRQa0C95rQ4E0qT/705p5ZvSiTOX395ODZCkSXmRs1W9cgkuQPJeHbhpVKQXWPdedNvbqQNpKdLCT0sF2bHFBjiFM8gQlaamJm3evFlNTU1uhwIAAOA403sh0/MHvLoG7pwQ+fR4PC+3mDlIevQuacw18XtOoD/wYh0YMkhacrc0alh8n/eWMdJDt0opHHWEx3ixDtx6vTRvWmSgFS8ZgcgA/voR8XtOIFH4qwpRqa6u1uOPP67q6mq3QwEAAHCc6b2Q6fkDXl4DnyqU/uZz0nVXX/lz3TxaWn5vfJ4L6G+8WgfSA9J/u0v6/Ceu/AD5kEHS/+/TkXsbMRyDF3m1DkwdLS27Rxodh2H5jQXSf79XGs0HZZAkuMQiAAAAAAAGG54pPfZZ6d1yadtBqc7mB+OLRkh3jOeT4kCy8vsja3hirrTlgPR+pdTZHf3+6QFp2hjp9vFScGDCwgSQQMMypMV3Sb+vkLZ9KNWctrf/uOHS7UXShNzExAckCgMyAAAAAAAMl+KXpo+LnFF2+IS064h0tCFygKw7fP62gwZI+Vm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+ "text/plain": [ + "
" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc_bonus = grover_algorithm(challenge_bonus, rep=1)\n", + "\n", + "qc_bonus.draw('mpl')" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'10010': 40, '00011': 47, '01111': 34, '10101': 31, '01001': 41, '00111': 28, '11111': 30, '11011': 37, '00001': 39, '01011': 41, '10100': 3164, '10001': 3212, '11010': 38, '11101': 40, '00101': 3080, '11000': 3170, '11100': 36, '10110': 38, '10000': 36, '01100': 3189, '00110': 3183, '00010': 34, '10111': 31, '01101': 42, '11110': 39, '01010': 48, '01000': 45, '01110': 51, '00100': 43, '00000': 36, '10011': 40, '11001': 37}\n" + ] + } + ], + "source": [ + "\n", + "counts_without_qiskit_convention = circuit_execute(qc_bonus, shots=20000)\n", + "print(counts_without_qiskit_convention)" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plot_histogram(counts_without_qiskit_convention, color='midnightblue')" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'10100': 3164, '10001': 3212, '00101': 3080, '11000': 3170, '01100': 3189, '00110': 3183}\n" + ] + } + ], + "source": [ + "possible_results = filter_values_above_average(counts_without_qiskit_convention)\n", + "\n", + "print(possible_results)" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "List 1: [['X', 'O', 'O'], ['X', 'X', 'O'], ['O', 'X', 'O']]\n", + "List 2: [['X', 'O', 'O'], ['X', 'X', 'O'], ['O', 'O', 'O']]\n", + "List 3: [['X', 'O', 'O'], ['X', 'O', 'O'], ['O', 'X', 'O']]\n", + "List 4: [['X', 'O', 'O'], ['X', 'X', 'X'], ['O', 'O', 'O']]\n", + "List 5: [['X', 'O', 'O'], ['X', 'O', 'X'], ['O', 'X', 'O']]\n", + "List 6: [['X', 'O', 'O'], ['X', 'O', 'O'], ['O', 'X', 'X']]\n" + ] + } + ], + "source": [ + "completed_lists = complete_lists_with_dictionary(challenge, possible_results)\n", + "\n", + "for i, lst in enumerate(completed_lists, start=1):\n", + " print(f'List {i}: {lst}')" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Challenge:\n", + "X | O | O\n", + "---------\n", + "X | | \n", + "---------\n", + "O | | \n", + "---------\n", + "\n", + "\n", + "Solution 1:\n", + "X | O | O\n", + "---------\n", + "X | X | O\n", + "---------\n", + "O | X | O\n", + "---------\n", + "\n", + "\n", + "Solution 2:\n", + "X | O | O\n", + "---------\n", + "X | X | O\n", + "---------\n", + "O | O | O\n", + "---------\n", + "\n", + "\n", + "Solution 3:\n", + "X | O | O\n", + "---------\n", + "X | O | O\n", + "---------\n", + "O | X | O\n", + "---------\n", + "\n", + "\n", + "Solution 4:\n", + "X | O | O\n", + "---------\n", + "X | X | X\n", + "---------\n", + "O | O | O\n", + "---------\n", + "\n", + "\n", + "Solution 5:\n", + "X | O | O\n", + "---------\n", + "X | O | X\n", + "---------\n", + "O | X | O\n", + "---------\n", + "\n", + "\n", + "Solution 6:\n", + "X | O | O\n", + "---------\n", + "X | O | O\n", + "---------\n", + "O | X | X\n", + "---------\n", + "\n", + "\n" + ] + } + ], + "source": [ + "print('Challenge:')\n", + "display_board(challenge)\n", + "print('\\n')\n", + "\n", + "for index, lst in enumerate(completed_lists):\n", + " print('Solution {}:'.format(index + 1))\n", + " display_board(lst)\n", + " print('\\n')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Post quantum analysis" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Para este caso tambien podemos hacer el analisis post cuantico. Para saber que jugadas podrían darnos una mayor probabilidad de ganar:\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "

\n", + "\"JuveYell\"\n", + "

\n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can observe that the optimal move for 'X' is marking the third playable box (in red), which logically results in an automatic win. On the other hand, if 'O' plays in the fourth possible box (in blue), it also increases our chances of winning, as the displayed results are for 'X' winning scenarios. Finally, we can notice that the second-best move for 'X' after 'O' has played is to choose the first available box (in green).\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The file `general_solution.ipynb` includes a function that generates a random initial game configuration. Subsequently, the execution of the algorithm yields results where 'X' emerges victorious. In such instances, post-quantum analysis could be performed, although results may vary across each execution. Two specific cases are highlighted for a comprehensive understanding.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3. Conclusion" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + " - The flexibility of the oracle demonstrates Grover's versatility in addressing specific game conditions." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Grover provides an adaptable quantum solution for Tic Tac Toe, though the outcomes are statistically variable due to the quantum nature of the algorithm.*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "WOMANIUM", + "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": "3.11.4" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/challenges/PIQUE challenge/QuantumVoyagers/app/qaoa/qaoa.ipynb b/challenges/PIQUE challenge/QuantumVoyagers/app/qaoa/qaoa.ipynb new file mode 100644 index 0000000..4f72b06 --- /dev/null +++ b/challenges/PIQUE challenge/QuantumVoyagers/app/qaoa/qaoa.ipynb @@ -0,0 +1,955 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "clyv3IRsJNaG", + "metadata": { + "id": "clyv3IRsJNaG" + }, + "outputs": [], + "source": [ + "!pip install h5py\n", + "!pip install typing-extensions\n", + "!pip install wheel" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "65DDjaGiFd_c", + "metadata": { + "id": "65DDjaGiFd_c" + }, + "outputs": [], + "source": [ + "!pip install docplex\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "DM3iU9TvGGCo", + "metadata": { + "id": "DM3iU9TvGGCo" + }, + "outputs": [], + "source": [ + "!pip install --upgrade azure-quantum\\[qiskit\\]\n", + "!pip install qiskit\n", + "!pip install cplex" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7QQ56rCZLsex", + "metadata": { + "id": "7QQ56rCZLsex" + }, + "outputs": [], + "source": [ + "!pip install openqaoa-qiskit" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "17552bd0", + "metadata": { + "id": "17552bd0" + }, + "outputs": [], + "source": [ + "%matplotlib notebook\n", + "\n", + "# Import external libraries to present an manipulate the data\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import pandas as pd\n", + "\n", + "# Import docplex model to generate the problem to optimize\n", + "from docplex.mp.model import Model\n", + "\n", + "# Import the libraries needed to employ the QAOA quantum algorithm using OpenQAOA\n", + "from openqaoa import QAOA\n", + "\n", + "# method to covnert a docplex model to a qubo problem\n", + "from openqaoa.problems.converters import FromDocplex2IsingModel\n", + "from openqaoa.backends import create_device\n", + "\n", + "# method to find the corrects states for the QAOA boject\n", + "from openqaoa.utilities import ground_state_hamiltonian" + ] + }, + { + "cell_type": "markdown", + "id": "c3672d85", + "metadata": { + "id": "c3672d85" + }, + "source": [ + "## 1) Tic Tac Toe Game\n", + "This problem can be solved by treating each cell as a variable, and our objective function aims to maximize the number of winning moves. For instance, if we want to address the following problem:\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "

\n", + "\"JuveYell\"\n", + "

\n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "So, for x_0, we observe it has 2 winning possibilities. On the other hand, x_1 has only one, x_2 has 0 winning possibilities, and x_3 has only 1 winning option. Therefore, our objective function is formulated as follows:\n", + "$$f_1(\\textbf{x}) = 2*x_0 + 1*x_1 + 0*x_2 + 1*x_3$$\n", + "\n", + "This objective function is subject to an equality constraint, as when the game starts with 0's, there should be a total of 4 X's played. This forms our constraint, but in this case, given an initial configuration, we subtract 2 X's:\n", + "\n", + "$$x_0 + x_1 + x_2 + x_3 = 2$$\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 95, + "id": "inv3grH1qNBI", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 481 + }, + "id": "inv3grH1qNBI", + "outputId": "4bd182b2-18a5-4ec6-8f97-87c20bb26cc3" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "// This file has been generated by DOcplex\n", + "// model name is: Basic Problem using minimize\n", + "// var contrainer section\n", + "dvar bool x[4];\n", + "\n", + "maximize\n", + " 2 x_0 + x_1 + x_3;\n", + " \n", + "subject to {\n", + " x_0 + x_1 + x_2 + x_3 == 2;\n", + "\n", + "}\n", + "None\n", + "Warning: Model name contains whitespaces: |Basic Problem using minimize|\n" + ] + }, + { + "data": { + "text/html": [ + "\n", + "
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\n", + "

\n", + "\"JuveYell\"\n", + "

\n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So, for x_0, we observe it has 2 winning possibilities. On the other hand, x_1 has only one, x_2 has only one too, x_3 has 0 winning possibilities, and x_4 has only 1 winning option. Therefore, our objective function is formulated as follows:\n", + "$$f_1(\\textbf{x}) = 2*x_0 + 1*x_1 + 1*x_2 + 0*x_3 + 1*x_4$$\n", + "\n", + "This objective function is subject to an equality constraint, as when the game starts with 0's, there should be a total of 4 X's played. This forms our constraint, but in this case, given an initial configuration, we subtract 2 X's:\n", + "\n", + "$$x_0 + x_1 + x_2 + x_3 + x_4= 2$$" + ] + }, + { + "cell_type": "code", + "execution_count": 94, + "id": "ed3023be", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 575 + }, + "id": "ed3023be", + "outputId": "699a3f4d-02d4-458d-8d34-a396229fb0ab" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "// This file has been generated by DOcplex\n", + "// model name is: Basic Problem using minimize\n", + "// var contrainer section\n", + "dvar bool x[5];\n", + "\n", + "maximize\n", + " 2 x_0 + x_1 + x_2 + x_4;\n", + " \n", + "subject to {\n", + " x_0 + x_1 + x_2 + x_3 + x_4 == 2;\n", + "\n", + "}\n", + "None\n", + "Warning: Model name contains whitespaces: |Basic Problem using minimize|\n" + ] + }, + { + "data": { + "text/html": [ + "\n", + "
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solutions_bitstringsbitstrings_energiesprobabilities
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of the QUBO problem\n", + "ising_encoding = qubo.ising_model\n", + "\n", + "# Print in a df the ising encoding (we need to remove keys: 'problem_instance' and 'metadata'))\n", + "ising_encoding_dict = ising_encoding.asdict(exclude_keys=['problem_instance', 'metadata'])\n", + "\n", + "#Specific local device usign qiskit backend\n", + "device = create_device(\"local\", 'qiskit.qasm_simulator')\n", + "#Is possible check the devices using qaoa.local_simulators, qaoa.cloud_provider\n", + "qaoa = QAOA(device)\n", + "\n", + "#Indicate the properties to the QAOA quantum algorithm,shots,seed\n", + "qaoa.set_backend_properties(n_shots=20, seed_simulator=1)\n", + "#check the p value and the variational init params\n", + "qaoa.set_circuit_properties(p=2, init_type=\"custom\", variational_params_dict={\"betas\":2*[0.01*np.pi],\"gammas\":2*[0.01*np.pi]})\n", + "\n", + "#Indicate the ising e ncoding model from docplex\n", + "qaoa.compile(ising_encoding)\n", + "\n", + "#Optimize the quantum algorithm\n", + "qaoa.optimize()\n", + "#Print in a df the best 10 solutions\n", + "results = pd.DataFrame(qaoa.result.lowest_cost_bitstrings(10))\n", + "results = results[results[\"bitstrings_energies\"]<0]\n", + "results" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "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": "3.10.6" + }, + "vscode": { + "interpreter": { + "hash": "d2582286b70c3b030a2fde61b871db03dec7fee33191883f4394b540a2eb90c7" + } + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/challenges/PIQUE 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challenge/QuantumVoyagers/pkg/__pycache__/quantum_utils_copy.cpython-311.pyc differ diff --git a/challenges/PIQUE challenge/QuantumVoyagers/pkg/__pycache__/utils.cpython-311.pyc b/challenges/PIQUE challenge/QuantumVoyagers/pkg/__pycache__/utils.cpython-311.pyc new file mode 100644 index 0000000..dc622b0 Binary files /dev/null and b/challenges/PIQUE challenge/QuantumVoyagers/pkg/__pycache__/utils.cpython-311.pyc differ diff --git a/challenges/PIQUE challenge/QuantumVoyagers/pkg/general_utils.py b/challenges/PIQUE challenge/QuantumVoyagers/pkg/general_utils.py new file mode 100644 index 0000000..af23e76 --- /dev/null +++ b/challenges/PIQUE challenge/QuantumVoyagers/pkg/general_utils.py @@ -0,0 +1,162 @@ +import random + + +def initialize_board(): + """ + Initializes a Tic Tac Toe board with empty spaces. + + Returns: + - board (list): A 3x3 grid representing the Tic Tac Toe board. + """ + board = [[' ' for _ in range(3)] for _ in range(3)] + return board + + +def make_move(board, player, row, column): + """ + Makes a move on the Tic Tac Toe board for the specified player. + + Parameters: + - board (list): The Tic Tac Toe board. + - player (str): The player making the move ('O' or 'X'). + - row (int): The row where the move is made. + - column (int): The column where the move is made. + + Returns: + - success (bool): True if the move is successful, False if the chosen position is already occupied. + """ + if board[row][column] == ' ': + board[row][column] = player + return True + else: + return False + + +def check_winner(board): + """ + Checks if there is a winner on the Tic Tac Toe board. + + Parameters: + - board (list): The Tic Tac Toe board. + + Returns: + - winner (bool): True if there is a winner, False otherwise. + """ + # Check rows and columns + for i in range(3): + if board[i][0] == board[i][1] == board[i][2] != ' ' or board[0][i] == board[1][i] == board[2][i] != ' ': + return True + + # Check diagonals + if board[0][0] == board[1][1] == board[2][2] != ' ' or board[0][2] == board[1][1] == board[2][0] != ' ': + return True + + return False + + +def generate_random_board(num_moves): + """ + Generates a random Tic Tac Toe board after a specified number of moves. + + Parameters: + - num_moves (int): The number of moves made on the board. + + Returns: + - board (list): A 3x3 grid representing the generated Tic Tac Toe board. + """ + players = ['O', 'X'] + + while True: + board = initialize_board() + moves_made = 0 + + while moves_made < num_moves: + current_player = players[moves_made % 2] + row = random.randint(0, 2) + column = random.randint(0, 2) + + if make_move(board, current_player, row, column): + moves_made += 1 + + if not check_winner(board): + return board + + +def display_board(board): + """ + Displays the Tic Tac Toe board. + + Parameters: + - board (list): The Tic Tac Toe board. + """ + for row in board: + print(" | ".join(row)) + print("-" * 9) + + +def complete_lists_with_dictionary(lists, dictionary): + """ + Completes lists with characters from a dictionary. + + Parameters: + - lists (list): A list of lists to be completed. + - dictionary (dict): A dictionary where keys are binary strings and values are probabilities. + + Returns: + - result (list): A list of lists with characters filled in from the dictionary. + """ + result = [] + + for key, value in dictionary.items(): + # Create a copy of the original list + new_list = [list(row) for row in lists] + + # Convert the binary value of the key into a list of characters 'O' and 'X' + characters = ['O' if bit == '0' else 'X' for bit in key] + + # Fill in the empty spaces in the new list with the corresponding characters + index = 0 + for i in range(len(new_list)): + for j in range(len(new_list[i])): + if new_list[i][j] == ' ': + new_list[i][j] = characters[index] + index += 1 + + result.append(new_list) + + return result + + +def filter_values_above_average(dictionary): + """ + Filters values above the average from a dictionary. + + Parameters: + - dictionary (dict): A dictionary where keys are binary strings and values are probabilities. + + Returns: + - filtered_dictionary (dict): A dictionary with values above the average. + """ + values = list(dictionary.values()) + average = sum(values) / len(values) + + # Calculate the difference between the maximum and minimum values + max_min_difference = max(values) - min(values) + + # Check if the difference is small compared to the average + if max_min_difference < 0.1 * average: + return dictionary + + # Filter values above the average + filtered_dictionary = {key: value for key, + value in dictionary.items() if value > average} + return filtered_dictionary + + +if __name__ == '__main__': + # Example of usage + num_moves = 5 + random_board = generate_random_board(num_moves) + print(random_board) + print('Board:') + display_board(random_board) diff --git a/challenges/PIQUE challenge/QuantumVoyagers/pkg/quantum_utils.py b/challenges/PIQUE challenge/QuantumVoyagers/pkg/quantum_utils.py new file mode 100644 index 0000000..b3ac2a5 --- /dev/null +++ b/challenges/PIQUE challenge/QuantumVoyagers/pkg/quantum_utils.py @@ -0,0 +1,292 @@ +from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute, Aer +from qiskit.circuit.library import XGate + + +def setting_initial_configuration(board): + """ + Initializes a quantum circuit with the given Tic Tac Toe board configuration. + + Args: + board (list of lists): Represents the Tic Tac Toe board. + + Returns: + QuantumCircuit: Quantum circuit with the specified initial configuration. + """ + n_qubits = 9 + counter_aux_qubits = 4 + aux_conditions_qubits = 8 + oracle_qubit = 1 + empty_spaces = sum(row.count(' ') for row in board) + + qreg_q = QuantumRegister( + n_qubits + counter_aux_qubits + aux_conditions_qubits + oracle_qubit, 'q') + + creg_c = ClassicalRegister(empty_spaces, 'c') + + qc = QuantumCircuit(qreg_q, creg_c) + + counter = 0 + for row in board: + for elem in row: + if elem == 'O': + qc.i(qreg_q[counter]) + elif elem == 'X': + qc.x(qreg_q[counter]) + else: + qc.h(qreg_q[counter]) + counter += 1 + + return qc + + + +def conditions_and_counter(): + """ + Creates a quantum circuit to apply conditions and count the number of 'X's on the board. + + Returns: + QuantumCircuit: Quantum circuit for conditions and counting. + """ + n_qubits = 9 + counter_aux_qubits = 4 + aux_conditions_qubits = 8 + oracle_qubit = 1 + + qreg_q = QuantumRegister( + n_qubits + counter_aux_qubits + aux_conditions_qubits + oracle_qubit, 'q') + + mcx = XGate().control(3) + + qc = QuantumCircuit(qreg_q) + + # 8 possible ways for 'X' to win the game + qc.barrier() + qc.mct([0, 3, 6], 13) + qc.mct([0, 4, 8], 14) + qc.mct([3, 4, 5], 15) + qc.mct([1, 4, 7], 16) + qc.mct([0, 1, 2], 17) + qc.mct([2, 5, 8], 18) + qc.mct([6, 7, 8], 19) + qc.mct([2, 4, 6], 20) + qc.barrier() + + # Bit adder, counting the number of 'X's on the board + qc.cx(qreg_q[0], qreg_q[9]) + qc.barrier() + + qc.ccx(qreg_q[1], qreg_q[9], qreg_q[10]) + qc.cx(qreg_q[1], qreg_q[9]) + qc.barrier() + + qc.ccx(qreg_q[2], qreg_q[9], qreg_q[10]) + qc.cx(qreg_q[2], qreg_q[9]) + qc.barrier() + + qc.append(mcx, [3, 9, 10, 11]) + qc.ccx(qreg_q[3], qreg_q[9], qreg_q[10]) + qc.cx(qreg_q[3], qreg_q[9]) + qc.barrier() + + qc.append(mcx, [4, 9, 10, 11]) + qc.ccx(qreg_q[4], qreg_q[9], qreg_q[10]) + qc.cx(qreg_q[4], qreg_q[9]) + qc.barrier() + + qc.append(mcx, [5, 9, 10, 11]) + qc.ccx(qreg_q[5], qreg_q[9], qreg_q[10]) + qc.cx(qreg_q[5], qreg_q[9]) + qc.barrier() + + qc.append(mcx, [6, 9, 10, 11]) + qc.ccx(qreg_q[6], qreg_q[9], qreg_q[10]) + qc.cx(qreg_q[6], qreg_q[9]) + qc.barrier() + + qc.append(mcx, [7, 9, 10, 11]) + qc.ccx(qreg_q[7], qreg_q[9], qreg_q[10]) + qc.cx(qreg_q[7], qreg_q[9]) + qc.barrier() + + qc.append(mcx, [8, 9, 10, 11]) + qc.ccx(qreg_q[8], qreg_q[9], qreg_q[10]) + qc.cx(qreg_q[8], qreg_q[9]) + qc.barrier() + + qc.x(qreg_q[9]) + qc.x(qreg_q[10]) + + qc.mct([9, 10, 11], 12) + + qc.barrier() + + return qc + +def oracle(): + """ + Creates a quantum circuit for the oracle part of the algorithm. + + Returns: + QuantumCircuit: Quantum circuit for the oracle. + """ + n_qubits = 9 + counter_aux_qubits = 4 + aux_conditions_qubits = 8 + oracle_qubit = 1 + + qreg_q = QuantumRegister( + n_qubits + counter_aux_qubits + aux_conditions_qubits + oracle_qubit, 'q') + + qc = QuantumCircuit(qreg_q) + + qc = qc.compose(conditions_and_counter()) + + qc.barrier() + qc.x(21) + qc.h(21) + qc.barrier() + + # Oracle + qc.mct([12, 13], 21) + qc.mct([12, 14], 21) + qc.mct([12, 15], 21) + qc.mct([12, 16], 21) + qc.mct([12, 17], 21) + qc.mct([12, 18], 21) + qc.mct([12, 19], 21) + qc.mct([12, 20], 21) + + qc.barrier() + qc = qc.compose(conditions_and_counter().inverse()) + + return qc + + +def diffuser(board): + """ + Creates a quantum circuit for the Grover Diffuser. + + Args: + board (list): The Tic Tac Toe board. + + Returns: + QuantumCircuit: Quantum circuit representing the Grover Diffuser. + """ + n_qubits = 9 + one_dimensional_list = [value for row in board for value in row] + index_empty_spaces = [i for i, value in enumerate( + one_dimensional_list) if value == ' '] + + qreg_q = QuantumRegister(n_qubits, 'q') + + qc = QuantumCircuit(qreg_q) + + for qubit in index_empty_spaces: + qc.h(qubit) + # Apply transformation |00..0> -> |11..1> (X-gates) + for qubit in index_empty_spaces: + qc.x(qubit) + + qc.barrier() + # Apply multiple controlled Z-gates + qc.h(index_empty_spaces[-1]) + # Toffoli with multicontrol + qc.mct(index_empty_spaces[:-1], index_empty_spaces[-1]) + qc.h(index_empty_spaces[-1]) + qc.barrier() + # Apply transformation |11..1> -> |00..0> + for qubit in index_empty_spaces: + qc.x(qubit) + # Apply transformation |00..0> -> |s> + for qubit in index_empty_spaces: + qc.h(qubit) + + # qc.measure([4,5,7,8],creg_c) + + return qc + + +def measurement(qc, board): + """ + Adds the measurement operation to the quantum circuit. + + Args: + qc (QuantumCircuit): Quantum circuit. + board (list): The Tic Tac Toe board. + + Returns: + QuantumCircuit: Quantum circuit with measurement operation. + """ + one_dimensional_list = [value for row in board for value in row] + index_empty_spaces = [i for i, value in enumerate( + one_dimensional_list) if value == ' '] + + qc.measure(index_empty_spaces, qc.clbits) + return qc + + + +def grover_algorithm(board, rep=1): + """ + Executes the Grover's algorithm for Tic Tac Toe. + + Args: + board (list): The initial state of the Tic Tac Toe board. + rep (int): Number of iterations of the algorithm. + + Returns: + QuantumCircuit: Quantum circuit representing the Grover's algorithm. + """ + qc = setting_initial_configuration(board) + qc.barrier() + + for _ in range(rep): + # Oracle + qc = qc.compose(oracle()) + qc.barrier() + # Diffuser + qc = qc.compose(diffuser(board)) + qc.barrier() + + # Measurement + qc = measurement(qc, board) + qc.barrier() + + return qc + + +def circuit_execute(qc, shots=10000): + """ + Executes the quantum circuit on a simulator. + + Args: + qc (QuantumCircuit): Quantum circuit. + shots (int): Number of shots for the simulation. + + Returns: + dict: Counts of the measurement outcomes. + """ + simulator = Aer.get_backend('qasm_simulator') + job = execute(qc, simulator, shots=shots) + result = job.result() + # Returns counts + counts = result.get_counts(qc) + + counts_without_qiskit_convention = { + key[::-1]: value for key, value in counts.items()} + + return counts_without_qiskit_convention + +if __name__ == '__main__': + # Example of usage + from general_utils import generate_random_board + + num_moves = 5 + board = generate_random_board(num_moves) + # print(board) + qc_init = setting_initial_configuration(board) + print(qc_init) + + # Oracle + print(oracle()) + # print(diffuser(board)) diff --git a/challenges/QOSF challenge/QuantumVoyagers/README.md b/challenges/QOSF challenge/QuantumVoyagers/README.md new file mode 100644 index 0000000..3c57f68 --- /dev/null +++ b/challenges/QOSF challenge/QuantumVoyagers/README.md @@ -0,0 +1,56 @@ +# Quantum Algorithms for Tic Tac Toe + +This repository contains Python code and Jupyter Notebooks implementing quantum algorithms, specifically Grover's algorithm and Quantum Approximate Optimization Algorithm (QAOA), to solve the Tic Tac Toe game. + +## Table of Contents + +- [Grover's Algorithm](#grovers-algorithm) + + - [General Solution](./app/grover/general_solution.ipynb) + - [Grover Circuit Complete Image](./app/grover/grover_circuit_complete_image) + - [Solution Notebook](./app/grover/solution.ipynb) + +- [QAOA](./app/qaoa/qaoa.ipynb) + +- [Images](./app/Images) + + - [Best Play - Regular](./app/Images/best_play.png) + - [Best Play - Bonus](./app/Images/best_play_bonus.png) + - [Parts Oracle Grover](./app/Images/parts_oracle_grover.jpg) + - [Tic Tac Toe Image](./app/Images/tic-tac-toe-1777880_1280.jpg) + +- [Package](./pkg) + - [General Utilities](./pkg/general_utils.py) + - [Quantum Utilities](./pkg/quantum_utils.py) + +## Grover's Algorithm + +### General Solution + +The [General Solution](./app/grover/general_solution.ipynb) notebook contains the Python code for Grover's algorithm, focusing on solving Tic Tac Toe. + +### Grover Circuit Complete Image + +The [Grover Circuit Complete Image](./app/grover/grover_circuit_complete_image) directory includes the LaTeX file (`file.tex`) and the complete Grover circuit in PDF format (`grover_circuit.pdf`). + +### Solution Notebook + +The [Solution Notebook](./app/grover/solution.ipynb) provides detailed information on the solution implemented using Grover's algorithm. + +## QAOA + +The [QAOA Notebook](./app/qaoa/qaoa.ipynb) contains the Python code for Quantum Approximate Optimization Algorithm applied to Tic Tac Toe. + +## Images + +Various images related to Tic Tac Toe and the algorithms used, such as best plays and the Tic Tac Toe game itself. + +## Package + +### General Utilities + +The [General Utilities](./pkg/general_utils.py) module includes Python functions used for Tic Tac Toe and algorithm implementations. + +### Quantum Utilities + +The [Quantum Utilities](./pkg/quantum_utils.py) module contains Python functions specific to quantum operations in the Tic Tac Toe algorithms. diff --git a/challenges/QOSF challenge/QuantumVoyagers/app/Images/best_play.png b/challenges/QOSF challenge/QuantumVoyagers/app/Images/best_play.png new file mode 100644 index 0000000..7e4bac7 Binary files /dev/null and b/challenges/QOSF challenge/QuantumVoyagers/app/Images/best_play.png differ diff --git a/challenges/QOSF challenge/QuantumVoyagers/app/Images/best_play_bonus.png b/challenges/QOSF challenge/QuantumVoyagers/app/Images/best_play_bonus.png new file mode 100644 index 0000000..6c62ae3 Binary files /dev/null and b/challenges/QOSF challenge/QuantumVoyagers/app/Images/best_play_bonus.png differ diff --git a/challenges/QOSF challenge/QuantumVoyagers/app/Images/image10.png b/challenges/QOSF challenge/QuantumVoyagers/app/Images/image10.png new file 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challenge/QuantumVoyagers/app/Images/parts_oracle_grover.jpg differ diff --git a/challenges/QOSF challenge/QuantumVoyagers/app/Images/tic-tac-toe-1777880_1280.jpg b/challenges/QOSF challenge/QuantumVoyagers/app/Images/tic-tac-toe-1777880_1280.jpg new file mode 100644 index 0000000..edcf6ab Binary files /dev/null and b/challenges/QOSF challenge/QuantumVoyagers/app/Images/tic-tac-toe-1777880_1280.jpg differ diff --git a/challenges/QOSF challenge/QuantumVoyagers/app/grover/general_solution.ipynb b/challenges/QOSF challenge/QuantumVoyagers/app/grover/general_solution.ipynb new file mode 100644 index 0000000..624ac9f --- /dev/null +++ b/challenges/QOSF challenge/QuantumVoyagers/app/grover/general_solution.ipynb @@ -0,0 +1,234 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit.visualization import plot_histogram\n", + "\n", + "import sys\n", + "sys.path.append('../../')\n", + "from pkg.general_utils import display_board, generate_random_board, complete_lists_with_dictionary, filter_values_above_average\n", + "from pkg.quantum_utils import grover_algorithm, circuit_execute" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[['O', 'X', ' '], [' ', ' ', 'O'], [' ', ' ', 'X']]" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "challenge = generate_random_board(num_moves=4)\n", + "challenge" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "O | X | \n", + "---------\n", + " | | O\n", + "---------\n", + " | | X\n", + "---------\n" + ] + } + ], + "source": [ + "display_board(challenge)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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x/vXuWg3K7fsK2kg5MNAMCIekqsopau86x40ckFKxZIAUXw5kWgYMzivU//vrmri2/fv7/q9e3fj/EtyixLp6+td167xv9/lYKuYCz/3bf+gnX/kfUbYWqcBc4GxfmfuI5l/yzZi3O1bfq7KyisQ3KMH++c73NMRf0udjyZ4LyJJmTJup44HG6BuMpGIucLYsb7b+/b69cW372MP/rF++81RiG5Rgn538Fd3xuX/q87FUzAVe+M8V+uGtfxtdY5ESbp0LWLm50jM/SNzrWZZC//Q9qbdHGl2u8M9+Lu8Vl8tz/qiE7WNi5UR5uh1c7uFjxQXn67t3vBvXtvd8/Vt68/2fJLhFyWX6e6Hp/UdmO33Vvrlz58b03nQ6YwpkwaC9jkBHR0efjy9fvlzNzc0qKCjQ2LFjY379mpoa3XzzzWf9fMqUKaqpie9gm/RJ8AxU+6S++y3Zk2BfQXSv4/FG/9zTdXZ0qaGhIfYNkTTt7dGvG9LZ2XnqeyzbZdq/eagnvjXS8rIHZ0Rfszz9R360ORBvBkjSkcPNagk4fDkrTollLEvx5UAmjIvTDSuMf53E7o7etO9vYHz/ayqlYi7Q3dmT9r8j0zAXOFtPd3zLxWR5s3X4ULN6Yl2jNcW85/j4l4q5QPORo2o6lln/J9yMucDZBvsK4962pyuU9v1tK+//EtmUzAW603++ZBrXzgV8ecpJ4MuFX14la+v78n79dnlnX6bee/5GoX/6nrKeWiKPx5OQfRxsPCh1Oj+P8I7o+6TaaHS2Z9583/T3QtP7D/c4dCj+S1iNKZCNHDlSx48f16ZNmzR79uwzHmtsbNRDDz0kSaquro7rze348eMaMmTIWT8vLi7Whx9+GFebJWnUqFEJuYJskN/X72PRrEGe57cnwVbYvllnrK+VOyhHpaWlkXeElBk8eHDUz/X5fKe+x7Jdxv2bZ8V3UKyjuy0j+tob7lau+s6CSDkw0AyQpOEjiuUvSuTHFAxELGNZii8HMmFcnC4vJ7bfyemy89K/v37/oH4fS8lcwJed9r8j0zAXOJsnO771gHt6O3VeyfAEtybxQlb/axymYi4wbPhQZQ1y/ux42JgLnM3j8SpsheX1xP4Z3JtrpX1/8wv6/3dLxVwgJ9eb9r8j07h1LmDl5upIol6roUHhHy2T54KJ8n75JnmysuS9daHCP/4PhV9epawvfiEh+zl/1PlpcQVZwcf/tpZlxXx8NNeXeWPc9PdC0/uPzBYOh09dXFRS0vcqGdHwWFYm3FZ+4O677z59//vfV3l5ud544w1NnDhRkrRhwwbddttt2r17t3p6enTPPfdo6dKlfb7Go48+qscee0x9/cpyc3O1ePFiPf74mcsILlq0SG+//XZMRbJgMKj8fPuMjUAgIL8/wjoHUWjaIX2wOv7t537DPkOss01665nYt7/gKqn8ovj3j8SLZb3g7du366abbtKKFSs0ZcqUqLerqqqKp2mOad4tbXkp9u1GTpKmXpf49iTa2z+275UUj4FmQFaudOXfSAk6uQ4JEOua4fHkQKZlgCRt+JnUejD27S67Xcofkfj2JNKROmnry/FvP9AcmPBZqeLS+PePxGMucLbjB6T3lse+3fDx0owvJr49ifbuT6UTTfFtO9AM8GZJV95nf0d6YC7Qt00rpGN7Y99u5kKpKHGrrSXFsX3Sphfj336gOTD2Mmn83Pj3j8Rz61wgGOrV0DW/HfDrWOGwQn/3kKyP6pT9r9+X5+PbqlihkEL3/52sffuV/cz/S8hSi8evukb+LOevY7Asaf1/SIHm2Led81fSoCEJb1JSmf5eaHr/kdkSVUNx5x0l+7B48WINGzZMBw4c0JQpUzRt2jRVVlZq1qxZGjdunK666ipJZ95/LBZDhw5VS0vLWT8/duyYiouLB9L0hCiIv4iamP2PdHb/GJiJEydq3bp1pwrLbjWsQhpUFPt2ZTMS3ZLkKHQwBwpLKI5lOlNyIJ7xPKQs/YtjUhrMBRzePwbGlAwYUib5h8W+XfmMhDclKZycC+SPoDiW6UzJgXjmAgUlUmEGfOZ1+r3Y6f1jYEzJgNOFV7wkq2aHvLffeqo4JkmerCxl/be/k8Ihhf7pe32eSJ+pPJ74cnD4uMwrjsXDxHFwOtP7D3cypkBWVlamtWvX6rrrrpPP59PevXtVXFysZ555RqtXr9bOnTslxV8gmzRpUp/3GqupqdGkSZMG1PZEGDzUvoLDER6pIAMOHKJ/OTk5Ki4uVk6Ou5fH83hjv7phSJlUdH5y2pNoThaq+TCc+UzJgZKJ9ntmLDLlqqi8fCk3/lUkB4wcyGymZIDHY1/hEIvCEqm4IinNSTjmAhgIU3Jg+LjYT3wZe2lmnAyW44vvhMBEcbJIj4EzJQNOsvbvV/g/fiLPpCp5v/QXZz3uqRgj760LZW37QOGXVznQwuQZOTnG+wx6pDEzk9actGLaOPg00/sPdzKmQCbZRaxXXnlFbW1tamtr0/r163XXXXcpGAxq79698nq9mjp1alyvff311+utt95SfX39qZ+tX79eu3bt0oIFCxLVhbh5PNLwsc7su7hcyiI3M9r+/ft19913a//+/U43JenOnyaNviS65/qHSdU3ZMaHYcm5DJDsAw3IbKbkgDdbmvElu5gUjYnznB1bsfB4pGEOjcWiUVJu/7dAQwYwJQMke+nksbMjP0+yz5Se/sXMmQsMq3CurcwFMp8pOeD12kum+gqje/74z0rnZdCJ9E6NxfzhUl4sB9yRdkzJgJM8o0crZ/V/KftfvitPVt+XQGd99SvK+c2rCbsPWbrIzrU/E+VEOX+f9DlpaHly25QuTBsHn2Z6/+FORhXI+rN9+3ZZlqXKyso+bzC4YsUKrVix4tQVYif/vnHjxlPPueuuuzRq1Ch94Qtf0CuvvKIVK1boq1/9qmbNmqUvfCE93iidWgYuU5afQ//a2tr05ptvqq2tzemmJJ3HI1VeYd83r78rLTxe++DZJV919mqMWA0eKhWPcWC/xeZMlt3MpBwYPMS+j8i5DiANKpKmXi+NvjhlzUoIp5aBYy6Q+UzKAEkaP8c+2NNfsdzjsQ+Iz/zL6Avq6cBXIA2f4MB+CzPnZAL0z6Qc8BXac4ERlZL6KSrnFUiT59tXj2USJ48LZMrJBOibSRkAu6g9c+G5jyEMHipV3yiVTktZsxxn+jgwvf9wJ+fv/pgGtm3bJqn/5RVvvvnmPv9+++23a9myZZKkwsJCrVmzRvfff79uueUWZWdn6/rrr9f3vvc9eb3pUYc8eU+F4NHU7TMv35kP4cBAeDxS+UVS6XTpyEfSkV3S4Z1SOGQvVfqZO6S8+O776LiyC+2bc6d0nzP4MIzM4yuQZvyF1N4iHdwm7d9oZ4A3275ydNjYzPx/XTjS/jrRlLp95gySzrsgdfsDEqW0Who1VWqukw7XSYc//HgukCPN/v9iXHoojZTPsOc3qVQ63T7BCMgkeX5p+hekzhNSw/vSvg2fzAWmXW+fSJOJ/6/9w+yT144fSN0+s3LtJdsAZJbBQ6SLbpaCx6SD70sHNn+Sg9O/KBWPzszPRABwugycziVepAKZZVl9fp0sjp00fvx4vfLKKwoEAmppadFPf/pTjRiRPjffOnllTCpNuNxeogLIRN4sqaRKmnrdJ0sLZOdmbnFMkkaMt4vlqTK42KyzyeA+g4dIEz77SQbk+D4+IJbBHwRTPRcYP1fK4pQsZCiv175SbOrnT5sL5GVucUySho62l1pMFV+hVH5h6vYHJJqv0H4vO30uMGJCZhbHTppwufq9Mi4Zxn3G/hwFIDP5i6XKK8/MwWFjMvszEQCclMFTusSJVCBzk+Hj7DNhU7Kv8fYydADSh8cjTf5z+4yv5O9Mmnwt9yAE0s3Qcvtq0lQoHmNfhQMgfXg80qQ/t6/oSIXJf86BcSDdFI2SKmamaF+l0uiLUrMvAACAWFEgk7RmzRpZlqXrrrvO6aakxMQr7XunxKI7KHW22d+jkTtYmnQNZ5O4RUlJiR5++GGVlJQ43RQkwOCh0sR5sW0TawZIUsUsacj5se0H6YsccJfKz9pXeMYi1hzIGWTfw4m5gDuQAe7iK5Cqro5tm3jmAuUXOXP/UyQHOeAu4z4j5Z8X2zax5kBWrl0kz+Sr7fAJMgBgHJjef7gTC94YKMcnXXiz9N7Ppa5AdNu8+9PoXz/749fPpBuW49yGDx+uRYsWOd0MJFDZdKmrTdrzTnTPjyUDJGnUFHspGrgHOeAuWbnSRTdJG39u31slGrHkQFaufQ+3WE/IQfoiA9xn1GR7LlC3NrrnxzoXKLnAPjEP7kEOuIs3W7rwS/Zxgfbj0W0TSw54s6UL/8Jemg3uQAYAjAPT+w934jweQw0eIl18S+IPXOXlS5d8RSpIn1uvIQFaW1v12muvqbW11emmIIHGzZHGfzbxr1s2w15akatG3IUccB9foXTJLYk/cJUzSLr4y/byTXAPMsCdKi6N/aryaIyaIk25jqtG3IYccJ88v31cID/Bn9+zfdJFN6f23sdIPjIAYByY3n+4Ex9ZDDZ4iHTp1xJ3b5CRk6RLb0/85BrOq6+v1wMPPKD6+nqnm4IE8niksZdKF33ZPlA+UDmDpGkL7CWbKI65DzngTr5Cadat9jJoiTCiUrpskVQ4MjGvh/RBBrjX6IvtYvngoQN/rWyfNOXz9okyXj5pug454E55fmnmX0pjZkpKwBx+2FjpstulIaUDfy2kFzIAYByY3n+4E0ssGi47z74/yHkT7eVV2g7F/hr+YfZSaudVJr59AJKveLR9QHv3OqlhmxTqjm17b5ZdIJ9wuX3/QQCZJStXuuAq+3287o9Sa2PsrzG42L6XSckFFMiBTDSkzD5xbs/bUv1Wqbcrtu09XqmkSqq8nGXWgUyUlSNVXmHPBT76g9TSEPtrDBoijb3MvoKUuQAAAMgUFMggSRpWYd9A+0STVL9FOrr33DfezRlkP79suv2BmgkwkNm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wT+gBsAYA2MiZAdnKlSslSTNmzOjxMVVV3m+2Jw/IrrrqKoVCIS1fvlzXXXddj9s+9dRTqq6u1gsvvKCbbrpJt9xyi/7zP/9Tb7/9tpYvXx6nvTBn69atmjJlirZu3Wq6FMTI5MF4uFNqSYGTKY/s6/myih/HxOWqko0MSH2d7ebOIpVS5wWBWPq5bneUZ5ylOHIg9Znsw0jE3Nlrfhyt8Tkk/xDHAkgFXZ3esNqUVDkW6Ak9YAeTg9rGFH9jJT0A1gAAGzkzINuzx7uew7Bhw7r9eGdnp1avXi3p1AFZWlp0T9GKFSs0ffp0XXjhhSf+berUqRoxYoR+97vfxVo2EDdtDWa/futRs18/GrFe8iLVL5UBN5juQdMZFI2uY1Ld3ti2JQeQCkz3YWsK5ADHArBZe5MUMXhVB9MZBEQiZn8WtTW6cUleAABSSYbpApKlublZktTa2v2dgZcuXara2lrl5ORo+PDhvj//li1bdMstt5zx7+PHj9eWLVt8f77jSktLox7S+TFv3jxfjw+FQpKkl156SevXr49qm2eeecZnVUikv/3cf2rCsKu6/dhlt0l9PuYeq32zPvp7+jc+/usca5b+8h9n/vudd3xD71S+GGW1ZvzVp36o6eO+6Hu71qYOFRX5zw3T/ORALBkgkQO9yfCCcj385e578GwZIEWfAz1lQOX2nbq5qPsM6i0GZg3R/7nznZi2/cE//0gvvP2/41xRYnEs4J7/76anNXnUzG4/loxjgfv+v7/R6ornoqzWjNtnPKJPls/zvV24UyoZNkKdXcfiX1QCcSzglgvySvVPX+3+BnvJOBbYX12joqJLo6w2OegBt6SnZehf5+/u8ePx+lnYUw9I0oiSUeroajt7sUlCD4A14M8P71irvJyhCoVCKirq+VY8tmL/3d5/qXc9Byff1mr69Om+culkzgzIhgwZoiNHjmjdunWaOnXqKR8LhUJ68MEHJen/Z+/vo7ys7zvx/zncDgx3ISgQIGIRwo0BEoON1VhtTSs12N1WG7vGX+zXY5I1/vTr8Ygn32+2X3PqWUPW0+6xZrembr/+TmtcG3S7rhrdptitcbsGi1DLTcwYbjI4ECYIDsONwMzvj6kkbkA+n3GYa/i8H49zOCN8Ptd1va4579eTS15zXZ8sXLgwTU1Nde//jTfeyIQJE37uzydOnJjvf//7far57dpOhf3799f1/oMHDx77Wuu227dvr7suTp39B7pO+NqIlqR57Mn30TSktvcdz487dgz6NfHG3r49B/LQ4QOD/tyOp54c6EsGJHJgMGnuOeOEr9WaAUnfc+DgocHfJ3tHnTgnT6Zj985Bf37/O9cC5enq6jzhawNxLbCr48eDfk3s3tO3588dPXokW7dt7udqTj3XAoU5NPqELw3EtcChtw4OuvWgB8pysn/rGYi/C7e1bUl39+D5/CY9gDVQn7c/f+3o0aMNdV61cv5ln38yeL8HO3f2/RnKxQzILrvssmzcuDErVqzIJz/5ycyZMydJsnr16lx33XXp6Oj9n+HFixdXWOXPmzp16im5g2z06BP/z9HxNDc3H/ta67bTpk2ruy5OnSM9J754eesk/yY8sqX3fwJ6upNDJ3nvifY1cvSQQb8mOrq29Gm7H3VsGPTndjz15EBfMiCRA4PJ6DEn/iv/ZBmQ1J4DJ9rXoSOdg349NKUpu/ZuyxnjP3jyN/+znp6eNDU1Zc+hHw368/vfuRYoz9GmE//EumuBXrv3b+3Tdq4FTux0/L40qpaRI0742kBcCxw8/OagWw96oDz7Du7JmOYJx32tv/4uPNF+9h96M1OnTqmt0AGiB7AG6jN06NBjXxvpvGrl/Ms+/2RwfQ+6u7uP3Vw0efLkPu+nqaenjCcgt7W1ZfHixfnJT36SYcOGZe7cuTl48GBaW1uzdOnSdHd359lnn803vvGN3Hjjjcfdx1133ZWvfOUrOd63bPLkybn66qtz//33v+PPr7zyyuzatSt///d/X3OtXV1dGTNmTJJk3759aWk5ybMu+qDeD9Q8fPhwOjs7M3bs2AwfPrymbebOnduX0jhFtr6U/OBv+7btRZ/v/Qm5g53Jdx/o2z4uuSUZduL/Jx8UjryVPP8nvZ9DVI9zP5VMOQ2Xez050JcMSOTAYNLTk/zdf0gOH/9Jwyf1XnNgxnnJhy7t27EH0pYXk9bn69tm1ITkl25I+nADeqVcC5SnbV2y6a/7tm1/XAtc/K9P/gi3qnUfSZ5/oP6snPfrybQPn5qaTiXXAuX57jeSg338XNL3mgMf+HAy/9f7duxTRQ+UZ81f9v0zZ99rD7xvRnLep/t27FNFD2AN1Of5P+n9TM+RY5JPfKHqagae8y/7/JPB9T3orxlK/9+aNEhNnz49zz//fK644oo0Nzdny5YtmThxYh544IE89dRTefXVV5MkixYt6tP+582bd9zPGtuwYUPmzZv3nmofDIYPH56JEyfW9Rcgg8u4vg/S37PREwf/cCzprbHef9waOSY5c/apqWcwkQGnv6amZGyFOVBlBtXjAx9Ohta5zGd85PQbjvWFHDj9VdmHI8cO/uFYkgwZlkyv838Hho86PX9Qpl4yoDG4Fug7PdAYquyBKo/dH/QA1gDQiIoZkCW9Q6wnn3wynZ2d6ezszIsvvpjPfe5z6erqypYtWzJkyJCce+65fdr3pz71qXz3u99NW1vbsT978cUX89prr2XZsmX9dQqV2bZtW2666aZs29bHH7WicuMm1/+Pvv3lfTOqOW5fzLooGV/jHcJDhyeL/kUyZOgpLWlQkAGN4X3Tqzv2hNPk6QMjRvfeFZoaB15nzk5mfPSUljRoyIHT35gzkmHN1Rz7dLoWOPuCZGKNT1odMjRZ+JvVXWMNJBnQGKrsxQkVXof0Bz3QGKrsgdPp78Lj0QNYA0AjKmpAdiLr169PT09PZs+efdxn6K5cuTIrV648dofY279/6aWXjr3nc5/7XKZOnZrf/M3fzJNPPpmVK1fmd3/3d3P++efnN3/zNwfsXE6Vzs7OPPfcc+nsPPGHuzO4DR2RTJlfzbGnLazmuH0xdHjykd9Ozjjn3d83cmzv4zHGDa5HyJ8yMqAxfODc3s9NGGjvPzsZNX7gj9tXZ8xKFv/Lkw8Spi3sHaaVcPdYIgcawZChyQcWVHPs6afRtcCQocmif5lM/tC7v2/E6OSjv1PtDx8MJBnQGKbO771TcqBNmJ6MmTTwx+1PeqAxvH9m72MSB9rIsb3XxKczPYA1ADSiCi6NB59XXnklyYkfr3j11Vcf9/ef/exn89BDDyVJxo0bl1WrVuXWW2/NNddck2HDhuVTn/pU/uiP/ihDhphDMjhMX5RsXzewxxw/9fR7nMqwEb13hr25s/f7tas1eWt/72tNQ5JzfyM5Y3YZd47RWN5+JOjO7w/scacvHtjj9YdJv5B84nPJju/35sCbO/75habkgx/tPafR76uyQuib6YuTbf8wsMccM6n2u7MHi6HDkw8vS87+eNK2Nvlxa/JWV+9rTUOS+Zcnk+dUM2iA92J4czJ5btL+TwN73NPxWoDG1DQkmbY4ea3Oz5x9r6YtTPzTEAAMPv6XLicfkPX09NS0n1mzZuXJJ5/st7qgv409M5k0K+l4beCOefbHB+5Y/W3c5GTcryXzfu2nH0I5YnTvPyrA6eqs85Mfv5rU+Ffbezb2zGTSafrTskP/+XMJp334Zz6ItiWZc2nVlUHfjX5f799jO2v/PPb37OyPn753Wo45I5n7yd5fP3stMLWiu/KhP8xckuzYmPQcHZjjtUws4zN7OX1MW5hseyk5fGBgjjd8VP2fbwkADAw/v5KTD8igkcz7ZDJs5MAca+r83oEcMHiMm5zM/MWBOVbTkGTB0moe6wic2Id+pfcf6wbCmbOTM0/yqEJgYLW8P5n1SwN0sKZk/lJPXmBwGTGq9wcfBsrcX+394QoAYPDxT1ZJVq1alZ6enlxxxRVVlzJoTZ48OXfeeWcmTz7NnpXHzxk5pvcfxurxVldysPOnjxaq9Thz6jwOg5cMaCxnf7z3roh69CUHfuGX6j8Og5ccaBwjRvf+wEw9+pIBw0clH7rs9L17jHeSAY3lg0uScVPr26YvOTBzSe8j1xuBHmgsk+ec/LMm/3d96YEz5zTOD4roAawBoBF5xCI1mTRpUq6//vqqy6CfTF2QdO1OtrxY2/u/9xf17X/YyGTxb/d+xgGNQQY0liHDksX/Mln9SHKoxs9XrjcHps4fuDvVGBhyoLGcOSeZdVHy2ndre3+9GTB0eLL4t3ofS0pjkAGNZciQ3s/cfemR5MCe2rapNwfOnN2bM41CDzSe+b/eO/Da+3pt76+3B8ZP7f3Mykb5QRE9gDUANCJ3kFGTvXv35plnnsnevXurLoV+MuuiZOYp+Hyw4aOSj16djHXXSEORAY2neVxy3qeTUeP7f99TFyTzGugfA+glBxrPzF88Nf94PWxk8pGrGueuEXrJgMYzsiU573eS0RP7f99nzknO/VRjPWZZDzSeoSOSj/x2MmF6/+97/LTeHxodNqL/910VPYA1ADSiBrpc5VRqa2vLbbfdlra2tqpLoZ80NSXnXJQs+I1kWD/d6TVherLk2mTclP7ZH4OHDGhMoyckS/5Vcsbs/tnfkGHJnEt7f1J2iCuMhiMHGk9TU+8jVz98Zf99Jtn4D/ReC0yY1j/7Y/CQAY2peVyy5HeTKfP6Z39NQ5NzPpF8+FON97ljeqAxDRvZOyT74Mf6b58zzks+elXjPVFFD2ANAI3IIxahcFPnJxM/mGz6m2TXD/q2j6Ejev9HePpid4zA6WZES7LwymTn95NXVyVv7e/bfiZM731Mzej39W99wKk3eU7yvunJ91clOzf1bR9DhiWzLkw+eF5j3TECJRg+Kjn3it67vr7/N8mhfX3bz/gPJPN+LRkzqX/rg1Nt6PBkziW9jwXd8Gyyf3ff9jN6YjL/107NHWkAwKlhQAZk5Jhk0W8m+zqStnVJ+/rk6Fsn365lUjJjcTJlfmM9OgJK09SUTJmbnHFO8uNXk7a1tX0Ww5ChyeS5vcNxj1KD09uI0b13fPzCLyXb1yWv/1Ny5NDJtxs9sTcDPrCg96fwgdPXmbOTSb+Q/PgHvdcCe2q4QaBpaO+Qffri3gGZH5bjdDZhWnLB7yU/2dLbAx2v1bbdpF/o7YH3n60HAOB0Y0AGHDNmUjL3V5PZFyf7diVv7kw6f5wcPpj0HO396fBR45Nxk5OxU3r/2/8AQOMYOqz3rtKp85ODb/5zBuxMunYn3Ud7+33YiGTMmf+cA5MNx6HRtEzsfVTqOZ9IOnf1ZsCbO3/mWmBo0vzP1wLjpiSjJrgWgEYyZGjvD81MmZsc7PxpBuzfnRw90tvvQ0f0ft7w2Mm9WWA4TiNpakomnd376639P+2BfR1J95Gkp6f3jrMxk356PTxidNVVAwB9ZUBGTZqbmzNv3rw0NzfYQ7Q5rqHDe38CdPwHqq6EwUIGlKd5XO+vM/vp88k4/cmBsgwZ1ntnqLtDeZsMKE/z2N5fZ5xTdSWDgx4oz4jRvXeFvf/sqisZHPQA1gDQiAzIqMmsWbPy+OOPV10GUBEZAMgBKJsMoHR6gNLpAawBoBH5CG0AAAAAAACKYkBGTTZs2JCFCxdmw4YNVZcCVEAGAHIAyiYDKJ0eoHR6AGsAaEQGZNSkp6cnhw8fTk9PT9WlABWQAYAcgLLJAEqnByidHsAaABqRARkAAAAAAABFMSADAAAAAACgKAZkAAAAAAAAFGVY1QVwepg1a1aeeOKJzJgxo+pSgArIAEAOQNlkAKXTA5ROD2ANAI3IgIyaNDc3Z/bs2VWXAVREBgByAMomAyidHqB0egBrAGhEHrFITbZv354vf/nL2b59e9WlABWQAYAcgLLJAEqnByidHsAaABqRARk12bNnTx577LHs2bOn6lKACsgAQA5A2WQApdMDlE4PYA0AjciADAAAAAAAgKIYkAEAAAAAAFAUAzIAAAAAAACKYkBGTSZNmpQbb7wxkyZNqroUoAIyAJADUDYZQOn0AKXTA1gDQCMyIKMmTU1NGTFiRJqamqouBaiADADkAJRNBlA6PUDp9ADWANCIDMioya5du/L1r389u3btqroUoAIyAJADUDYZQOn0AKXTA1gDQCMyIAMAAAAAAKAoBmQAAAAAAAAUxYAMAAAAAACAohiQUZPx48dn2bJlGT9+fNWlABWQAYAcgLLJAEqnByidHsAaABrRsKoL4PQwffr0fO1rX6u6DKAiMgCQA1A2GUDp9ACl0wNYA0AjcgcZNTl06FC2bt2aQ4cOVV0KUAEZAMgBKJsMoHR6gNLpAawBoBEZkFGT1tbWXH755Wltba26FKACMgCQA1A2GUDp9ACl0wNYA0AjMiADAAAAAACgKAZkAAAAAAAAFMWADAAAAAAAgKIYkAEAAAAAAFCUYVUXwOlhwYIF2bhxY9VlABWRAYAcgLLJAEqnByidHsAaABqRO8gAAAAAAAAoigEZNdm8eXOuueaabN68uepSgArIAEAOQNlkAKXTA5ROD2ANAI3IIxapyf79+7Nu3brs37+/6lLglDuwN+l4LXlzZ9K5s/f3Rw/3vnaoK1n7X5Jxk5P3zUgmTE+amqqtdyDIAErS3Z3s3pLs2d6bAZ27kre6el87tC958c97M2DclGTSrGRkS6XlDhg5QEkOdia7Wnsz4M23rwXe6n3tUFey9vFk7OTkfdOT933QtQCUQA9QOj2ANQA0IgMygCQ9PclPNidta5OOH77bG3uHZx2v9f529MRk+qLkA+cmw0YORKXAqfJWV7L9laRtXXKo88Tv6/zn4fn2f0yahiRnzklmfCSZMG3gagX6X09P8sa25Edrk47W3t8f/4291wodP0w2Jxk14Z+vBT6cDG8euHoBAAB4bwzIgOId7Ew2Ppv8ZEv92+7fnbz6XLJ1dTLv15JJv9Dv5QGnWE9P0r4heXVVcuRQndt2Jzs39f6aMj/50K/4B3I4HR3qSjb9de9dY/U6sCf5wf/ovRaY+8nkzNn9Xh4AAACngAEZULQdG5ONf/3Txyb11aF9vY9bmnpuMveyZKh0hdPC4QPJ+m+f5M7RGu3YkOzemixYmrx/5nvfHzAwfvxqsvG/J4cPvrf9vLU/+cf/mkyem8z/tWToiP6pDwAAgFNjSNUFcHqYNm1aVqxYkWnTPD+KxrHtH5J/euq9D8d+Vvs/JWsfS4704z4HAxlAIzrUlfzDo/0zHHvbW//82UQ7v99/+xws5ACNaPs/Jv/4xHsfjv2snZuSNSvrvyN1sJMBlE4PUDo9gDUANCL3OFCTCRMm5Morr6y6DOg3bet6H414Krzxo96fIF/8L5MhDZKyMoBGc/hg8vLKZF9H/++7pzv5pyd7+/+MWf2//6rIARpN+4beO8dOhb2v9w7LP3JVMnT4qTnGQJMBlE4PUDo9gDUANCJ3kFGT3bt35+GHH87u3burLgXeszd3Jt//m1N7jN1bkx/+z1N7jIEkA2g0m76T7Nt16vbf09N7h+rBN0/dMQaaHKCRdP2k9/NHT6U925PWvzu1xxhIMoDS6QFKpwewBoBGZEBGTdrb23P33Xenvb296lLgPek+mmx4pvcOj3qc/5nkos/3fq3VltXJ3gZpGRlAI/nxD3ofgVaPvmTA0bd6707p6anvWIOVHKBRdHf3fvZg99H6tutLDvzo5d47yxuBDKB0eoDS6QGsAaARFTkg6+joyPLly3POOeekubk5M2bMyK233pqurq7ccMMNaWpqyv333191mcApsO2lvt01MqIlaR7b+7VmPcmGZxvnH8ehERx9K9n01/Vv16cMSPKTLfUP44BTq21t8uaO+rfraw5seLZ3KAcAAMDg0iCfjlO7tWvXZunSpdmxY0daWloyf/78vP7667nvvvvy2muvHbtNePHixdUWCvS77qPJtjUDe8yujt7HLb5/5sAeFzi+HZuSt/YP7DG3vZRMmTewxwSOr6cn+dE/DOwxD+xJOl5Lzpw9sMcFAADg3RV1B1lHR0eWLVuWHTt25Pbbb097e3vWrFmTHTt2ZMWKFXnqqaeyevXqNDU1ZeHChVWXC/SzXa3JW10Df9y2tQN/TODn9fQkP1o78Md9c2fjPG4VTnc/2Zwc2Dvwx3UtAAAAMPgUNSC75ZZb0tbWlptvvjn33ntvxo4de+y15cuXZ9GiRTly5EhmzpyZcePGVVjp4NPS0pILL7wwLS11PlMGBpH29dUcd9dryVsHqjl2f5EBNIJ9Hcm+H1dz7Krypz/JARpBVb24e2tysLOaY/cXGUDp9ACl0wNYA0AjKuYRixs3bsyjjz6aSZMm5Z577jnue84777ysW7cuixYtOvZnbW1t+epXv5rvfe97WbduXd566630HOcDhWp93+lq5syZefDBB6suA/qsp6fCOzh6ks6dp/djFmUAjeDNCu/iaoQ7yOQAjaDKXnxzR+9nmJ2uZACl0wOUTg9gDQCNqJg7yB555JF0d3fn2muvzZgxY477nlGjRiXJOwZkra2teeyxxzJlypQsWbLkhPuv9X2nq6NHj2bfvn05evRo1aVAnxx8Mzlc4V1cb+6o7tj9QQbQCKrsw30dvZ+DeDqTA5zu3jrQez1QFdcCcHrTA5ROD2ANAI2omAHZqlWrkiSXXnrpCd/T1taW5J0Dsosvvjjt7e154oknctlll51w21rfd7ratGlTlixZkk2bNlVdCvRJV0e1x99X8fHfKxlAI6iyD3uOJvt3V3f8/iAHON25FnhvZACl0wOUTg9gDQCNqJhHLG7dujVJctZZZx339SNHjuSFF15I8s4B2ZAhtc0Qa31fvWbPnn1K9n399dfX9f729t7n0Tz99NN5+eWXa9rmoYceqrMqOHXOn7MsN/3Gfzz+a59JRpzkEdojW3769aLPn/h9b3Ul3/uLn//zZ57671n6hf+jxmoHRj050JcMSOQAg8sfXPvXmXHGvOO+drIcqDUDkhPnwBVLr8xrO9bUWO2p51qA0iw6+1dz22/+/4772kBcC/zd376QT/1/P11jtQPDtQCl0wOUTg9gDdTnD29YnYljp6a9vT3TpzfeE8ROxvmXff7J4PoedHd3H/vviy66qK5c+lnFDMi6urqSJAcOHP8Za48++mg6OjoyduzYnH322QNZ2rt6+y+f/rZ///663n/w4MFjX2vddvv27XXXBafKG5PeOOFrI1pq/0yQpiF9+/yQQ4feGnQ9UU8O9CUDEjnA4HLkyJETvlZrDvQ1A5JkV8euQdUTrgUozYxxJ76NcyCuBd5yLQCDjh6gdHoAa6A+bz9e8ujRow11XrVy/mWffzJ4vwc7d+7s87bFDMimTJmSN954I2vWrMkFF1zwjtfa29tzxx13JEkWLlyYpqamKko8rqlTp56SO8hGjx5d1/ubm5uPfa1122nTptVdF5wqLeNGnfC1t7pOvv3Ilt5/EOvpTg69y/tPtK+mYd2DrifqyYG+ZEAiBxhcunP4hK+dLAdqzYB329e4CWMy7cjg6QnXApRmTMXXAhlydND1hGsBSqcHKJ0ewBqoz9ChQ499baTzqpXzL/v8k8H1Peju7j52c9HkyZP7vJ+mnp6env4qajC75ZZb8sd//MeZMWNGvvOd72TOnDlJktWrV+e6667LD3/4wxw+fDhf/OIXc//99x93H3fddVe+8pWv5GTfslrfdyJdXV0ZM2ZMkmTfvn1paTnJ8176oN7nBa9fvz5XXXVVVq5cmQULFtS0zdy5c/tSGpwS+99I/ud/6vv2F32+96fFD3Ym332g/u1/4Zd6fw0m9eRAXzIgkQMMLuufSdr/qW/bvtcMaGpKLrklGTq8b8c/FVwLUJpDXcnzx3/ack3eaw6ctSSZ/ct9P/6p4FqA0ukBSqcHsAbq8/yfJIf2JSPHJJ/4QtXVDDznX/b5J4Pre9BfM5Ri7iBbvnx5vvnNb+ZHP/pRFixYkLlz5+bgwYNpbW3N0qVLM3PmzDz77LPv+PwxfmrOnDl54YUXMnZsH58rBRUbNSEZNjI5cqia44/t+w8yDAoygEYwbnLfB2TvVcukwTUc6ws5wOluZEvv/8gd2lfN8V0LwOlND1A6PYA1ADSi/n923yA1ffr0PP/887niiivS3NycLVu2ZOLEiXnggQfy1FNP5dVXX00SA7ITGD58eCZOnJjhw0/zf92jWE1Nybgp1R2/ymP3BxlAI6g0A07zfxhP5ACNwbVA38kASqcHKJ0ewBoAGlExA7IkmTdvXp588sl0dnams7MzL774Yj73uc+lq6srW7ZsyZAhQ3LuuedWXeagtG3bttx0003Ztm1b1aVAn02ZV81xJ57V+1PrpzMZQCMYNyUZ/b5qjj1lfjXH7U9ygEZQ1bXA+A8koydUc+z+IgMonR6gdHoAawBoREUNyE5k/fr16enpyezZs4/7IZMrV67MypUrs2HDhnf8/qWXXurT+05HnZ2dee6559LZ2Vl1KdBnkz+UDG8e+ONOXzzwx+xvMoBG0NRUTT+2TEzeN2Pgj9vf5ACN4IxzkhEV/NCKawE4/ekBSqcHsAaARlTMZ5C9m1deeSXJiR+vePXVVx/395/97Gfz0EMP1f0+oBpDhyfTFiVbXhy4Y44an0yaNXDHA97d1AXJay8kR98auGPO+GjvcA6o3pChyYyPJK99d+COOaIlOXPOwB0PAACA2hiQ5eQDsp6enpr2U+v7gOqc/YvJzk3Jgb0Dc7y5v5YMca8uDBrDm5M5lyYbnx2Y442fmkxbODDHAmrzwY8lOzYkXbsH5nhzP5kM9X9dAAAAg45/ts3JB2RA4xg6Ipn36/Vv91ZXcrCz92utpi1M3n9W/ccCTq0PnJu8f2Z92/QlA4YMTeZfnjS52oJBZeiwZP7SJHXe2dmXHJgyLznznPqOAwAAwMDws4xJVq1aVXUJg97kyZNz5513ZvLkyVWXAu/ZxA8mv/BLyQ//Z+3bfO8v6jvG2MnJ7Evq22YwkwE0kqam3sHV6m8mB9+sbZt6MyDpvWuk5f31bzdYyQEayfipyexfTn7wt7VvU28OtExKPvSr9W0zmMkASqcHKJ0ewBoAGpEBGTWZNGlSrr/++qrLgH5z9gXJ0cPJ1tX9v+8xZyQf+e1k2Ij+33dVZACNZuSY5KO/k6x5tPeOkP72oV/pvVOtkcgBGs1ZH+u9FvjhC/2/79ETk49e1ftY10YhAyidHqB0egBrAGhEHvpDTfbu3Ztnnnkme/cO0Ac3wSnW1JScc3HvXV79+fiz989Mzvt0MmJ0/+1zMJABNKLRE5KP/W4ybkr/7XPo8GTBbyQzPtp/+xws5ACN6BcuSOZe1vtI1P7yvhnJx67pHcQ3EhlA6fQApdMDWANAIzIgoyZtbW257bbb0tbWVnUp0G+amnp/evwXr+t9JOJ78fZnmy3+7cb6afG3yQAaVfO45GP/KjnnE0nTe/wH8olnJR+/Ppk6v19KG3TkAI1q+uLkF/8/vY9dfC+GDu99pOJHf6fxflAmkQGgByidHsAaABqRRywCxRtzRrLkXyXtG5K2tUnnztq3HT4q+cCHkxkfSZrHnrISgVNoyJBk5i8mZ8xOfrQmaV/f+9i1Wk2Y3psBZ87pHbwDp5+W9/feUdq+sfda4M322rcd1px8YEHvnaOjxp+yEgEAAOhnBmQA6X200rQP935m0Js7kl2tvYOyN3cmhw/89H1NQ5Oxk5KxU5L3Te/9B/WhkhQaQsvE3ketnXNxsvP7yZ7tvTnQ1ZH09Pz0fSNaeh/LOG5y71BszKTqagb6T9OQ3kHXBxb0/v2/6we9X9/c8b9dCwzp/eGacZOTCdN6c2Do8OrqBgAAoG/8sy7Az2hq6n3E0tuPWerp6b2TpPtI7z+IDR3Re7cJ0LiGjegdmE/7cO/vu4/25kBPd+9AfOiIausDTr1xk3t/Jce5Fhjev59ZBgAAQDUMyKhJc3Nz5s2bl+bmBvxwJXgXTU29/1iewv9BXAZQsiFD/WN4Igcol2uBXjKA0ukBSqcHsAaARmRARk1mzZqVxx9/vOoygIrIAEAOQNlkAKXTA5ROD2ANAI3Ig8IAAAAAAAAoigEZNdmwYUMWLlyYDRs2VF0KUAEZAMgBKDmj43cAAQAASURBVJsMoHR6gNLpAawBoBEZkFGTnp6eHD58OD09PVWXAlRABgByAMomAyidHqB0egBrAGhEBmQAAAAAAAAUxYAMAAAAAACAohiQAQAAAAAAUJRhVRfA6WHWrFl54oknMmPGjKpLASogAwA5AGWTAZROD1A6PYA1ADQiAzJq0tzcnNmzZ1ddBlARGQDIASibDKB0eoDS6QGsAaARecQiNdm+fXu+/OUvZ/v27VWXAlRABgByAMomAyidHqB0egBrAGhEBmTUZM+ePXnssceyZ8+eqksBKiADADkAZZMBlE4PUDo9gDUANCIDMgAAAAAAAIpiQAYAAAAAAEBRDMgAAAAAAAAoigEZNRkyZEiWLFmSIUMsGSiRDADkAJRNBlA6PUDp9ADWANCIJBo16e7uzurVq9Pd3V11KUAFZAAgB6BsMoDS6QFKpwewBoBGZEAGAAAAAABAUQzIAAAAAAAAKIoBGQAAAAAAAEUxIKMm48ePz7JlyzJ+/PiqSwEqIAMAOQBlkwGUTg9QOj2ANQA0omFVF8DpYfr06fna175WdRlARWQAIAegbDKA0ukBSqcHsAaARuQOMmpy6NChbN26NYcOHaq6FKACMgCQA1A2GUDp9ACl0wNYA0AjMiCjJq2trbn88svT2tpadSlABWQAIAegbDKA0ukBSqcHsAaARmRABgAAAAAAQFEMyAAAAAAAACiKARkAAAAAAABFMSADAAAAAACgKMOqLoDTw4IFC7Jx48aqywAqIgMAOQBlkwGUTg9QOj2ANQA0IneQAQAAAAAAUBQDMmqyefPmXHPNNdm8eXPVpQAVkAGAHICyyQBKpwconR7AGgAakQEZNdm/f3/WrVuX/fv3V10KUAEZAMgBKJsMoHR6gNLpAawBoBEZkAEAAAAAAFAUAzIAAAAAAACKYkAGAAAAAABAUQzIqMm0adOyYsWKTJs2repSgArIAEAOQNlkAKXTA5ROD2ANAI1oWNUFcHqYMGFCrrzyyqrLACoiAwA5AGWTAZROD1A6PYA1ADQid5BRk927d+fhhx/O7t27qy4FqIAMAOQAlE0GUDo9QOn0ANYA0IgMyKhJe3t77r777rS3t1ddClABGQDIASibDKB0eoDS6QGsAaARFTkg6+joyPLly3POOeekubk5M2bMyK233pqurq7ccMMNaWpqyv333191mQAAAAAAAJwCxX0G2dq1a7N06dLs2LEjLS0tmT9/fl5//fXcd999ee21147dJrx48eJqCwUAAAAAAOCUKOoOso6Ojixbtiw7duzI7bffnvb29qxZsyY7duzIihUr8tRTT2X16tVpamrKwoULqy4XAAAAAACAU6CoAdktt9yStra23Hzzzbn33nszduzYY68tX748ixYtypEjRzJz5syMGzeuwkoHn5aWllx44YVpaWmpuhSgAjIAkANQNhlA6fQApdMDWANAIyrmEYsbN27Mo48+mkmTJuWee+457nvOO++8rFu3LosWLTr2Z21tbfnqV7+a733ve1m3bl3eeuut9PT0/Ny2K1euzCOPPJKXXnopu3btygc/+MH89m//dr70pS9lzJgxp+y8BsrMmTPz4IMPVl0GUBEZAMgBKJsMoHR6gNLpAawBoBEVcwfZI488ku7u7lx77bUnHFiNGjUqSd4xIGttbc1jjz2WKVOmZMmSJSfc/7333puhQ4fm3/7bf5tvf/vb+df/+l/nP/7H/5jLL7883d3d/XsyFTh69Gj27duXo0ePVl0KUAEZAMgBKJsMoHR6gNLpAawBoBEVMyBbtWpVkuTSSy894Xva2tqSvHNAdvHFF6e9vT1PPPFELrvsshNu+9/+23/LX/7lX+baa6/NL//yL+fWW2/N/fffnxdeeCHf/e53++ksqrNp06YsWbIkmzZtqroUoAIyAJADUDYZQOn0AKXTA1gDQCMq5hGLW7duTZKcddZZx339yJEjeeGFF5K8c0A2ZEhtM8Qzzjjj5/7sYx/7WJJk+/btddX6s2bPnl1zDfW4/vrr63p/e3t7kuTpp5/Oyy+/XNM2Dz30UJ1VAQOpnhzoSwYkcgAGM9cCgGsBSqcHKJ0ewBqozx/esDoTx05Ne3t7pk8/8ZPGGpXzL/v8k8H1PfjZp/ZddNFFdeXSzypmQNbV1ZUkOXDgwHFff/TRR9PR0ZGxY8fm7LPP7pdjPvfcc0mSefPm9Xkfb//l09/2799f1/sPHjx47Gut276XwSBw6tWTA33JgEQOwGDmWgBwLUDp9ACl0wNYA/V5+/GSR48ebajzqpXzL/v8k8H7Pdi5c2efty1mQDZlypS88cYbWbNmTS644IJ3vNbe3p477rgjSbJw4cI0NTW95+Nt3749/+bf/JtcfvnlWbx4cZ/3M3Xq1FNyB9no0aPren9zc/Oxr7VuO23atLrrAgZOPTnQlwxI5AAMZq4FANcClE4PUDo9gDVQn6FDhx772kjnVSvnX/b5J4Pre9Dd3X3s5qLJkyf3eT9NPT09Pf1V1GB2yy235I//+I8zY8aMfOc738mcOXOSJKtXr851112XH/7whzl8+HC++MUv5v777z/uPu6666585Stfycm+Zfv27csll1ySHTt2ZPXq1Zk6dWpdtXZ1dWXMmDHH9tXS0lLX9rWo93nB69evz1VXXZWVK1dmwYIFNW0zd+7cvpQGDJB6cqAvGZDIARjMXAsArgUonR6gdHoAa6A+z/9JcmhfMnJM8okvVF3NwHP+ZZ9/Mri+B/01QynmDrLly5fnm9/8Zn70ox9lwYIFmTt3bg4ePJjW1tYsXbo0M2fOzLPPPvuOzx/riwMHDmTZsmXZvHlznn/++bqHY4PVnDl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+ "text/plain": [ + "
" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = grover_algorithm(challenge, rep=1)\n", + "qc.draw('mpl')" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'01110': 389, '01101': 352, '01001': 333, '01000': 365, '00011': 4738, '11100': 342, '11000': 377, '11010': 351, '10111': 326, '11001': 360, '10100': 355, '10010': 344, '01011': 383, '10001': 332, '10110': 350, '00110': 379, '00010': 330, '10011': 334, '00000': 380, '00001': 345, '11111': 354, '11011': 355, '10101': 353, '00101': 4615, '11101': 341, '01100': 347, '10000': 380, '00111': 329, '11110': 372, '01010': 348, '00100': 329, '01111': 412}\n" + ] + } + ], + "source": [ + "\n", + "counts_without_qiskit_convention = circuit_execute(qc, shots=20000)\n", + "print(counts_without_qiskit_convention)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plot_histogram(counts_without_qiskit_convention, color='midnightblue')" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'00011': 4738, '00101': 4615}\n" + ] + } + ], + "source": [ + "possible_results = filter_values_above_average(counts_without_qiskit_convention)\n", + "\n", + "print(possible_results)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "List 1: [['O', 'X', 'O'], ['O', 'O', 'O'], ['X', 'X', 'X']]\n", + "List 2: [['O', 'X', 'O'], ['O', 'X', 'O'], ['O', 'X', 'X']]\n" + ] + } + ], + "source": [ + "completed_lists = complete_lists_with_dictionary(challenge, possible_results)\n", + "\n", + "for i, lst in enumerate(completed_lists, start=1):\n", + " print(f'List {i}: {lst}')" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Challenge:\n", + "O | X | \n", + "---------\n", + " | | O\n", + "---------\n", + " | | X\n", + "---------\n", + "\n", + "\n", + "Solution 1:\n", + "O | X | O\n", + "---------\n", + "O | O | O\n", + "---------\n", + "X | X | X\n", + "---------\n", + "\n", + "\n", + "Solution 2:\n", + "O | X | O\n", + "---------\n", + "O | X | O\n", + "---------\n", + "O | X | X\n", + "---------\n", + "\n", + "\n" + ] + } + ], + "source": [ + "print('Challenge:')\n", + "display_board(challenge)\n", + "print('\\n')\n", + "\n", + "for index, lst in enumerate(completed_lists):\n", + " print('Solution {}:'.format(index + 1))\n", + " display_board(lst)\n", + " print('\\n')" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "WOMANIUM", + "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": "3.11.4" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/challenges/QOSF challenge/QuantumVoyagers/app/grover/grover_circuit_complete_image/file.tex b/challenges/QOSF challenge/QuantumVoyagers/app/grover/grover_circuit_complete_image/file.tex new file mode 100644 index 0000000..1122f84 --- /dev/null +++ b/challenges/QOSF challenge/QuantumVoyagers/app/grover/grover_circuit_complete_image/file.tex @@ -0,0 +1,33 @@ +\documentclass[border=2px]{standalone} + +\usepackage[braket, qm]{qcircuit} +\usepackage{graphicx} + +\begin{document} +\scalebox{1.0}{ +\Qcircuit @C=1.0em @R=0.2em @!R { \\ + \nghost{{q}_{0} : } & \lstick{{q}_{0} : } & \gate{\mathrm{X}} \barrier[0em]{21} & \qw \barrier[0em]{21} & \qw & \ctrl{3} & \ctrl{4} & \qw & \qw & \ctrl{1} & \qw & \qw & \qw \barrier[0em]{21} & \qw & \ctrl{9} \barrier[0em]{21} & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw \barrier[0em]{21} & \qw \barrier[0em]{21} & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw \barrier[0em]{21} & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw \barrier[0em]{21} & \qw & \ctrl{9} \barrier[0em]{21} & \qw & \qw & \qw & \qw & \ctrl{1} & \qw & \qw & \ctrl{4} & \ctrl{3} \barrier[0em]{21} & \qw \barrier[0em]{21} & \qw & \qw & \qw \barrier[0em]{8} & \qw & \qw & \qw & \qw \barrier[0em]{8} & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw & \qw & \qw \barrier[0em]{21} & \qw & \qw & \qw\\ + \nghost{{q}_{1} : } & \lstick{{q}_{1} : } & \gate{\mathrm{I}} & \qw & \qw & \qw & \qw & \qw & \ctrl{3} & \ctrl{1} & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{8} & \ctrl{8} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{8} & \ctrl{8} & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{1} & \ctrl{3} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{2} : } & \lstick{{q}_{2} : } & \gate{\mathrm{I}} & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{15} & \ctrl{3} & \qw & \ctrl{2} & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{7} & \ctrl{7} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{7} & \ctrl{7} & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{2} & \qw & \ctrl{3} & \ctrl{15} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{3} : } & \lstick{{q}_{3} : } & \gate{\mathrm{X}} & \qw & \qw & \ctrl{3} & \qw & \ctrl{1} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{6} & \ctrl{6} & \ctrl{6} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{6} & \ctrl{6} & \ctrl{6} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{1} & \qw & \ctrl{3} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{4} : } & \lstick{{q}_{4} : } & \gate{\mathrm{H}} & \qw & \qw & \qw & \ctrl{4} & \ctrl{1} & \ctrl{3} & \qw & \qw & \qw & \ctrl{2} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{5} & \ctrl{5} & \ctrl{5} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{5} & \ctrl{5} & \ctrl{5} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{2} & \qw & \qw & \qw & \ctrl{3} & \ctrl{1} & \ctrl{4} & \qw & \qw & \qw & \gate{\mathrm{H}} & \gate{\mathrm{X}} & \qw & \qw & \ctrl{1} & \qw & \qw & \gate{\mathrm{X}} & \gate{\mathrm{H}} & \qw & \meter & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{5} : } & \lstick{{q}_{5} : } & \gate{\mathrm{H}} & \qw & \qw & \qw & \qw & \ctrl{10} & \qw & \qw & \ctrl{3} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{4} & \ctrl{4} & \ctrl{4} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{4} & \ctrl{4} & \ctrl{4} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{3} & \qw & \qw & \ctrl{10} & \qw & \qw & \qw & \qw & \gate{\mathrm{H}} & \gate{\mathrm{X}} & \qw & \qw & \ctrl{2} & \qw & \qw & \gate{\mathrm{X}} & \gate{\mathrm{H}} & \qw & \qw & \meter & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{6} : } & \lstick{{q}_{6} : } & \gate{\mathrm{I}} & \qw & \qw & \ctrl{7} & \qw & \qw & \qw & \qw & \qw & \ctrl{1} & \ctrl{14} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{3} & \ctrl{3} & \ctrl{3} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{3} & \ctrl{3} & \ctrl{3} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{14} & \ctrl{1} & \qw & \qw & \qw & \qw & \qw & \ctrl{7} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{7} : } & \lstick{{q}_{7} : } & \gate{\mathrm{H}} & \qw & \qw & \qw & \qw & \qw & \ctrl{9} & \qw & \qw & \ctrl{1} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{2} & \ctrl{2} & \ctrl{2} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{2} & \ctrl{2} & \ctrl{2} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{1} & \qw & \qw & \ctrl{9} & \qw & \qw & \qw & \qw & \qw & \gate{\mathrm{H}} & \gate{\mathrm{X}} & \qw & \qw & \ctrl{1} & \qw & \qw & \gate{\mathrm{X}} & \gate{\mathrm{H}} & \qw & \qw & \qw & \meter & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{8} : } & \lstick{{q}_{8} : } & \gate{\mathrm{H}} & \qw & \qw & \qw & \ctrl{6} & \qw & \qw & \qw & \ctrl{10} & \ctrl{11} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{1} & \ctrl{1} & \ctrl{1} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{1} & \ctrl{1} & \ctrl{1} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{11} & \ctrl{10} & \qw & \qw & \qw & \ctrl{6} & \qw & \qw & \qw & \gate{\mathrm{H}} & \gate{\mathrm{X}} & \qw & \gate{\mathrm{H}} & \targ & \gate{\mathrm{H}} & \qw & \gate{\mathrm{X}} & \gate{\mathrm{H}} & \qw & \qw & \qw & \qw & \meter & \qw & \qw & \qw\\ + \nghost{{q}_{9} : } & \lstick{{q}_{9} : } & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \ctrl{1} & \targ & \qw & \ctrl{1} & \targ & \qw & \ctrl{1} & \ctrl{1} & \targ & \qw & \ctrl{1} & \ctrl{1} & \targ & \qw & \ctrl{1} & \ctrl{1} & \targ & \qw & \ctrl{1} & \ctrl{1} & \targ & \qw & \ctrl{1} & \ctrl{1} & \targ & \qw & \ctrl{1} & \ctrl{1} & \targ & \qw & \gate{\mathrm{X}} & \ctrl{1} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{1} & \gate{\mathrm{X}} & \qw & \targ & \ctrl{1} & \ctrl{1} & \qw & \targ & \ctrl{1} & \ctrl{1} & \qw & \targ & \ctrl{1} & \ctrl{1} & \qw & \targ & \ctrl{1} & \ctrl{1} & \qw & \targ & \ctrl{1} & \ctrl{1} & \qw & \targ & \ctrl{1} & \ctrl{1} & \qw & \targ & \ctrl{1} & \qw & \targ & \ctrl{1} & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{10} : } & \lstick{{q}_{10} : } & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \targ & \qw & \qw & \ctrl{1} & \targ & \qw & \qw & \ctrl{1} & \targ & \qw & \qw & \ctrl{1} & \targ & \qw & \qw & \ctrl{1} & \targ & \qw & \qw & \ctrl{1} & \targ & \qw & \qw & \ctrl{1} & \targ & \qw & \qw & \gate{\mathrm{X}} & \ctrl{1} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{1} & \gate{\mathrm{X}} & \qw & \qw & \targ & \ctrl{1} & \qw & \qw & \targ & \ctrl{1} & \qw & \qw & \targ & \ctrl{1} & \qw & \qw & \targ & \ctrl{1} & \qw & \qw & \targ & \ctrl{1} & \qw & \qw & \targ & \ctrl{1} & \qw & \qw & \targ & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{11} : } & \lstick{{q}_{11} : } & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \ctrl{1} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{1} & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{12} : } & \lstick{{q}_{12} : } & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \ctrl{1} & \ctrl{2} & \ctrl{3} & \ctrl{4} & \ctrl{5} & \ctrl{6} & \ctrl{7} & \ctrl{8} & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{13} : } & \lstick{{q}_{13} : } & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{8} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{14} : } & \lstick{{q}_{14} : } & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{7} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{15} : } & \lstick{{q}_{15} : } & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{6} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{16} : } & \lstick{{q}_{16} : } & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{5} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{17} : } & \lstick{{q}_{17} : } & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{4} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{18} : } & \lstick{{q}_{18} : } & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{3} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{19} : } & \lstick{{q}_{19} : } & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{2} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{20} : } & \lstick{{q}_{20} : } & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \ctrl{1} & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{{q}_{21} : } & \lstick{{q}_{21} : } & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \gate{\mathrm{X}} & \gate{\mathrm{H}} & \qw & \targ & \targ & \targ & \targ & \targ & \targ & \targ & \targ & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw & \qw\\ + \nghost{\mathrm{{c} : }} & \lstick{\mathrm{{c} : }} & \lstick{/_{_{4}}} \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \cw & \dstick{_{_{\hspace{0.0em}0}}} \cw \ar @{<=} [-18,0] & \dstick{_{_{\hspace{0.0em}1}}} \cw \ar @{<=} [-17,0] & \dstick{_{_{\hspace{0.0em}2}}} \cw \ar @{<=} [-15,0] & \dstick{_{_{\hspace{0.0em}3}}} \cw \ar @{<=} [-14,0] & \cw & \cw & \cw\\ +\\ }} +\end{document} \ No newline at end of file diff --git a/challenges/QOSF challenge/QuantumVoyagers/app/grover/grover_circuit_complete_image/grover_circuit.pdf b/challenges/QOSF challenge/QuantumVoyagers/app/grover/grover_circuit_complete_image/grover_circuit.pdf new file mode 100644 index 0000000..01817bc Binary files /dev/null and b/challenges/QOSF challenge/QuantumVoyagers/app/grover/grover_circuit_complete_image/grover_circuit.pdf differ diff --git a/challenges/QOSF challenge/QuantumVoyagers/app/grover/solution.ipynb b/challenges/QOSF challenge/QuantumVoyagers/app/grover/solution.ipynb new file mode 100644 index 0000000..6081169 --- /dev/null +++ b/challenges/QOSF challenge/QuantumVoyagers/app/grover/solution.ipynb @@ -0,0 +1,834 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Solving Tic Tac Toe with Quantum Computing\n", + "In this notebook, we will explore how to apply quantum algorithms to solve the game of Tic Tac Toe. We will use two popular quantum algorithms: the Grover algorithm and the Quantum Approximate Optimization Algorithm (QAOA)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1. Introduction" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1.1 Overview of Tic Tac Toe\n", + "\n", + "Tic Tac Toe, also known as Noughts and Crosses, is a classic two-player game where players take turns marking spaces on a 3x3 grid. The grid is initially empty, and players alternate placing their symbols ('X' or 'O') in an attempt to form a horizontal, vertical, or diagonal line of three of their symbols. The game ends when one player achieves this goal, resulting in a win, or if the entire grid is filled without a winner, leading to a draw.\n", + "\n", + "#### Key Rules:\n", + "\n", + "1. **Players:** Two players, typically represented by 'X' and 'O'.\n", + "2. **Grid:** A 3x3 square grid.\n", + "3. **Objective:** Form a line of three of your symbols horizontally, vertically, or diagonally.\n", + "4. **Turns:** Players take turns to place their symbol in an empty grid space.\n", + "5. **Winning:** The game ends when a player forms a line of three symbols, declaring them the winner.\n", + "6. **Draw:** If the grid is fully occupied and no player has won, the game is a draw.\n", + "\n", + "Tic Tac Toe is a simple yet strategic game often used for educational purposes to teach basic game theory concepts. Now, let's explore how quantum algorithms can be applied to enhance the strategies involved in playing Tic Tac Toe.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "

\n", + "\"JuveYell\"\n", + "

\n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2. Grover's Algorithm" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 2.1 Explanation of Grover's Quantum Search Algorithm\n", + "\n", + "Grover's Quantum Search Algorithm, developed by Lov Grover in 1996, is a potent quantum algorithm designed to perform a quadratic speedup in searching an unsorted database compared to the best classical algorithms. This algorithm relies on the principles of amplitude amplification, enabling efficient solution discovery within a large solution space.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Key Concepts:\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "1. **Amplitude Amplification:**\n", + "In the quest for a marked element in a quantum list, we start in a uniform superposition:\n", + "\n", + " $$ \\ket{s} = \\frac{1}{\\sqrt{N}} \\sum_{x=0}^{N-1} \\ket{x} $$\n", + "\n", + " When measured in the standard basis, the probability of finding the correct element is $ \\frac{1}{N} = \\frac{1}{2^n} $. Amplitude amplification improves this probability by extending the amplitude of the marked element and reducing others. The algorithm's geometric interpretation involves two reflections generating a rotation in a two-dimensional plane. Introducing an additional state $ \\ket{s'} $, perpendicular to $ \\ket{w} $, achieves this by eliminating $ \\ket{w} $ from $ \\ket{s} $ and adjusting the scale." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Image obtained from the Qiskit Textbook

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "2. **Oracle:**\n", + " In quantum algorithms like Grover's, an oracle designates specific states as solutions. In Tic Tac Toe, it flips the sign of the probability amplitude for correct states:\n", + " $$U_\\omega\\ket{x}=\\begin{cases}\n", + " \\ket{x},& \\text{si } x\\neq \\omega\\\\\n", + " -\\ket{x},& \\text{si } x= \\omega\n", + " \\end{cases}\n", + " $$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Image obtained from the Qiskit Textbook

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "3. **Grover Diffusion Operator:**\n", + " The Grover diffusion operator enhances the amplitudes of marked states and suppresses unmarked states. It involves a sequence of quantum gates:\n", + " $$U_s=2\\ket{s}\\bra{s}-\\mathbb{1}$$\n", + " This sequence concentrates probability amplitudes on marked states, contributing to the algorithm's efficiency." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Image obtained from the Qiskit Textbook

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, Grover's algorithm looks like:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Imagen obtenida del Qiskit Textbook

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "#### Application in Tic Tac Toe:\n", + "\n", + "For Tic Tac Toe, Grover's algorithm can be applied to search for optimal moves on the game board. By defining the oracle to identify winning board configurations and implementing the Grover diffusion operator, we can efficiently determine the optimal moves that lead to victory.\n", + "\n", + "
\n", + "

\n", + "\"JuveYell\"\n", + "

\n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The concept revolves around assigning a qubit to each box, such that when the qubit is in the state |1>, it represents 'X', and when in the state |0>, it represents 'O'. The empty spaces are filled with Hadamard gates, as these states are the ones sought by the Grover's algorithm.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For this case, our Oracle consists of two crucial components. First, there are the eight victory conditions detailed in the preceding figure. However, it is essential to filter only valid plays based on both logic and the rules established earlier. Therefore, the Oracle is composed of two parts:\n", + "\n", + "1. **Victory Conditions:**\n", + " - The eight specific conditions determining a win in the game.\n", + "\n", + "2. **X's Counter:**\n", + " - A mechanism to count the total number of 'X' on the board. Since in any game where 'O' starts, there must be a total of 5 'O' and 4 'X', our counter verifies the presence of exactly 4 'X'.\n", + "\n", + "Finally, it is imperative to mark the states that meet any of the eight winning conditions, always ensuring there are exactly 4 'X' throughout the game. For this reason, we implement eight controlled-NOT gates, one for each winning condition, targeting the oracle qubit. This approach ensures the validity of winning plays while adhering to the restriction of having 4 'X' in the game.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "

\n", + "\"JuveYell\"\n", + "

\n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the preceding image, we can identify the most crucial part of our circuit. Each number represents a component of the total circuit:\n", + "\n", + "1. **Tic Tac Toe Representation Circuit:**\n", + " - This circuit represents the Tic Tac Toe game, where 'H' denotes empty spaces, NOT gates represent 'X's, and 'I's represent 'O's.\n", + "\n", + "2. **Oracle Sub-Circuit:**\n", + " - This sub-circuit is part of the oracle and encompasses all possible winning scenarios (8 in total).\n", + "\n", + "3. **Counter:**\n", + " - The counter activates a Multi-Controlled NOT gate only if the number of 'X's is equal to 4.\n", + "\n", + "4. **State | - >:**\n", + " - This state, when the required conditions are met, changes sign, marking the desired state.\n", + "\n", + "5. **Toffoli Gates:**\n", + " - Toffoli gates determine the sought-after states, activating when the necessary conditions are fulfilled.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The remainder of the circuit corresponds to the inverse of circuits 2 and 3 from the preceding figure, followed by the application of the diffuser. Finally, the qubits in the 'H' states are measured, as these are the ones sought based on the established conditions.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we will see the results of implementing Grover's algorithm for our specific problem." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit.visualization import plot_histogram\n", + "\n", + "import sys\n", + "sys.path.append('../../')\n", + "from pkg.general_utils import display_board, complete_lists_with_dictionary, filter_values_above_average\n", + "from pkg.quantum_utils import grover_algorithm, circuit_execute" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Setting up the board the way it is asked to solve it" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "X | O | O\n", + "---------\n", + "X | | \n", + "---------\n", + "O | | \n", + "---------\n" + ] + } + ], + "source": [ + "challenge = [['X', 'O', 'O'], ['X', ' ', ' '], ['O', ' ', ' ']]\n", + "display_board(challenge)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Building the complete circuit and graphing" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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Q1Q8+Om0NGCCteiF+z2dZ6v6n70ldndJ1+Qr/9Gfyf/o2+a4dEbfXGFc4Tr6zzp9+Y9oaSM8erZlLf9PnY389Uxoy6NL7Dwn86fu3vnDx7c60Sf+8+cKfl1dWKy/vliijdUdaSkA//G+x3Shpxbd/oHXvrIhzRM77xqyVuuX6+2zvV/nhcd2Xd2P8A0ogE3uBm778PRXc+KU+H7tcHYi2BkgXrwOPPbFcFTtWRxmtO7447W8055N/ZXu/syFp7Ohx6uhM7usuDxtynb77l+/EtO/fLP57vbn33+IcUWKZdnw0MGS47v279y76eLzqwMVqwLHjDcrLK44yWnf45NOPllTK77d/r90f/NOP9NO3n0pAVM566K7v6tOTvmJ7vxPVLcrLK0pARH0Ln3Pd3hkzZtj6u/lcDMh6CYUiF9pua2vr8/G1a9eqvr5eGRkZGjVqVM/PU1JSNGDAgPO2TUtLk8/n0/79+2OO5+PCG2+trfb+wm5vb+/5Hu2+NTU1tuMCAABwghO9kNS/+yE7eXgx/760tcZ2eo3f51ddbZ26ujvjHFEMAgOVFsenC7++XtbeD+R/6GvyT7tFXY/+N3X/0/eU8twK+Xy+uLzGsdpjUnsMH9e/QqatgausjIs+NmSQNHRwdM/j90e/7bnCVv96P/oyaGDft1mIRltre7/PLxpnY7xBlV+pSZe/ib3AxLaL/z0XbR2ItQZI0pkzzf3q/ehLKNT38cBonDh+Ui1tjfELxg0dMf7hSmppCfX7P9/eTDs+mtF+6ZMwEl0HLPn61fvRF78/JabhmCR1tJ/t9/lFoyPGvjzF514vcPz48Zj3ZUDWy/Dhw3X69Gnt2rVL06ZNO++x2tpaLV26VJJUXFx83j8Ix40bpx07dpy3/c6dO2VZlhoaYr/A6ogRIxJyBtngwfaqWCAQ6Pke7b65ubm24wIAAHCCE72Q1L/7ITt5eDH/voT9sQ3IQu2Nyhl+TZyjiY01YIDidf9zq6ZG4R+/LN/14+T/8v3ypaTI/+A8hf/t/yr8+nqlfOHzcXmda0dc68oZZKatgcFXZV70sTNRHA8eEogcEAuHpTOXWCoXfa7us/3q/biYjs42DUy7zOl0fbBSOpIiv8vptGK79lZz+6mky9/EXmBg2sWPL12uDkRbAy71XOmDB/ar96MvVkpsB4Y7uzo09OoMZVrBOEfkrODAAZff6CJ8aV39/s+3N9OOjw4IDr3k4/GqAxd7Hqs7Of6uPNN6SkMGX217v25fW1Lkdzldiu2DAs1tzvYC4XC45+SinJycmJ/HZ1leuEJu/CxZskQ/+MEPlJ+frzfffFPjxo2TFBl2zZ8/X4cPH1ZnZ6ceffRRrVy5sme/n/zkJ/rqV7+qb3/72/rGN76h6upqffWrX9WBAwdUWFio0tLSqGMIhUJKT498cq2lpUXBYPz/crV7rdz9+/fr/vvv1yuvvKKJEydGtU9RkXOnVAIAANjhRC8k9e9+yM574MX8+xJqkH73Y/v75ZVIRXfHP55YhLq7dNWW/7ri57HCYXX/9VJZH5Ur9f/8QL7rrov8vLtb3Y/9tawjVUpd9S9xudTi6TvvVjDF+c9umrYGusPSf/8PqbM7tv2/9YXIp8UbW6VvvWZ//wnXSg9f/Fbf/cb+X0buvWHX9EXSoIvPIJPG6Wrp/Z/Z32/0dGn0tMtv15+Y2AtsOSCtj+0KVFdcAyTpsc9Ko4bFtq9T2s9Iv/2hJJtHS4dPkCZ9LiEhOW73K9KpSnv7+FOl2/4/KXVgQkJKGNOOj1qW9HevSK0xfi7pSuvA2Bxp8V2xvbaTyn4tVcdQK6c9JAXtz9X6nTPHpd//xP5+I6dKhZ+OfzwXE68Zinl3V76MZcuW6eqrr9bRo0c1ceJETZ48WYWFhbr55ps1evRo3XnnnZLOv/+YJD344INavny5vv3tb2vYsGG66aabdMcdd2jKlCkaMSJ+1+d3y7hx47R9+/aegSEAAIBJTO+FTMk/mCVl9X0r4kvKmxL3UFwXfuVVWQdK5f/agz3DMUnypaQo5W/+Wgp3q/ufvidTPm/phTWQ4pdyr3Lv9fOT5IBRLOs5e4w3hmOSNDTX/sE9n1/KnZyYePoTL9SB/Cz3Xtvnc7cGRSswRBo2xv5++VPiHoprYqmDIyYk33AsFsleB3w+Kc/FOuBmDbIjr+Ty2/R2Vb43hmOSNCRHGhLDOCM3hvetP2BA1kteXp62bdume+65R4FAQJWVlcrKytKqVau0ceNGHTx4UNKFAzKfz6fvfOc7qq+v1969e3X8+HH90z/9kz766CN96lOfciOVuEpLS1NWVpbS0uJ5RwMAAIDkYHovZFL+Y2ZIdm47MGKilN7PPw1vl1VVpfD//Yl844vk//MvXvC4r2Ck/A/Ok7XvDwq/vt6FCJ3nlTXg5pAqWQ6KZY6Qcmx82N+fKo2Znrh4nObz/fHT3zZuMTjyJukKbt+WNLxQB/KybP3RxtXwTGlAktzoZfSnpBQbf8zXjIvtYHJ/lT1auuq6y2/3sbRBUsHNiYunP/FCHXDz7+Nk6QXSs6VrbXzww58ijbk1cfG4YeytkQ/ARCv/Bmnw0ISFk1AMyPowfvx4bdiwQc3NzWpubtaOHTv08MMPKxQKqbKyUn6/X5MmTepz34yMDBUXF+vqq6/Wv/3bv6mtrU0PPfSQwxnEX1VVlR555BFVVVW5HQoAAIDjTO+FTMo/c4RUPCdy0PtyhhVK4z+b+Jic5rvuOqVt/E+l/u9/li+l72lhylceUNqvNsXtPmT9nVfWwA02DnjG0+AB0rjh7rx2LCbMjBwgvpyUNKnkPimjf9yCMG6yR0sT/kxRTVJyi713UPBivFAHBg2Qiq5157VviOEMbbdkXBNZ29EMya4eJU2cFRkue4XPH+mFMqP4XUkbJE35ojRoaMLD6he8UAfcWosDU6UJSXR7rqK7IsPvy/GnSJNnS0Ndqq2JknWdNOkeyRfFBweHT5DGJcFltC+GAZkN+/fvl2VZKiwsvOBGjO+9956eeeYZvfHGG9q4caMef/xxfeMb39CKFSs0ZkwM52b3M83Nzdq6dauam5vdDgUAAMBxpvdCpuWfPUaa+hdSzvV9f3JycJZ0/Wek4tn2zjZD8vLKGhg1TLp2qPOv+8kxyXPmiCSlpErF90UO9gzu45JwvhRp+PhInbi6wOnonHHtJOmmuZF62JeMa6QJsyL3X/TSYOBSvFIHZrhwZbgUv3RLkh0ayxopTZ0XOfDb1wHiQUOlwtulki/YO9ssWaQFpE98KXJm/cCMCx/3p0bOsJk6L/LhIlN4oQ7kZUmjsp1/3ZtGSYEkWisfD76u/0zkMuy9+fyRAdpNfyENG+t8fE7IuT7SCwwrVJ8fmknPjnxYcOIse2eb9TdJ1KK6b9++fZIuvLyiJA0cOFC/+MUv9Mwzz6irq0uTJ0/W2rVrdf/99zsdJgAAAIArlHFN5B/FHSGp/rB0cKvUfTZywGjaQ+YcEIa3+HzSrddLa3c495p+nzS90LnXixe/X7ruRin/E9LpKmnvf0ZqQOpA6VN/KQ2I7T7wSWVorjTlC1Jbk3SqUvro7T/WwUHSzfOpg8lq/AgpO12qb3HuNadcJw0Z5NzrxUt6tjTpc9K426X6Q9KH5/QCn1ro/TWQkiaNukUaebPUUCHt2/inOjh9UeR9QHKacb1UUe/c6/nkznD+Svl8kUsH5k2RGqulva9JXX9cA9MeMuPywpkjpJLPS+3N0qkK6eBbf+oFPvk1b9TBJJ7tOe9SA7LJkyfrnXfe0ZkzZ9Ta2qodO3YwHAMAAACS3MCglDtZSh0Q+X9/qjf+IQhzfXK0NNLBe5F9ZoKU3cfZB8nC54ucSfJxDUhJM2M4dq5BmVJeyTl1MIU6mMz8ful+B+8XFUiTZt/g3OslwoDBkbOlTO0F/P7I2aTn1kGGY8nthpFSYY5zr3fr9dKIoc69Xrz5fNJV+VLKOWvAhOHYuQIZkcsqe7EXYEBmw6UGZAAAAAAA9Hd+v/QX06RUB44GDM+U/szGTe4BOKNohHOXPPzCjdLQwZffDoBz/D5p7i3OXP44O126Z0riXweIFQMyG7Zs2SLLsnTPPfe4HYrjcnJytHz5cuXkOPjxAgAAgH7C9F7I9PwBr62BnEzpz6fa2+dMm9TYGvkejUCaNH+6lMp9+uARXqsD991o74wOuzVAkm4skG4ebTcyoP/yUh24Ol36ss2zSe3WgQEp0oPTpYHc5An9GL+eiEp2drYWLFjgdhgAAACuML0XMj1/wItrYNpYqe2stH53dNv/8+bon3tgqrTodin3qphCA/olr9WBQJr0/90prXxTOnHm8tvbqQGSNCkvcraqVy7BBUjeqwM3jYr0Auvei257O3UgLUVa+GmpIDu22ACncAYZotLU1KTNmzerqanJ7VAAAAAcZ3ovZHr+gFfXwJ0TIp8ej+flFjMHSY/eJY25Jn7PCfQHXqwDQwZJS+6WRg2L7/PeMkZ66FYphaOO8Bgv1oFbr5fmTYsMtOIlIxAZwF8/In7PCSQKf1UhKtXV1Xr88cdVXV3tdigAAACOM70XMj1/wMtr4FOF0t98Trru6it/rptHS8vvjc9zAf2NV+tAekD6b3dJn//ElR8gHzJI+v99OnJvI4Zj8CKv1oGpo6Vl90ij4zAsv7FA+u/3SqP5oAySBJdYBAAAAADAYMMzpcc+K71bLm07KNXZ/GB80QjpjvF8UhxIVn5/ZA1PzJW2HJDer5Q6u6PfPz0gTRsj3T5eCg5MWJgAEmhYhrT4Lun3FdK2D6Wa0/b2Hzdcur1ImpCbmPiARGFABgAAAACA4VL80vRxkTPKDp+Qdh2RjjZEDpB1h8/fdtAAKT8rcl+Rm0dL2RnuxAwgvq4ZEjn7a84N0s4Kqfx4pA40tp6/nU/SsCGROjAhVyrJl1LjeHk2AO7w+yOXSP3kaKmyXtpVKVWdko41Xjg0D6RFasB1V0s3j5FyhrgRMXDlGJABAAA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+ "text/plain": [ + "
" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = grover_algorithm(challenge, rep=1)\n", + "\n", + "qc.draw('mpl')" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'\\\\documentclass[border=2px]{standalone}\\n\\n\\\\usepackage[braket, qm]{qcircuit}\\n\\\\usepackage{graphicx}\\n\\n\\\\begin{document}\\n\\\\scalebox{1.0}{\\n\\\\Qcircuit @C=1.0em @R=0.2em @!R { \\\\\\\\\\n\\t \\t\\\\nghost{{q}_{0} : } & \\\\lstick{{q}_{0} : } & \\\\gate{\\\\mathrm{X}} \\\\barrier[0em]{21} & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\ctrl{3} & \\\\ctrl{4} & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\ctrl{9} \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\ctrl{9} \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\ctrl{4} & \\\\ctrl{3} \\\\barrier[0em]{21} & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{8} & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{8} & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw \\\\barrier[0em]{21} & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{1} : } & \\\\lstick{{q}_{1} : } & \\\\gate{\\\\mathrm{I}} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{3} & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{8} & \\\\ctrl{8} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{8} & \\\\ctrl{8} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\ctrl{3} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{2} : } & \\\\lstick{{q}_{2} : } & \\\\gate{\\\\mathrm{I}} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{15} & \\\\ctrl{3} & \\\\qw & \\\\ctrl{2} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{7} & \\\\ctrl{7} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{7} & \\\\ctrl{7} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{2} & \\\\qw & \\\\ctrl{3} & \\\\ctrl{15} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{3} : } & \\\\lstick{{q}_{3} : } & \\\\gate{\\\\mathrm{X}} & \\\\qw & \\\\qw & \\\\ctrl{3} & \\\\qw & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{6} & \\\\ctrl{6} & \\\\ctrl{6} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{6} & \\\\ctrl{6} & \\\\ctrl{6} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\qw & \\\\ctrl{3} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{4} : } & \\\\lstick{{q}_{4} : } & \\\\gate{\\\\mathrm{H}} & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{4} & \\\\ctrl{1} & \\\\ctrl{3} & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{2} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{5} & \\\\ctrl{5} & \\\\ctrl{5} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{5} & \\\\ctrl{5} & \\\\ctrl{5} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{2} & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{3} & \\\\ctrl{1} & \\\\ctrl{4} & \\\\qw & \\\\qw & \\\\qw & \\\\gate{\\\\mathrm{H}} & \\\\gate{\\\\mathrm{X}} & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\gate{\\\\mathrm{X}} & \\\\gate{\\\\mathrm{H}} & \\\\qw & \\\\meter & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{5} : } & \\\\lstick{{q}_{5} : } & \\\\gate{\\\\mathrm{H}} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{10} & \\\\qw & \\\\qw & \\\\ctrl{3} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{4} & \\\\ctrl{4} & \\\\ctrl{4} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{4} & \\\\ctrl{4} & \\\\ctrl{4} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{3} & \\\\qw & \\\\qw & \\\\ctrl{10} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\gate{\\\\mathrm{H}} & \\\\gate{\\\\mathrm{X}} & \\\\qw & \\\\qw & \\\\ctrl{2} & \\\\qw & \\\\qw & \\\\gate{\\\\mathrm{X}} & \\\\gate{\\\\mathrm{H}} & \\\\qw & \\\\qw & \\\\meter & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{6} : } & \\\\lstick{{q}_{6} : } & \\\\gate{\\\\mathrm{I}} & \\\\qw & \\\\qw & \\\\ctrl{7} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\ctrl{14} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{3} & \\\\ctrl{3} & \\\\ctrl{3} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{3} & \\\\ctrl{3} & \\\\ctrl{3} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{14} & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{7} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{7} : } & \\\\lstick{{q}_{7} : } & \\\\gate{\\\\mathrm{H}} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{9} & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{2} & \\\\ctrl{2} & \\\\ctrl{2} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{2} & \\\\ctrl{2} & \\\\ctrl{2} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\ctrl{9} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\gate{\\\\mathrm{H}} & \\\\gate{\\\\mathrm{X}} & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\gate{\\\\mathrm{X}} & \\\\gate{\\\\mathrm{H}} & \\\\qw & \\\\qw & \\\\qw & \\\\meter & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{8} : } & \\\\lstick{{q}_{8} : } & \\\\gate{\\\\mathrm{H}} & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{6} & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{10} & \\\\ctrl{11} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\ctrl{1} & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\ctrl{1} & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{11} & \\\\ctrl{10} & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{6} & \\\\qw & \\\\qw & \\\\qw & \\\\gate{\\\\mathrm{H}} & \\\\gate{\\\\mathrm{X}} & \\\\qw & \\\\gate{\\\\mathrm{H}} & \\\\targ & \\\\gate{\\\\mathrm{H}} & \\\\qw & \\\\gate{\\\\mathrm{X}} & \\\\gate{\\\\mathrm{H}} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\meter & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{9} : } & \\\\lstick{{q}_{9} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\ctrl{1} & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\ctrl{1} & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\ctrl{1} & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\ctrl{1} & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\ctrl{1} & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\ctrl{1} & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\gate{\\\\mathrm{X}} & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\gate{\\\\mathrm{X}} & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\ctrl{1} & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\ctrl{1} & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\ctrl{1} & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\ctrl{1} & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\ctrl{1} & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\ctrl{1} & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{10} : } & \\\\lstick{{q}_{10} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\targ & \\\\qw & \\\\qw & \\\\gate{\\\\mathrm{X}} & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\gate{\\\\mathrm{X}} & \\\\qw & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\targ & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{11} : } & \\\\lstick{{q}_{11} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{12} : } & \\\\lstick{{q}_{12} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\ctrl{2} & \\\\ctrl{3} & \\\\ctrl{4} & \\\\ctrl{5} & \\\\ctrl{6} & \\\\ctrl{7} & \\\\ctrl{8} & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{13} : } & \\\\lstick{{q}_{13} : } & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{8} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{14} : } & \\\\lstick{{q}_{14} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{7} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{15} : } & \\\\lstick{{q}_{15} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{6} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{16} : } & \\\\lstick{{q}_{16} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{5} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{17} : } & \\\\lstick{{q}_{17} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{4} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{18} : } & \\\\lstick{{q}_{18} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{3} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{19} : } & \\\\lstick{{q}_{19} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{2} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{20} : } & \\\\lstick{{q}_{20} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\ctrl{1} & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{{q}_{21} : } & \\\\lstick{{q}_{21} : } & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\gate{\\\\mathrm{X}} & \\\\gate{\\\\mathrm{H}} & \\\\qw & \\\\targ & \\\\targ & \\\\targ & \\\\targ & \\\\targ & \\\\targ & \\\\targ & \\\\targ & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw & \\\\qw\\\\\\\\\\n\\t \\t\\\\nghost{\\\\mathrm{{c} : }} & \\\\lstick{\\\\mathrm{{c} : }} & \\\\lstick{/_{_{4}}} \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\cw & \\\\dstick{_{_{\\\\hspace{0.0em}0}}} \\\\cw \\\\ar @{<=} [-18,0] & \\\\dstick{_{_{\\\\hspace{0.0em}1}}} \\\\cw \\\\ar @{<=} [-17,0] & \\\\dstick{_{_{\\\\hspace{0.0em}2}}} \\\\cw \\\\ar @{<=} [-15,0] & \\\\dstick{_{_{\\\\hspace{0.0em}3}}} \\\\cw \\\\ar @{<=} [-14,0] & \\\\cw & \\\\cw & \\\\cw\\\\\\\\\\n\\\\\\\\ }}\\n\\\\end{document}'" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc.draw('latex_source', filename='./grover_circuit_complete_image/file.tex')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Running the complete circuit and graphing the results" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'1011': 288, '0000': 293, '1000': 296, '0011': 317, '1101': 293, '1100': 7852, '1110': 315, '0111': 323, '1001': 7791, '1010': 319, '0010': 286, '1111': 329, '0101': 323, '0001': 298, '0110': 348, '0100': 329}\n" + ] + } + ], + "source": [ + "counts_without_qiskit_convention = circuit_execute(qc, shots=20000)\n", + "print(counts_without_qiskit_convention)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plot_histogram(counts_without_qiskit_convention, color='midnightblue')" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'1100': 7852, '1001': 7791}\n" + ] + } + ], + "source": [ + "possible_results = filter_values_above_average(counts_without_qiskit_convention)\n", + "\n", + "print(possible_results)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "List 1: [['X', 'O', 'O'], ['X', 'X', 'X'], ['O', 'O', 'O']]\n", + "List 2: [['X', 'O', 'O'], ['X', 'X', 'O'], ['O', 'O', 'X']]\n" + ] + } + ], + "source": [ + "completed_lists = complete_lists_with_dictionary(challenge, possible_results)\n", + "\n", + "for i, lst in enumerate(completed_lists, start=1):\n", + " print(f'List {i}: {lst}')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Printing all possible valid results" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Challenge:\n", + "X | O | O\n", + "---------\n", + "X | | \n", + "---------\n", + "O | | \n", + "---------\n", + "\n", + "\n", + "Solution 1:\n", + "X | O | O\n", + "---------\n", + "X | X | X\n", + "---------\n", + "O | O | O\n", + "---------\n", + "\n", + "\n", + "Solution 2:\n", + "X | O | O\n", + "---------\n", + "X | X | O\n", + "---------\n", + "O | O | X\n", + "---------\n", + "\n", + "\n" + ] + } + ], + "source": [ + "print('Challenge:')\n", + "display_board(challenge)\n", + "print('\\n')\n", + "\n", + "for index, lst in enumerate(completed_lists):\n", + " print('Solution {}:'.format(index + 1))\n", + " display_board(lst)\n", + " print('\\n')\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Post quantum analysis" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is evident for us that there are only two ways to win if we play as 'X'. The first is with the move |1100>, and the second is with the move |1001>, as shown in the results obtained by the implemented Grover's algorithm. Furthermore, we observe that for both winning plays, the 'X's played in the first available position. This implies that making this move increases the probability of winning, which makes sense since having this move with the 'X's provides two winning options in the next turn. However, if we analyze the 'O' move, meaning if 'O' plays in the third available position, then a guaranteed win is ensured, as the subsequent moves of 'X' become irrelevant.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "

\n", + "\"JuveYell\"\n", + "

\n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Bonus" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "X | O | O\n", + "---------\n", + "X | | \n", + "---------\n", + " | | \n", + "---------\n" + ] + } + ], + "source": [ + "challenge_bonus = [['X', 'O', 'O'], ['X', ' ', ' '], [' ', ' ', ' ']]\n", + "display_board(challenge_bonus)" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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YyJkB2cqVKyVJM2bM6PExVVXeb7YnD8iuuuoqhUIhLV++XNddd12P2z711FOqrq7WCy+8oJtuukm33HKL/vM//1Nvv/22li9fHqe9MGfr1q2aMmWKtm7daroUxMjkwXi4U2pJgZMpj+zr+bKKH8fE5aqSjQxIfZ3t5s4ilVLnBYFY+rlud5RnnKU4ciD1mezDSMTc2Wt+HK3xOST/EMcCSAVdnd6w2pRUORboCT1gB5OD2sYUf2MlPQDWAAAbOTMg27PHu57DsGHDuv14Z2enVq9eLenUAVlaWnRP0YoVKzR9+nRdeOGFJ/5t6tSpGjFihH73u9/FWjYQN20NZr9+61GzXz8asV7yItUvlQE3mO5B0xkUja5jUt3e2LYlB5AKTPdhawrkAMcCsFl7kxQxeFUH0xkERCJmfxa1NbpxSV4AAFJJhukCkqW5uVmS1Nra/Z2Bly5dqtraWuXk5Gj48OG+P/+WLVt0yy23nPHv48eP15YtW3x/vuNKS0ujHtL5MW/ePF+PD4VCkqSXXnpJ69evj2qbZ555xmdVSKS//dx/asKwq7r92GW3SX0+5h6rfbM++nv6Nz7+6xxrlv7yH2f++513fEPvVL4YZbVm/NWnfqjp477oe7vWpg4VFfnPDdP85EAsGSCRA73J8IJyPfzl7nvwbBkgRZ8DPWVA5fadurmo+wzqLQZmDdH/ufOdmLb9wT//SC+8/b/jXFFicSzgnv/vpqc1edTMbj+WjGOB+/6/v9HqiueirNaM22c8ok+Wz/O9XbhTKhk2Qp1dx+JfVAJxLOCWC/JK9U9f7f4Ge8k4FthfXaOiokujrDY56AG3pKdl6F/n7+7x4/H6WdhTD0jSiJJR6uhqO3uxSUIPgDXgzw/vWKu8nKEKhUIqKur5Vjy2Yv/d3n+pdz0HJ9/Wavr06b5y6WTODMiGDBmiI0eOaN26dZo6deopHwuFQnrwwQclSWX/P3t/H+Vlfd+J/8/hdmC4C0GBABGLEG4MkBhsrMZqa1qpwe622tg1/mK/HpOs8adfj0c8+X6z/ZpTzxqynnaPNbs1dfv1d1rj2qDbddXoNsVujds1WIRabmLGcJPBgTBBcBhuBGZ+f0wlcQPy+YzDXMPn/Xicwxnh87mu63XNeb+eXPKa6/osXJimpqa69//GG29kwoQJP/fnEydOzPe///0+1fx2bafC/v3763r/wYMHj32tddvt27fXXRenzv4DXSd8bURL0jz25PtoGlLb+47nxx07Bv2aeGNv354DeejwgUF/bsdTTw70JQMSOTCYNPecccLXas2ApO85cPDQ4O+TvaNOnJMn07F756A/v/+da4HydHV1nvC1gbgW2NXx40G/Jnbv6dvz544ePZKt2zb3czWnnmuBwhwafcKXBuJa4NBbBwfdetADZTnZv/UMxN+F29q2pLt78Hx+kx7AGqjP25+/dvTo0YY6r1o5/7LPPxm834OdO/v+DOViBmSXXXZZNm7cmBUrVuSTn/xk5syZkyRZvXp1rrvuunR09P7P8OLFiyus8udNnTr1lNxBNnr0if/n6Hiam5uPfa1122nTptVdF6fOkZ4TX7y8dZJ/Ex7Z0vs/AT3dyaGTvPdE+xo5esigXxMdXVv6tN2POjYM+nM7nnpyoC8ZkMiBwWT0mBP/lX+yDEhqz4ET7evQkc5Bvx6a0pRde7fljPEfPPmb/1lPT0+ampqy59CPBv35/e9cC5TnaNOJf2LdtUCv3fu39mk71wIndjp+XxpVy8gRJ3xtIK4FDh5+c9CtBz1Qnn0H92RM84TjvtZffxeeaD/7D72ZqVOn1FboANEDWAP1GTp06LGvjXRetXL+ZZ9/Mri+B93d3cduLpo8eXKf99PU01PGE5Db2tqyePHi/OQnP8mwYcMyd+7cHDx4MK2trVm6dGm6u7vz7LPP5hvf+EZuvPHG4+7jrrvuyle+8pUc71s2efLkXH311bn//vvf8edXXnlldu3alb//+7+vudaurq6MGTMmSbJv3760tJzkWRd9UO8Hah4+fDidnZ0ZO3Zshg8fXtM2c+fO7UtpnCJbX0p+8Ld92/aiz/f+hNzBzuS7D/RtH5fckgw78f+TDwpH3kqe/5PezyGqx7mfSqachsu9nhzoSwYkcmAw6elJ/u4/JIeP/6Thk3qvOTDjvORDl/bt2ANpy4tJ6/P1bTNqQvJLNyR9uAG9Uq4FytO2Ltn0133btj+uBS7+1yd/hFvVuo8kzz9Qf1bO+/Vk2odPTU2nkmuB8nz3G8nBPn4u6XvNgQ98OJn/63079qmiB8qz5i/7/pmz77UH3jcjOe/TfTv2qaIHsAbq8/yf9H6m58gxySe+UHU1A8/5l33+yeD6HvTXDKX/b00apKZPn57nn38+V1xxRZqbm7Nly5ZMnDgxDzzwQJ566qm8+uqrSZJFixb1af/z5s077meNbdiwIfPmzXtPtQ8Gw4cPz8SJE+v6C5DBZVzfB+nv2eiJg384lvTWWO8/bo0ck5w5+9TUM5jIgNNfU1MytsIcqDKD6vGBDydD61zmMz5y+g3H+kIOnP6q7MORYwf/cCxJhgxLptf5vwPDR52ePyhTLxnQGFwL9J0eaAxV9kCVx+4PegBrAGhExQzIkt4h1pNPPpnOzs50dnbmxRdfzOc+97l0dXVly5YtGTJkSM4999w+7ftTn/pUvvvd76atre3Yn7344ot57bXXsmzZsv46hcps27YtN910U7Zt6+OPWlG5cZPr/0ff/vK+GdUcty9mXZSMr/EO4aHDk0X/Ihky9JSWNCjIgMbwvunVHXvCafL0gRGje+8KTY0DrzNnJzM+ekpLGjTkwOlvzBnJsOZqjn06XQucfUEyscYnrQ4Zmiz8zequsQaSDGgMVfbihAqvQ/qDHmgMVfbA6fR34fHoAawBoBEVNSA7kfXr16enpyezZ88+7jN0V65cmZUrVx67Q+zt37/00kvH3vO5z30uU6dOzW/+5m/mySefzMqVK/O7v/u7Of/88/Obv/mbA3Yup0pnZ2eee+65dHae+MPdGdyGjkimzK/m2NMWVnPcvhg6PPnIbydnnPPu7xs5tvfxGOMG1yPkTxkZ0Bg+cG7v5yYMtPefnYwaP/DH7aszZiWL/+XJBwnTFvYO00q4eyyRA41gyNDkAwuqOfb00+haYMjQZNG/TCZ/6N3fN2J08tHfqfaHDwaSDGgMU+f33ik50CZMT8ZMGvjj9ic90BjeP7P3MYkDbeTY3mvi05kewBoAGlEFl8aDzyuvvJLkxI9XvPrqq4/7+89+9rN56KGHkiTjxo3LqlWrcuutt+aaa67JsGHD8qlPfSp/9Ed/lCFDzCEZHKYvSravG9hjjp96+j1OZdiI3jvD3tzZ+/3a1Zq8tb/3taYhybm/kZwxu4w7x2gsbz8SdOf3B/a40xcP7PH6w6RfSD7xuWTH93tz4M0d//xCU/LBj/ae0+j3VVkh9M30xcm2fxjYY46ZVPvd2YPF0OHJh5clZ388aVub/Lg1eaur97WmIcn8y5PJc6oZNMB7Mbw5mTw3af+ngT3u6XgtQGNqGpJMW5y8Vudnzr5X0xYm/mkIAAYf/0uXkw/Ienp6atrPrFmz8uSTT/ZbXdDfxp6ZTJqVdLw2cMc8++MDd6z+Nm5yMu7Xknm/9tMPoRwxuvcfFeB0ddb5yY9fTWr8q+09G3tmMuk0/WnZof/8uYTTPvwzH0Tbksy5tOrKoO9Gv6/377GdtX8e+3t29sdP3zstx5yRzP1k76+fvRaYWtFd+dAfZi5JdmxMeo4OzPFaJpbxmb2cPqYtTLa9lBw+MDDHGz6q/s+3BAAGhp9fyckHZNBI5n0yGTZyYI41dX7vQA4YPMZNTmb+4sAcq2lIsmBpNY91BE7sQ7/S+491A+HM2cmZJ3lUITCwWt6fzPqlATpYUzJ/qScvMLiMGNX7gw8DZe6v9v5wBQAw+PgnqySrVq1KT09PrrjiiqpLGbQmT56cO++8M5Mnn2bPyuPnjBzT+w9j9XirKznY+dNHC9V6nDl1HofBSwY0lrM/3ntXRD36kgO/8Ev1H4fBSw40jhGje39gph59yYDho5IPXXb63j3GO8mAxvLBJcm4qfVt05ccmLmk95HrjUAPNJbJc07+WZP/u770wJlzGucHRfQA1gDQiDxikZpMmjQp119/fdVl0E+mLki6didbXqzt/d/7i/r2P2xksvi3ez/jgMYgAxrLkGHJ4n+ZrH4kOVTj5yvXmwNT5w/cnWoMDDnQWM6ck8y6KHntu7W9v94MGDo8WfxbvY8lpTHIgMYyZEjvZ+6+9EhyYE9t29SbA2fO7s2ZRqEHGs/8X+8deO19vbb319sD46f2fmZlo/ygiB7AGgAakTvIqMnevXvzzDPPZO/evVWXQj+ZdVEy8xR8PtjwUclHr07GumukociAxtM8Ljnv08mo8f2/76kLknkN9I8B9JIDjWfmL56af7weNjL5yFWNc9cIvWRA4xnZkpz3O8noif2/7zPnJOd+qrEes6wHGs/QEclHfjuZML3/9z1+Wu8PjQ4b0f/7rooewBoAGlEDXa5yKrW1teW2225LW1tb1aXQT5qaknMuShb8RjKsn+70mjA9WXJtMm5K/+yPwUMGNKbRE5Il/yo5Y3b/7G/IsGTOpb0/KTvEFUbDkQONp6mp95GrH76y/z6TbPwHeq8FJkzrn/0xeMiAxtQ8Llnyu8mUef2zv6ahyTmfSD78qcb73DE90JiGjewdkn3wY/23zxnnJR+9qvGeqKIHsAaARuQRi1C4qfOTiR9MNv1NsusHfdvH0BG9/yM8fbE7RuB0M6IlWXhlsvP7yaurkrf2920/E6b3PqZm9Pv6tz7g1Js8J3nf9OT7q5Kdm/q2jyHDklkXJh88r7HuGIESDB+VnHtF711f3/+b5NC+vu1n/AeSeb+WjJnUv/XBqTZ0eDLnkt7Hgm54Ntm/u2/7GT0xmf9rp+aONADg1DAgAzJyTLLoN5N9HUnbuqR9fXL0rZNv1zIpmbE4mTK/sR4dAaVpakqmzE3OOCf58atJ29raPothyNBk8tze4bhHqcHpbcTo3js+fuGXku3rktf/KTly6OTbjZ7YmwEfWND7U/jA6evM2cmkX0h+/IPea4E9Ndwg0DS0d8g+fXHvgMwPy3E6mzAtueD3kp9s6e2Bjtdq227SL/T2wPvP1gMAcLoxIAOOGTMpmfuryeyLk327kjd3Jp0/Tg4fTHqO9v50+KjxybjJydgpvf/tfwCgcQwd1ntX6dT5ycE3/zkDdiZdu5Puo739PmxEMubMf86ByYbj0GhaJvY+KvWcTySdu3oz4M2dP3MtMDRp/udrgXFTklETXAtAIxkytPeHZqbMTQ52/jQD9u9Ojh7p7fehI3o/b3js5N4sMBynkTQ1JZPO7v311v6f9sC+jqT7SNLT03vH2ZhJP70eHjG66qoBgL4yIKMmzc3NmTdvXpqbG+wh2hzX0OG9PwE6/gNVV8JgIQPK0zyu99eZ/fT5ZJz+5EBZhgzrvTPU3aG8TQaUp3ls768zzqm6ksFBD5RnxOjeu8Lef3bVlQwOegBrAGhEBmTUZNasWXn88cerLgOoiAwA5ACUTQZQOj1A6fQA1gDQiHyENgAAAAAAAEUxIKMmGzZsyMKFC7Nhw4aqSwEqIAMAOQBlkwGUTg9QOj2ANQA0IgMyatLT05PDhw+np6en6lKACsgAQA5A2WQApdMDlE4PYA0AjciADAAAAAAAgKIYkAEAAAAAAFAUAzIAAAAAAACKMqzqAjg9zJo1K0888URmzJhRdSlABWQAIAegbDKA0ukBSqcHsAaARmRARk2am5sze/bsqssAKiIDADkAZZMBlE4PUDo9gDUANCKPWKQm27dvz5e//OVs37696lKACsgAQA5A2WQApdMDlE4PYA0AjciAjJrs2bMnjz32WPbs2VN1KUAFZAAgB6BsMoDS6QFKpwewBoBGZEAGAAAAAABAUQzIAAAAAAAAKIoBGQAAAAAAAEUxIKMmkyZNyo033phJkyZVXQpQARkAyAEomwygdHqA0ukBrAGgERmQUZOmpqaMGDEiTU1NVZcCVEAGAHIAyiYDKJ0eoHR6AGsAaEQGZNRk165d+frXv55du3ZVXQpQARkAyAEomwygdHqA0ukBrAGgERmQAQAAAAAAUBQDMgAAAAAAAIpiQAYAAAAAAEBRDMioyfjx47Ns2bKMHz++6lKACsgAQA5A2WQApdMDlE4PYA0AjWhY1QVwepg+fXq+9rWvVV0GUBEZAMgBKJsMoHR6gNLpAawBoBG5g4yaHDp0KFu3bs2hQ4eqLgWogAwA5ACUTQZQOj1A6fQA1gDQiAzIqElra2suv/zytLa2Vl0KUAEZAMgBKJsMoHR6gNLpAawBoBEZkAEAAAAAAFAUAzIAAAAAAACKYkAGAAAAAABAUQzIAAAAAAAAKMqwqgvg9LBgwYJs3Lix6jKAisgAQA5A2WQApdMDlE4PYA0AjcgdZAAAAAAAABTFgIyabN68Oddcc002b95cdSlABWQAIAegbDKA0ukBSqcHsAaARuQRi9Rk//79WbduXfbv3191KXDKHdibdLyWvLkz6dzZ+/ujh3tfO9SVrP0vybjJyftmJBOmJ01N1dY7EGQAJenuTnZvSfZs782Azl3JW129rx3al7z4570ZMG5KMmlWMrKl0nIHjBygJAc7k12tvRnw5tvXAm/1vnaoK1n7eDJ2cvK+6cn7PuhaAEqgByidHsAaABqRARlAkp6e5Cebk7a1SccP3+2NvcOzjtd6fzt6YjJ9UfKBc5NhIweiUuBUeasr2f5K0rYuOdR54vd1/vPwfPs/Jk1DkjPnJDM+kkyYNnC1Av2vpyd5Y1vyo7VJR2vv74//xt5rhY4fJpuTjJrwz9cCH06GNw9cvQAAALw3BmRA8Q52JhufTX6ypf5t9+9OXn0u2bo6mfdryaRf6PfygFOspydp35C8uio5cqjObbuTnZt6f02Zn3zoV/wDOZyODnUlm/66966xeh3Yk/zgf/ReC8z9ZHLm7H4vDwAAgFPAgAwo2o6Nyca//uljk/rq0L7exy1NPTeZe1kyVLrCaeHwgWT9t09y52iNdmxIdm9NFixN3j/zve8PGBg/fjXZ+N+Twwff237e2p/8439NJs9N5v9aMnRE/9QHAADAqTGk6gI4PUybNi0rVqzItGmeH0Xj2PYPyT899d6HYz+r/Z+StY8lR/pxn4OBDKARHepK/uHR/hmOve2tf/5sop3f7799DhZygEa0/R+Tf3zivQ/HftbOTcmalfXfkTrYyQBKpwconR7AGgAakXscqMmECRNy5ZVXVl0G9Ju2db2PRjwV3vhR70+QL/6XyZAGSVkZQKM5fDB5eWWyr6P/993TnfzTk739f8as/t9/VeQAjaZ9Q++dY6fC3td7h+UfuSoZOvzUHGOgyQBKpwconR7AGgAakTvIqMnu3bvz8MMPZ/fu3VWXAu/ZmzuT7//NqT3G7q3JD//nqT3GQJIBNJpN30n27Tp1++/p6b1D9eCbp+4YA00O0Ei6ftL7+aOn0p7tSevfndpjDCQZQOn0AKXTA1gDQCMyIKMm7e3tufvuu9Pe3l51KfCedB9NNjzTe4dHPc7/THLR53u/1mrL6mRvg7SMDKCR/PgHvY9Aq0dfMuDoW713p/T01HeswUoO0Ci6u3s/e7D7aH3b9SUHfvRy753ljUAGUDo9QOn0ANYA0IiKHJB1dHRk+fLlOeecc9Lc3JwZM2bk1ltvTVdXV2644YY0NTXl/vvvr7pM4BTY9lLf7hoZ0ZI0j+39WrOeZMOzjfOP49AIjr6VbPrr+rfrUwYk+cmW+odxwKnVtjZ5c0f92/U1BzY82zuUAwAAYHBpkE/Hqd3atWuzdOnS7NixIy0tLZk/f35ef/313HfffXnttdeO3Sa8ePHiagsF+l330WTbmoE9ZldH7+MW3z9zYI8LHN+OTclb+wf2mNteSqbMG9hjAsfX05P86B8G9pgH9iQdryVnzh7Y4wIAAPDuirqDrKOjI8uWLcuOHTty++23p729PWvWrMmOHTuyYsWKPPXUU1m9enWampqycOHCqssF+tmu1uStroE/btvagT8m8PN6epIfrR344765s3Eetwqnu59sTg7sHfjjuhYAAAAYfIoakN1yyy1pa2vLzTffnHvvvTdjx4499try5cuzaNGiHDlyJDNnzsy4ceMqrHTwaWlpyYUXXpiWljqfKQODSPv6ao6767XkrQPVHLu/yAAawb6OZN+Pqzl2VfnTn+QAjaCqXty9NTnYWc2x+4sMoHR6gNLpAawBoBEV84jFjRs35tFHH82kSZNyzz33HPc95513XtatW5dFixYd+7O2trZ89atfzfe+972sW7cub731VnqO84FCtb7vdDVz5sw8+OCDVZcBfdbTU+EdHD1J587T+zGLMoBG8GaFd3E1wh1kcoBGUGUvvrmj9zPMTlcygNLpAUqnB7AGgEZUzB1kjzzySLq7u3PttddmzJgxx33PqFGjkuQdA7LW1tY89thjmTJlSpYsWXLC/df6vtPV0aNHs2/fvhw9erTqUqBPDr6ZHK7wLq43d1R37P4gA2gEVfbhvo7ez0E8nckBTndvHei9HqiKawE4vekBSqcHsAaARlTMgGzVqlVJkksvvfSE72lra0vyzgHZxRdfnPb29jzxxBO57LLLTrhtre87XW3atClLlizJpk2bqi4F+qSro9rj76v4+O+VDKARVNmHPUeT/burO35/kAOc7lwLvDcygNLpAUqnB7AGgEZUzCMWt27dmiQ566yzjvv6kSNH8sILLyR554BsyJDaZoi1vq9es2fPPiX7vv766+t6f3t77/Nonn766bz88ss1bfPQQw/VWRWcOufPWZabfuM/Hv+1zyQjTvII7ZEtP/160edP/L63upLv/cXP//kzT/33LP3C/1FjtQOjnhzoSwYkcoDB5Q+u/evMOGPecV87WQ7UmgHJiXPgiqVX5rUda2qs9tRzLUBpFp39q7ntN/9/x31tIK4F/u5vX8in/r+frrHageFagNLpAUqnB7AG6vOHN6zOxLFT097enunTG+8JYifj/Ms+/2RwfQ+6u7uP/fdFF11UVy79rGIGZF1dXUmSAweO/4y1Rx99NB0dHRk7dmzOPvvsgSztXb39l09/279/f13vP3jw4LGvtW67ffv2uuuCU+WNSW+c8LURLbV/JkjTkL59fsihQ28Nup6oJwf6kgGJHGBwOXLkyAlfqzUH+poBSbKrY9eg6gnXApRmxrgT38Y5ENcCb7kWgEFHD1A6PYA1UJ+3Hy959OjRhjqvWjn/ss8/Gbzfg507d/Z522IGZFOmTMkbb7yRNWvW5IILLnjHa+3t7bnjjjuSJAsXLkxTU1MVJR7X1KlTT8kdZKNHj67r/c3Nzce+1rrttGnT6q4LTpWWcaNO+NpbXSfffmRL7z+I9XQnh97l/SfaV9Ow7kHXE/XkQF8yIJEDDC7dOXzC106WA7VmwLvta9yEMZl2ZPD0hGsBSjOm4muBDDk66HrCtQCl0wOUTg9gDdRn6NChx7420nnVyvmXff7J4PoedHd3H7u5aPLkyX3eT1NPT09PfxU1mN1yyy354z/+48yYMSPf+c53MmfOnCTJ6tWrc9111+WHP/xhDh8+nC9+8Yu5//77j7uPu+66K1/5yldysm9Zre87ka6urowZMyZJsm/fvrS0nOR5L31Q7/OC169fn6uuuiorV67MggULatpm7ty5fSkNTon9byT/8z/1ffuLPt/70+IHO5PvPlD/9r/wS72/BpN6cqAvGZDIAQaX9c8k7f/Ut23fawY0NSWX3JIMHd63458KrgUozaGu5PnjP225Ju81B85aksz+5b4f/1RwLUDp9ACl0wNYA/V5/k+SQ/uSkWOST3yh6moGnvMv+/yTwfU96K8ZSjF3kC1fvjzf/OY386Mf/SgLFizI3Llzc/DgwbS2tmbp0qWZOXNmnn322Xd8/hg/NWfOnLzwwgsZO7aPz5WCio2akAwbmRw5VM3xx/b9BxkGBRlAIxg3ue8DsveqZdLgGo71hRzgdDeypfd/5A7tq+b4rgXg9KYHKJ0ewBoAGlH/P7tvkJo+fXqef/75XHHFFWlubs6WLVsyceLEPPDAA3nqqafy6quvJokB2QkMHz48EydOzPDhp/m/7lGspqZk3JTqjl/lsfuDDKARVJoBp/k/jCdygMbgWqDvZACl0wOUTg9gDQCNqJgBWZLMmzcvTz75ZDo7O9PZ2ZkXX3wxn/vc59LV1ZUtW7ZkyJAhOffcc6suc1Datm1bbrrppmzbtq3qUqDPpsyr5rgTz+r9qfXTmQygEYybkox+XzXHnjK/muP2JzlAI6jqWmD8B5LRE6o5dn+RAZROD1A6PYA1ADSiogZkJ7J+/fr09PRk9uzZx/2QyZUrV2blypXZsGHDO37/0ksv9el9p6POzs4899xz6ezsrLoU6LPJH0qGNw/8cacvHvhj9jcZQCNoaqqmH1smJu+bMfDH7W9ygEZwxjnJiAp+aMW1AJz+9ACl0wNYA0AjKuYzyN7NK6+8kuTEj1e8+uqrj/v7z372s3nooYfqfh9QjaHDk2mLki0vDtwxR41PJs0auOMB727qguS1F5Kjbw3cMWd8tHc4B1RvyNBkxkeS1747cMcc0ZKcOWfgjgcAAEBtDMhy8gFZT09PTfup9X1Adc7+xWTnpuTA3oE53txfS4a4VxcGjeHNyZxLk43PDszxxk9Npi0cmGMBtfngx5IdG5Ku3QNzvLmfTIb6vy4AAIBBxz/b5uQDMqBxDB2RzPv1+rd7qys52Nn7tVbTFibvP6v+YwGn1gfOTd4/s75t+pIBQ4Ym8y9PmlxtwaAydFgyf2mSOu/s7EsOTJmXnHlOfccBAABgYPhZxiSrVq2quoRBb/LkybnzzjszefLkqkuB92ziB5Nf+KXkh/+z9m2+9xf1HWPs5GT2JfVtM5jJABpJU1Pv4Gr1N5ODb9a2Tb0ZkPTeNdLy/vq3G6zkAI1k/NRk9i8nP/jb2repNwdaJiUf+tX6thnMZACl0wOUTg9gDQCNyICMmkyaNCnXX3991WVAvzn7guTo4WTr6v7f95gzko/8djJsRP/vuyoygEYzckzy0d9J1jzae0dIf/vQr/TeqdZI5ACN5qyP9V4L/PCF/t/36InJR6/qfaxro5ABlE4PUDo9gDUANCIP/aEme/fuzTPPPJO9ewfog5vgFGtqSs65uPcur/58/Nn7ZybnfToZMbr/9jkYyAAa0egJycd+Nxk3pf/2OXR4suA3khkf7b99DhZygEb0Cxckcy/rfSRqf3nfjORj1/QO4huJDKB0eoDS6QGsAaARGZBRk7a2ttx2221pa2uruhToN01NvT89/ovX9T4S8b14+7PNFv92Y/20+NtkAI2qeVzysX+VnPOJpOk9/gP5xLOSj1+fTJ3fL6UNOnKARjV9cfKL/5/exy6+F0OH9z5S8aO/03g/KJPIANADlE4PYA0AjcgjFoHijTkjWfKvkvYNSdvapHNn7dsOH5V84MPJjI8kzWNPWYnAKTRkSDLzF5MzZic/WpO0r+997FqtJkzvzYAz5/QO3oHTT8v7e+8obd/Yey3wZnvt2w5rTj6woPfO0VHjT1mJAAAA9DMDMoD0Plpp2od7PzPozR3JrtbeQdmbO5PDB376vqahydhJydgpyfum9/6D+lBJCg2hZWLvo9bOuTjZ+f1kz/beHOjqSHp6fvq+ES29j2UcN7l3KDZmUnU1A/2naUjvoOsDC3r//t/1g96vb+74364FhvT+cM24ycmEab05MHR4dXUDAADQN/5ZF+BnNDX1PmLp7ccs9fT03knSfaT3H8SGjui92wRoXMNG9A7Mp3249/fdR3tzoKe7dyA+dES19QGn3rjJvb+S41wLDO/fzywDAACgGgZk1KS5uTnz5s1Lc3MDfrgSvIumpt5/LE/h/yAuAyjZkKH+MTyRA5TLtUAvGUDp9ACl0wNYA0AjMiCjJrNmzcrjjz9edRlARWQAIAegbDKA0ukBSqcHsAaARuRBYQAAAAAAABTFgIyabNiwIQsXLsyGDRuqLgWogAwA5ACUTQZQOj1A6bNk9JgAAQAASURBVPQA1gDQiAzIqElPT08OHz6cnp6eqksBKiADADkAZZMBlE4PUDo9gDUANCIDMgAAAAAAAIpiQAYAAAAAAEBRDMgAAAAAAAAoyrCqC+D0MGvWrDzxxBOZMWNG1aUAFZABgByAsskASqcHKJ0ewBoAGpEBGTVpbm7O7Nmzqy4DqIgMAOQAlE0GUDo9QOn0ANYA0Ig8YpGabN++PV/+8pezffv2qksBKiADADkAZZMBlE4PUDo9gDUANCIDMmqyZ8+ePPbYY9mzZ0/VpQAVkAGAHICyyQBKpwconR7AGgAakQEZAAAAAAAARTEgAwAAAAAAoCgGZAAAAAAAABTFgIyaDBkyJEuWLMmQIZYMlEgGAHIAyiYDKJ0eoHR6AGsAaEQSjZp0d3dn9erV6e7urroUoAIyAJADUDYZQOn0AKXTA1gDQCMyIAMAAAAAAKAoBmQAAAAAAAAUxYAMAAAAAACAohiQUZPx48dn2bJlGT9+fNWlABWQAYAcgLLJAEqnByidHsAaABrRsKoL4PQwffr0fO1rX6u6DKAiMgCQA1A2GUDp9ACl0wNYA0AjcgcZNTl06FC2bt2aQ4cOVV0KUAEZAMgBKJsMoHR6gNLpAawBoBEZkFGT1tbWXH755Wltba26FKACMgCQA1A2GUDp9ACl0wNYA0AjMiADAAAAAACgKAZkAAAAAAAAFMWADAAAAAAAgKIYkAEAAAAAAFCUYVUXwOlhwYIF2bhxY9VlABWRAYAcgLLJAEqnByidHsAaABqRO8gAAAAAAAAoigEZNdm8eXOuueaabN68uepSgArIAEAOQNlkAKXTA5ROD2ANAI3IgIya7N+/P+vWrcv+/furLgWogAwA5ACUTQZQOj1A6fQA1gDQiAzIAAAAAAAAKIoBGQAAAAAAAEUxIAMAAAAAAKAoBmTUZNq0aVmxYkWmTZtWdSlABWQAIAegbDKA0ukBSqcHsAaARjSs6gI4PUyYMCFXXnll1WUAFZEBgByAsskASqcHKJ0ewBoAGpE7yKjJ7t278/DDD2f37t1VlwJUQAYAcgDKJgMonR6gdHoAawBoRAZk1KS9vT1333132tvbqy4FqIAMAOQAlE0GUDo9QOn0ANYA0IiKHJB1dHRk+fLlOeecc9Lc3JwZM2bk1ltvTVdXV2644YY0NTXl/vvvr7pMAAAAAAAAToHiPoNs7dq1Wbp0aXbs2JGWlpbMnz8/r7/+eu6777689tprx24TXrx4cbWFAgAAAAAAcEoUdQdZR0dHli1blh07duT2229Pe3t71qxZkx07dmTFihV56qmnsnr16jQ1NWXhwoVVlwsAAAAAAMApUNSA7JZbbklbW1tuvvnm3HvvvRk7duyx15YvX55FixblyJEjmTlzZsaNG1dhpYNPS0tLLrzwwrS0tFRdClABGQDIASibDKB0eoDS6QGsAaARFfOIxY0bN+bRRx/NpEmTcs899xz3Peedd17WrVuXRYsWHfuztra2fPWrX833vve9rFu3Lm+99VZ6enp+btuVK1fmkUceyUsvvZRdu3blgx/8YH77t387X/rSlzJmzJhTdl4DZebMmXnwwQerLgOoiAwA5ACUTQZQOj1A6fQA1gDQiIq5g+yRRx5Jd3d3rr322hMOrEaNGpUk7xiQtba25rHHHsuUKVOyZMmSE+7/3nvvzdChQ/Nv/+2/zbe//e3863/9r/Mf/+N/zOWXX57u7u7+PZkKHD16NPv27cvRo0erLgWogAwA5ACUTQZQOj1A6fQA1gDQiIoZkK1atSpJcumll57wPW1tbUneOSC7+OKL097enieeeCKXXXbZCbf9b//tv+Uv//Ivc+211+aXf/mXc+utt+b+++/PCy+8kO9+97v9dBbV2bRpU5YsWZJNmzZVXQpQARkAyAEomwygdHqA0ukBrAGgERXziMWtW7cmSc4666zjvn7kyJG88MILSd45IBsypLYZ4hlnnPFzf/axj30sSbJ9+/a6av1Zs2fPrrmGelx//fV1vb+9vT1J8vTTT+fll1+uaZuHHnqozqqAgVRPDvQlAxI5AIOZawHAtQCl0wOUTg9gDdTnD29YnYljp6a9vT3Tp5/4SWONyvmXff7J4Poe/OxT+y666KK6culnFTMg6+rqSpIcOHDguK8/+uij6ejoyNixY3P22Wf3yzGfe+65JMm8efP6vI+3//Lpb/v376/r/QcPHjz2tdZt38tgEDj16smBvmRAIgdgMHMtALgWoHR6gNLpAayB+rz9eMmjR4821HnVyvmXff7J4P0e7Ny5s8/bFjMgmzJlSt54442sWbMmF1xwwTtea29vzx133JEkWbhwYZqamt7z8bZv355/82/+TS6//PIsXry4z/uZOnXqKbmDbPTo0XW9v7m5+djXWredNm1a3XUBA6eeHOhLBiRyAAYz1wKAawFKpwconR7AGqjP0KFDj31tpPOqlfMv+/yTwfU96O7uPnZz0eTJk/u8n6aenp6e/ipqMLvlllvyx3/8x5kxY0a+853vZM6cOUmS1atX57rrrssPf/jDHD58OF/84hdz//33H3cfd911V77yla/kZN+yffv25ZJLLsmOHTuyevXqTJ06ta5au7q6MmbMmGP7amlpqWv7WtT7vOD169fnqquuysqVK7NgwYKatpk7d25fSgMGSD050JcMSOQADGauBQDXApROD1A6PYA1UJ/n/yQ5tC8ZOSb5xBeqrmbgOf+yzz8ZXN+D/pqhFHMH2fLly/PNb34zP/rRj7JgwYLMnTs3Bw8eTGtra5YuXZqZM2fm2Weffcfnj/XFgQMHsmzZsmzevDnPP/983cOxwWrOnDl54YUXMnb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+ "text/plain": [ + "
" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc_bonus = grover_algorithm(challenge_bonus, rep=1)\n", + "\n", + "qc_bonus.draw('mpl')" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'10010': 40, '00011': 47, '01111': 34, '10101': 31, '01001': 41, '00111': 28, '11111': 30, '11011': 37, '00001': 39, '01011': 41, '10100': 3164, '10001': 3212, '11010': 38, '11101': 40, '00101': 3080, '11000': 3170, '11100': 36, '10110': 38, '10000': 36, '01100': 3189, '00110': 3183, '00010': 34, '10111': 31, '01101': 42, '11110': 39, '01010': 48, '01000': 45, '01110': 51, '00100': 43, '00000': 36, '10011': 40, '11001': 37}\n" + ] + } + ], + "source": [ + "\n", + "counts_without_qiskit_convention = circuit_execute(qc_bonus, shots=20000)\n", + "print(counts_without_qiskit_convention)" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plot_histogram(counts_without_qiskit_convention, color='midnightblue')" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'10100': 3164, '10001': 3212, '00101': 3080, '11000': 3170, '01100': 3189, '00110': 3183}\n" + ] + } + ], + "source": [ + "possible_results = filter_values_above_average(counts_without_qiskit_convention)\n", + "\n", + "print(possible_results)" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "List 1: [['X', 'O', 'O'], ['X', 'X', 'O'], ['O', 'X', 'O']]\n", + "List 2: [['X', 'O', 'O'], ['X', 'X', 'O'], ['O', 'O', 'O']]\n", + "List 3: [['X', 'O', 'O'], ['X', 'O', 'O'], ['O', 'X', 'O']]\n", + "List 4: [['X', 'O', 'O'], ['X', 'X', 'X'], ['O', 'O', 'O']]\n", + "List 5: [['X', 'O', 'O'], ['X', 'O', 'X'], ['O', 'X', 'O']]\n", + "List 6: [['X', 'O', 'O'], ['X', 'O', 'O'], ['O', 'X', 'X']]\n" + ] + } + ], + "source": [ + "completed_lists = complete_lists_with_dictionary(challenge, possible_results)\n", + "\n", + "for i, lst in enumerate(completed_lists, start=1):\n", + " print(f'List {i}: {lst}')" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Challenge:\n", + "X | O | O\n", + "---------\n", + "X | | \n", + "---------\n", + "O | | \n", + "---------\n", + "\n", + "\n", + "Solution 1:\n", + "X | O | O\n", + "---------\n", + "X | X | O\n", + "---------\n", + "O | X | O\n", + "---------\n", + "\n", + "\n", + "Solution 2:\n", + "X | O | O\n", + "---------\n", + "X | X | O\n", + "---------\n", + "O | O | O\n", + "---------\n", + "\n", + "\n", + "Solution 3:\n", + "X | O | O\n", + "---------\n", + "X | O | O\n", + "---------\n", + "O | X | O\n", + "---------\n", + "\n", + "\n", + "Solution 4:\n", + "X | O | O\n", + "---------\n", + "X | X | X\n", + "---------\n", + "O | O | O\n", + "---------\n", + "\n", + "\n", + "Solution 5:\n", + "X | O | O\n", + "---------\n", + "X | O | X\n", + "---------\n", + "O | X | O\n", + "---------\n", + "\n", + "\n", + "Solution 6:\n", + "X | O | O\n", + "---------\n", + "X | O | O\n", + "---------\n", + "O | X | X\n", + "---------\n", + "\n", + "\n" + ] + } + ], + "source": [ + "print('Challenge:')\n", + "display_board(challenge)\n", + "print('\\n')\n", + "\n", + "for index, lst in enumerate(completed_lists):\n", + " print('Solution {}:'.format(index + 1))\n", + " display_board(lst)\n", + " print('\\n')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Post quantum analysis" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Para este caso tambien podemos hacer el analisis post cuantico. Para saber que jugadas podrían darnos una mayor probabilidad de ganar:\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "

\n", + "\"JuveYell\"\n", + "

\n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can observe that the optimal move for 'X' is marking the third playable box (in red), which logically results in an automatic win. On the other hand, if 'O' plays in the fourth possible box (in blue), it also increases our chances of winning, as the displayed results are for 'X' winning scenarios. Finally, we can notice that the second-best move for 'X' after 'O' has played is to choose the first available box (in green).\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The file `general_solution.ipynb` includes a function that generates a random initial game configuration. Subsequently, the execution of the algorithm yields results where 'X' emerges victorious. In such instances, post-quantum analysis could be performed, although results may vary across each execution. Two specific cases are highlighted for a comprehensive understanding.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3. Conclusion" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + " - The flexibility of the oracle demonstrates Grover's versatility in addressing specific game conditions." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Grover provides an adaptable quantum solution for Tic Tac Toe, though the outcomes are statistically variable due to the quantum nature of the algorithm.*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "WOMANIUM", + "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": "3.11.4" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/challenges/QOSF challenge/QuantumVoyagers/app/qaoa/qaoa.ipynb b/challenges/QOSF challenge/QuantumVoyagers/app/qaoa/qaoa.ipynb new file mode 100644 index 0000000..4f72b06 --- /dev/null +++ b/challenges/QOSF challenge/QuantumVoyagers/app/qaoa/qaoa.ipynb @@ -0,0 +1,955 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "clyv3IRsJNaG", + "metadata": { + "id": "clyv3IRsJNaG" + }, + "outputs": [], + "source": [ + "!pip install h5py\n", + "!pip install typing-extensions\n", + "!pip install wheel" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "65DDjaGiFd_c", + "metadata": { + "id": "65DDjaGiFd_c" + }, + "outputs": [], + "source": [ + "!pip install docplex\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "DM3iU9TvGGCo", + "metadata": { + "id": "DM3iU9TvGGCo" + }, + "outputs": [], + "source": [ + "!pip install --upgrade azure-quantum\\[qiskit\\]\n", + "!pip install qiskit\n", + "!pip install cplex" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7QQ56rCZLsex", + "metadata": { + "id": "7QQ56rCZLsex" + }, + "outputs": [], + "source": [ + "!pip install openqaoa-qiskit" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "17552bd0", + "metadata": { + "id": "17552bd0" + }, + "outputs": [], + "source": [ + "%matplotlib notebook\n", + "\n", + "# Import external libraries to present an manipulate the data\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import pandas as pd\n", + "\n", + "# Import docplex model to generate the problem to optimize\n", + "from docplex.mp.model import Model\n", + "\n", + "# Import the libraries needed to employ the QAOA quantum algorithm using OpenQAOA\n", + "from openqaoa import QAOA\n", + "\n", + "# method to covnert a docplex model to a qubo problem\n", + "from openqaoa.problems.converters import FromDocplex2IsingModel\n", + "from openqaoa.backends import create_device\n", + "\n", + "# method to find the corrects states for the QAOA boject\n", + "from openqaoa.utilities import ground_state_hamiltonian" + ] + }, + { + "cell_type": "markdown", + "id": "c3672d85", + "metadata": { + "id": "c3672d85" + }, + "source": [ + "## 1) Tic Tac Toe Game\n", + "This problem can be solved by treating each cell as a variable, and our objective function aims to maximize the number of winning moves. For instance, if we want to address the following problem:\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "

\n", + "\"JuveYell\"\n", + "

\n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "So, for x_0, we observe it has 2 winning possibilities. On the other hand, x_1 has only one, x_2 has 0 winning possibilities, and x_3 has only 1 winning option. Therefore, our objective function is formulated as follows:\n", + "$$f_1(\\textbf{x}) = 2*x_0 + 1*x_1 + 0*x_2 + 1*x_3$$\n", + "\n", + "This objective function is subject to an equality constraint, as when the game starts with 0's, there should be a total of 4 X's played. This forms our constraint, but in this case, given an initial configuration, we subtract 2 X's:\n", + "\n", + "$$x_0 + x_1 + x_2 + x_3 = 2$$\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 95, + "id": "inv3grH1qNBI", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 481 + }, + "id": "inv3grH1qNBI", + "outputId": "4bd182b2-18a5-4ec6-8f97-87c20bb26cc3" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "// This file has been generated by DOcplex\n", + "// model name is: Basic Problem using minimize\n", + "// var contrainer section\n", + "dvar bool x[4];\n", + "\n", + "maximize\n", + " 2 x_0 + x_1 + x_3;\n", + " \n", + "subject to {\n", + " x_0 + x_1 + x_2 + x_3 == 2;\n", + "\n", + "}\n", + "None\n", + "Warning: Model name contains whitespaces: |Basic Problem using minimize|\n" + ] + }, + { + "data": { + "text/html": [ + "\n", + "
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\n", + "

\n", + "\"JuveYell\"\n", + "

\n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So, for x_0, we observe it has 2 winning possibilities. On the other hand, x_1 has only one, x_2 has only one too, x_3 has 0 winning possibilities, and x_4 has only 1 winning option. Therefore, our objective function is formulated as follows:\n", + "$$f_1(\\textbf{x}) = 2*x_0 + 1*x_1 + 1*x_2 + 0*x_3 + 1*x_4$$\n", + "\n", + "This objective function is subject to an equality constraint, as when the game starts with 0's, there should be a total of 4 X's played. This forms our constraint, but in this case, given an initial configuration, we subtract 2 X's:\n", + "\n", + "$$x_0 + x_1 + x_2 + x_3 + x_4= 2$$" + ] + }, + { + "cell_type": "code", + "execution_count": 94, + "id": "ed3023be", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 575 + }, + "id": "ed3023be", + "outputId": "699a3f4d-02d4-458d-8d34-a396229fb0ab" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "// This file has been generated by DOcplex\n", + "// model name is: Basic Problem using minimize\n", + "// var contrainer section\n", + "dvar bool x[5];\n", + "\n", + "maximize\n", + " 2 x_0 + x_1 + x_2 + x_4;\n", + " \n", + "subject to {\n", + " x_0 + x_1 + x_2 + x_3 + x_4 == 2;\n", + "\n", + "}\n", + "None\n", + "Warning: Model name contains whitespaces: |Basic Problem using minimize|\n" + ] + }, + { + "data": { + "text/html": [ + "\n", + "
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solutions_bitstringsbitstrings_energiesprobabilities
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of the QUBO problem\n", + "ising_encoding = qubo.ising_model\n", + "\n", + "# Print in a df the ising encoding (we need to remove keys: 'problem_instance' and 'metadata'))\n", + "ising_encoding_dict = ising_encoding.asdict(exclude_keys=['problem_instance', 'metadata'])\n", + "\n", + "#Specific local device usign qiskit backend\n", + "device = create_device(\"local\", 'qiskit.qasm_simulator')\n", + "#Is possible check the devices using qaoa.local_simulators, qaoa.cloud_provider\n", + "qaoa = QAOA(device)\n", + "\n", + "#Indicate the properties to the QAOA quantum algorithm,shots,seed\n", + "qaoa.set_backend_properties(n_shots=20, seed_simulator=1)\n", + "#check the p value and the variational init params\n", + "qaoa.set_circuit_properties(p=2, init_type=\"custom\", variational_params_dict={\"betas\":2*[0.01*np.pi],\"gammas\":2*[0.01*np.pi]})\n", + "\n", + "#Indicate the ising e ncoding model from docplex\n", + "qaoa.compile(ising_encoding)\n", + "\n", + "#Optimize the quantum algorithm\n", + "qaoa.optimize()\n", + "#Print in a df the best 10 solutions\n", + "results = pd.DataFrame(qaoa.result.lowest_cost_bitstrings(10))\n", + "results = results[results[\"bitstrings_energies\"]<0]\n", + "results" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "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": "3.10.6" + }, + "vscode": { + "interpreter": { + "hash": "d2582286b70c3b030a2fde61b871db03dec7fee33191883f4394b540a2eb90c7" + } + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/challenges/QOSF 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column): + """ + Makes a move on the Tic Tac Toe board for the specified player. + + Parameters: + - board (list): The Tic Tac Toe board. + - player (str): The player making the move ('O' or 'X'). + - row (int): The row where the move is made. + - column (int): The column where the move is made. + + Returns: + - success (bool): True if the move is successful, False if the chosen position is already occupied. + """ + if board[row][column] == ' ': + board[row][column] = player + return True + else: + return False + + +def check_winner(board): + """ + Checks if there is a winner on the Tic Tac Toe board. + + Parameters: + - board (list): The Tic Tac Toe board. + + Returns: + - winner (bool): True if there is a winner, False otherwise. + """ + # Check rows and columns + for i in range(3): + if board[i][0] == board[i][1] == board[i][2] != ' ' or board[0][i] == board[1][i] == board[2][i] != ' ': + return True + + # Check diagonals + if board[0][0] == board[1][1] == board[2][2] != ' ' or board[0][2] == board[1][1] == board[2][0] != ' ': + return True + + return False + + +def generate_random_board(num_moves): + """ + Generates a random Tic Tac Toe board after a specified number of moves. + + Parameters: + - num_moves (int): The number of moves made on the board. + + Returns: + - board (list): A 3x3 grid representing the generated Tic Tac Toe board. + """ + players = ['O', 'X'] + + while True: + board = initialize_board() + moves_made = 0 + + while moves_made < num_moves: + current_player = players[moves_made % 2] + row = random.randint(0, 2) + column = random.randint(0, 2) + + if make_move(board, current_player, row, column): + moves_made += 1 + + if not check_winner(board): + return board + + +def display_board(board): + """ + Displays the Tic Tac Toe board. + + Parameters: + - board (list): The Tic Tac Toe board. + """ + for row in board: + print(" | ".join(row)) + print("-" * 9) + + +def complete_lists_with_dictionary(lists, dictionary): + """ + Completes lists with characters from a dictionary. + + Parameters: + - lists (list): A list of lists to be completed. + - dictionary (dict): A dictionary where keys are binary strings and values are probabilities. + + Returns: + - result (list): A list of lists with characters filled in from the dictionary. + """ + result = [] + + for key, value in dictionary.items(): + # Create a copy of the original list + new_list = [list(row) for row in lists] + + # Convert the binary value of the key into a list of characters 'O' and 'X' + characters = ['O' if bit == '0' else 'X' for bit in key] + + # Fill in the empty spaces in the new list with the corresponding characters + index = 0 + for i in range(len(new_list)): + for j in range(len(new_list[i])): + if new_list[i][j] == ' ': + new_list[i][j] = characters[index] + index += 1 + + result.append(new_list) + + return result + + +def filter_values_above_average(dictionary): + """ + Filters values above the average from a dictionary. + + Parameters: + - dictionary (dict): A dictionary where keys are binary strings and values are probabilities. + + Returns: + - filtered_dictionary (dict): A dictionary with values above the average. + """ + values = list(dictionary.values()) + average = sum(values) / len(values) + + # Calculate the difference between the maximum and minimum values + max_min_difference = max(values) - min(values) + + # Check if the difference is small compared to the average + if max_min_difference < 0.1 * average: + return dictionary + + # Filter values above the average + filtered_dictionary = {key: value for key, + value in dictionary.items() if value > average} + return filtered_dictionary + + +if __name__ == '__main__': + # Example of usage + num_moves = 5 + random_board = generate_random_board(num_moves) + print(random_board) + print('Board:') + display_board(random_board) diff --git a/challenges/QOSF challenge/QuantumVoyagers/pkg/quantum_utils.py b/challenges/QOSF challenge/QuantumVoyagers/pkg/quantum_utils.py new file mode 100644 index 0000000..b3ac2a5 --- /dev/null +++ b/challenges/QOSF challenge/QuantumVoyagers/pkg/quantum_utils.py @@ -0,0 +1,292 @@ +from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute, Aer +from qiskit.circuit.library import XGate + + +def setting_initial_configuration(board): + """ + Initializes a quantum circuit with the given Tic Tac Toe board configuration. + + Args: + board (list of lists): Represents the Tic Tac Toe board. + + Returns: + QuantumCircuit: Quantum circuit with the specified initial configuration. + """ + n_qubits = 9 + counter_aux_qubits = 4 + aux_conditions_qubits = 8 + oracle_qubit = 1 + empty_spaces = sum(row.count(' ') for row in board) + + qreg_q = QuantumRegister( + n_qubits + counter_aux_qubits + aux_conditions_qubits + oracle_qubit, 'q') + + creg_c = ClassicalRegister(empty_spaces, 'c') + + qc = QuantumCircuit(qreg_q, creg_c) + + counter = 0 + for row in board: + for elem in row: + if elem == 'O': + qc.i(qreg_q[counter]) + elif elem == 'X': + qc.x(qreg_q[counter]) + else: + qc.h(qreg_q[counter]) + counter += 1 + + return qc + + + +def conditions_and_counter(): + """ + Creates a quantum circuit to apply conditions and count the number of 'X's on the board. + + Returns: + QuantumCircuit: Quantum circuit for conditions and counting. + """ + n_qubits = 9 + counter_aux_qubits = 4 + aux_conditions_qubits = 8 + oracle_qubit = 1 + + qreg_q = QuantumRegister( + n_qubits + counter_aux_qubits + aux_conditions_qubits + oracle_qubit, 'q') + + mcx = XGate().control(3) + + qc = QuantumCircuit(qreg_q) + + # 8 possible ways for 'X' to win the game + qc.barrier() + qc.mct([0, 3, 6], 13) + qc.mct([0, 4, 8], 14) + qc.mct([3, 4, 5], 15) + qc.mct([1, 4, 7], 16) + qc.mct([0, 1, 2], 17) + qc.mct([2, 5, 8], 18) + qc.mct([6, 7, 8], 19) + qc.mct([2, 4, 6], 20) + qc.barrier() + + # Bit adder, counting the number of 'X's on the board + qc.cx(qreg_q[0], qreg_q[9]) + qc.barrier() + + qc.ccx(qreg_q[1], qreg_q[9], qreg_q[10]) + qc.cx(qreg_q[1], qreg_q[9]) + qc.barrier() + + qc.ccx(qreg_q[2], qreg_q[9], qreg_q[10]) + qc.cx(qreg_q[2], qreg_q[9]) + qc.barrier() + + qc.append(mcx, [3, 9, 10, 11]) + qc.ccx(qreg_q[3], qreg_q[9], qreg_q[10]) + qc.cx(qreg_q[3], qreg_q[9]) + qc.barrier() + + qc.append(mcx, [4, 9, 10, 11]) + qc.ccx(qreg_q[4], qreg_q[9], qreg_q[10]) + qc.cx(qreg_q[4], qreg_q[9]) + qc.barrier() + + qc.append(mcx, [5, 9, 10, 11]) + qc.ccx(qreg_q[5], qreg_q[9], qreg_q[10]) + qc.cx(qreg_q[5], qreg_q[9]) + qc.barrier() + + qc.append(mcx, [6, 9, 10, 11]) + qc.ccx(qreg_q[6], qreg_q[9], qreg_q[10]) + qc.cx(qreg_q[6], qreg_q[9]) + qc.barrier() + + qc.append(mcx, [7, 9, 10, 11]) + qc.ccx(qreg_q[7], qreg_q[9], qreg_q[10]) + qc.cx(qreg_q[7], qreg_q[9]) + qc.barrier() + + qc.append(mcx, [8, 9, 10, 11]) + qc.ccx(qreg_q[8], qreg_q[9], qreg_q[10]) + qc.cx(qreg_q[8], qreg_q[9]) + qc.barrier() + + qc.x(qreg_q[9]) + qc.x(qreg_q[10]) + + qc.mct([9, 10, 11], 12) + + qc.barrier() + + return qc + +def oracle(): + """ + Creates a quantum circuit for the oracle part of the algorithm. + + Returns: + QuantumCircuit: Quantum circuit for the oracle. + """ + n_qubits = 9 + counter_aux_qubits = 4 + aux_conditions_qubits = 8 + oracle_qubit = 1 + + qreg_q = QuantumRegister( + n_qubits + counter_aux_qubits + aux_conditions_qubits + oracle_qubit, 'q') + + qc = QuantumCircuit(qreg_q) + + qc = qc.compose(conditions_and_counter()) + + qc.barrier() + qc.x(21) + qc.h(21) + qc.barrier() + + # Oracle + qc.mct([12, 13], 21) + qc.mct([12, 14], 21) + qc.mct([12, 15], 21) + qc.mct([12, 16], 21) + qc.mct([12, 17], 21) + qc.mct([12, 18], 21) + qc.mct([12, 19], 21) + qc.mct([12, 20], 21) + + qc.barrier() + qc = qc.compose(conditions_and_counter().inverse()) + + return qc + + +def diffuser(board): + """ + Creates a quantum circuit for the Grover Diffuser. + + Args: + board (list): The Tic Tac Toe board. + + Returns: + QuantumCircuit: Quantum circuit representing the Grover Diffuser. + """ + n_qubits = 9 + one_dimensional_list = [value for row in board for value in row] + index_empty_spaces = [i for i, value in enumerate( + one_dimensional_list) if value == ' '] + + qreg_q = QuantumRegister(n_qubits, 'q') + + qc = QuantumCircuit(qreg_q) + + for qubit in index_empty_spaces: + qc.h(qubit) + # Apply transformation |00..0> -> |11..1> (X-gates) + for qubit in index_empty_spaces: + qc.x(qubit) + + qc.barrier() + # Apply multiple controlled Z-gates + qc.h(index_empty_spaces[-1]) + # Toffoli with multicontrol + qc.mct(index_empty_spaces[:-1], index_empty_spaces[-1]) + qc.h(index_empty_spaces[-1]) + qc.barrier() + # Apply transformation |11..1> -> |00..0> + for qubit in index_empty_spaces: + qc.x(qubit) + # Apply transformation |00..0> -> |s> + for qubit in index_empty_spaces: + qc.h(qubit) + + # qc.measure([4,5,7,8],creg_c) + + return qc + + +def measurement(qc, board): + """ + Adds the measurement operation to the quantum circuit. + + Args: + qc (QuantumCircuit): Quantum circuit. + board (list): The Tic Tac Toe board. + + Returns: + QuantumCircuit: Quantum circuit with measurement operation. + """ + one_dimensional_list = [value for row in board for value in row] + index_empty_spaces = [i for i, value in enumerate( + one_dimensional_list) if value == ' '] + + qc.measure(index_empty_spaces, qc.clbits) + return qc + + + +def grover_algorithm(board, rep=1): + """ + Executes the Grover's algorithm for Tic Tac Toe. + + Args: + board (list): The initial state of the Tic Tac Toe board. + rep (int): Number of iterations of the algorithm. + + Returns: + QuantumCircuit: Quantum circuit representing the Grover's algorithm. + """ + qc = setting_initial_configuration(board) + qc.barrier() + + for _ in range(rep): + # Oracle + qc = qc.compose(oracle()) + qc.barrier() + # Diffuser + qc = qc.compose(diffuser(board)) + qc.barrier() + + # Measurement + qc = measurement(qc, board) + qc.barrier() + + return qc + + +def circuit_execute(qc, shots=10000): + """ + Executes the quantum circuit on a simulator. + + Args: + qc (QuantumCircuit): Quantum circuit. + shots (int): Number of shots for the simulation. + + Returns: + dict: Counts of the measurement outcomes. + """ + simulator = Aer.get_backend('qasm_simulator') + job = execute(qc, simulator, shots=shots) + result = job.result() + # Returns counts + counts = result.get_counts(qc) + + counts_without_qiskit_convention = { + key[::-1]: value for key, value in counts.items()} + + return counts_without_qiskit_convention + +if __name__ == '__main__': + # Example of usage + from general_utils import generate_random_board + + num_moves = 5 + board = generate_random_board(num_moves) + # print(board) + qc_init = setting_initial_configuration(board) + print(qc_init) + + # Oracle + print(oracle()) + # print(diffuser(board)) diff --git a/challenges/openqaoa challenge/QuantumVoyagers/Image/image11.png b/challenges/openqaoa challenge/QuantumVoyagers/Image/image11.png new file mode 100644 index 0000000..067b0dd Binary files /dev/null and b/challenges/openqaoa challenge/QuantumVoyagers/Image/image11.png differ diff --git a/challenges/openqaoa challenge/QuantumVoyagers/challenge_openqaoa.ipynb b/challenges/openqaoa challenge/QuantumVoyagers/challenge_openqaoa.ipynb new file mode 100644 index 0000000..539eb3f --- /dev/null +++ b/challenges/openqaoa challenge/QuantumVoyagers/challenge_openqaoa.ipynb @@ -0,0 +1,1739 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "UXfAFmJAu1zx" + }, + "source": [ + "# Challenge: OpenQAOA\n", + "\n", + "Quantum computing is used extensively for modelling and solving combinatorial optimisation problems. The purpose of this is to find a problem with binary clauses where the amount of states is immense and difficult to solve with classical resources. This type of problem is known as NP-hard. in order to uncover the correct answers, quantum computing produces algorithms of NP-complexity. On the other hand, in quantum computing, we are interested in representing such a model in a quantum circuit and being able to find the optimal states that satisfy the cost function using a classical optimizer.\n", + "\n", + "Multiple companies work around computers and generate an SDK that can generate quantum circuits, in this challenge, we focus on a fundamental step of the Quantum Approximate Optimization Algorithm (QAOA) algorithm. Before starting the quantum part, one must model a problem in terms of 0 and 1 and convert it into a Quadratic unconstrained binary optimization (QUBO) form that can then be converted into an Ising model to find the optimal states. To validate the model one makes use of OpenQAOA, an SDK focused on circuitry of the QAOA algorithm.\n", + "\n", + "If you want to know more about this SDK you can check the following link https://openqaoa.entropicalabs.com/\n", + "\n", + "**NOTES**:\n", + ">\n", + "> * To run on real QPU or simulators you can use [qbraid](https://account.qbraid.com/)\n", + ">\n", + "> * The [OpenQAOA workflow](https://openqaoa.entropicalabs.com/workflows/customise-the-QAOA-workflow/#the-circuit-properties)\n", + ">\n", + "> * To guide you, you can check out [examples of problems in OpenQAOA](https://github.com/entropicalabs/openqaoa/tree/main/examples/community_tutorials)" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 1000 + }, + "id": "wYvBlJm1vCLU", + "outputId": "5e9ae279-b6dc-4e3f-b5bb-0ed047f1c4a8" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Collecting 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collected packages: ply, websockets, typing-extensions, symengine, rustworkx, python-markdown-math, pyqir, py, portalocker, pbr, ntlm-auth, isodate, dill, deprecated, decorator, caio, stevedore, retry, azure-core, aiofile, requests-ntlm, qiskit-terra, msrest, azure-storage-blob, qiskit-ionq, qiskit-ibmq-provider, qiskit-aer, msal, qiskit, msal-extensions, qiskit-qir, azure-identity, azure-quantum\n", + " Attempting uninstall: typing-extensions\n", + " Found existing installation: typing_extensions 4.5.0\n", + " Uninstalling typing_extensions-4.5.0:\n", + " Successfully uninstalled typing_extensions-4.5.0\n", + " Attempting uninstall: decorator\n", + " Found existing installation: decorator 4.4.2\n", + " Uninstalling decorator-4.4.2:\n", + " Successfully uninstalled decorator-4.4.2\n", + "\u001b[31mERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.\n", + "ipython 7.34.0 requires jedi>=0.16, which is not installed.\n", + "moviepy 1.0.3 requires decorator<5.0,>=4.0.2, but you have decorator 5.1.1 which is incompatible.\n", + "tensorflow-probability 0.22.0 requires typing-extensions<4.6.0, but you have typing-extensions 4.8.0 which is incompatible.\u001b[0m\u001b[31m\n", + "\u001b[0mSuccessfully installed aiofile-3.8.8 azure-core-1.29.5 azure-identity-1.15.0 azure-quantum-0.28.302812 azure-storage-blob-12.19.0 caio-0.9.13 decorator-5.1.1 deprecated-1.2.14 dill-0.3.7 isodate-0.6.1 msal-1.25.0 msal-extensions-1.0.0 msrest-0.7.1 ntlm-auth-1.5.0 pbr-6.0.0 ply-3.11 portalocker-2.8.2 py-1.11.0 pyqir-0.8.0 python-markdown-math-0.8 qiskit-0.43.3 qiskit-aer-0.12.2 qiskit-ibmq-provider-0.20.2 qiskit-ionq-0.4.4 qiskit-qir-0.3.1 qiskit-terra-0.24.2 requests-ntlm-1.1.0 retry-0.9.2 rustworkx-0.13.2 stevedore-5.1.0 symengine-0.9.2 typing-extensions-4.8.0 websockets-12.0\n" + ] + }, + { + "data": { + "application/vnd.colab-display-data+json": { + "pip_warning": { + "packages": [ + "decorator" + ] + } + } + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Requirement already satisfied: qiskit in /usr/local/lib/python3.10/dist-packages (0.43.3)\n", + "Requirement already satisfied: qiskit-terra==0.24.2 in /usr/local/lib/python3.10/dist-packages (from qiskit) (0.24.2)\n", + "Requirement already satisfied: qiskit-aer==0.12.2 in /usr/local/lib/python3.10/dist-packages (from qiskit) (0.12.2)\n", + "Requirement already satisfied: qiskit-ibmq-provider==0.20.2 in /usr/local/lib/python3.10/dist-packages (from qiskit) (0.20.2)\n", + "Requirement already satisfied: numpy>=1.16.3 in /usr/local/lib/python3.10/dist-packages (from qiskit-aer==0.12.2->qiskit) (1.23.5)\n", + "Requirement already satisfied: scipy>=1.0 in /usr/local/lib/python3.10/dist-packages (from qiskit-aer==0.12.2->qiskit) (1.11.3)\n", 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ipython-7.34.0\n", + "\u001b[31mERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.\n", + "google-colab 1.0.0 requires ipython==7.34.0, but you have ipython 8.17.2 which is incompatible.\u001b[0m\u001b[31m\n", + "\u001b[0mSuccessfully installed asttokens-2.4.1 autoray-0.6.7 executing-2.0.1 ipython-8.17.2 jedi-0.19.1 openqaoa-core-0.2.3 openqaoa-qiskit-0.2.3 pure-eval-0.2.2 qiskit-0.45.0 qiskit-ibm-provider-0.7.2 qiskit-terra-0.45.0 semantic-version-2.10.0 stack-data-0.6.3\n" + ] + }, + { + "data": { + "application/vnd.colab-display-data+json": { + "pip_warning": { + "packages": [ + "IPython" + ] + } + } + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "!pip install docplex\n", + "!pip install h5py\n", + "!pip install typing-extensions\n", + "!pip install wheel\n", + "!pip install --upgrade azure-quantum\\[qiskit\\]\n", + "!pip install qiskit\n", + "!pip install cplex\n", + "!pip install openqaoa-qiskit" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "nxUZikB1u1z1" + }, + "source": [ + "# Problem to solve\n", + "\n", + "Find a real-world problem that can benefit from the application of combinatorial optimization. Consult the list of [OpenQAOA](https://openqaoa.entropicalabs.com/) problem classes to find references.\n", + "\n", + "Your solution's innovativeness will be rewarded with extra points.\n", + "\n", + "The process is the following\n", + "\n", + "![wf.png](attachment:wf.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Kxt5UK1pu1z1" + }, + "source": [ + "## Part 1: Define your problem and solve it using QAOA\n", + "Considering the examples based on OpenQAOA, we already have different classes and methods that facilitate the construction of quantum circuits, but to generate a QUBO we will rely on docplex.\n", + "\n", + "You can find more information on QAOA [examples](https://github.com/entropicalabs/openqaoa/tree/main/examples) and how to generate [QUBOs](https://openqaoa.entropicalabs.com/problems/what-is-a-qubo/) in the [OpenQAOA documentation](https://openqaoa.entropicalabs.com/). The code is available on [GitHub](https://github.com/entropicalabs/openqaoa/tree/main) and you can find more details of implementation in the [API reference](https://el-openqaoa.readthedocs.io/en/main/index.html)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1) Tic Tac Toe Game\n", + "This problem can be solved by treating each cell as a variable, and our objective function aims to maximize the number of winning moves. For instance, if we want to address the following problem:\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "

\n", + "\"JuveYell\"\n", + "

\n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So, for x_0, we observe it has 2 winning possibilities. On the other hand, x_1 has only one, x_2 has only one too, x_3 has 0 winning possibilities, and x_4 has only 1 winning option. Therefore, our objective function is formulated as follows:\n", + "$$f_1(\\textbf{x}) = 2*x_0 + 1*x_1 + 1*x_2 + 0*x_3 + 1*x_4$$\n", + "\n", + "This objective function is subject to an equality constraint, as when the game starts with 0's, there should be a total of 4 X's played. This forms our constraint, but in this case, given an initial configuration, we subtract 2 X's:\n", + "\n", + "$$x_0 + x_1 + x_2 + x_3 + x_4= 2$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "id": "PTkbAZxDu1z2" + }, + "outputs": [], + "source": [ + "%matplotlib notebook\n", + "\n", + "# Import external libraries to present an manipulate the data\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import pandas as pd\n", + "\n", + "# Import docplex model to generate the problem to optimize\n", + "from docplex.mp.model import Model\n", + "\n", + "# Import the libraries needed to employ the QAOA quantum algorithm using OpenQAOA\n", + "from openqaoa import QAOA\n", + "\n", + "# method to covnert a docplex model to a qubo problem\n", + "from openqaoa.problems.converters import FromDocplex2IsingModel #check this method and properties\n", + "from openqaoa.backends import create_device\n", + "\n", + "# method to find the correct states for the QAOA object\n", + "from openqaoa.utilities import ground_state_hamiltonian" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "id": "DbPRjxw3u1z4" + }, + "outputs": [], + "source": [ + "# inputs\n", + "\n", + "\n", + "def Problem():\n", + " # initialize a model\n", + " mdl = Model(\"Tic_Tac_Toe_Problem_using_maximize\")\n", + " # indicate the binary variables\n", + " n_vars = 5\n", + "\n", + " # Using binary variables for this model\n", + " x = mdl.binary_var_list(n_vars, name=\"x\")\n", + " # define the objective function\n", + " obj_func = 2*x[0] + x[1] + 1*x[2] + 0*x[3] + 1*x[4]\n", + " mdl.maximize(obj_func)\n", + " # add the constraints\n", + " mdl.add_constraint(x[0] + x[1] + x[2] + x[3] + x[4] == 2)\n", + " #qubo = FromDocplex2IsingModel(mdl)\n", + " return mdl#return model, check FromDocplex2IsingModel" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "i34LQrzbu1z5", + "outputId": "a79c2515-b188-4c4b-ab17-7409b6eca188" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "// This file has been generated by DOcplex\n", + "// model name is: Tic_Tac_Toe_Problem_using_maximize\n", + "// var contrainer section\n", + "dvar bool x[5];\n", + "\n", + "// single vars section\n", + "dvar bool x_0;\n", + "dvar bool x_1;\n", + "dvar bool x_2;\n", + "dvar bool x_3;\n", + "dvar bool x_4;\n", + "\n", + "minimize\n", + " - 26 x_0 - 25 x_1 - 25 x_2 - 24 x_3 - 25 x_4 [ 6 x_0^2 + 12 x_0*x_1\n", + " + 12 x_0*x_2 + 12 x_0*x_3 + 12 x_0*x_4 + 6 x_1^2 + 12 x_1*x_2 + 12 x_1*x_3\n", + " + 12 x_1*x_4 + 6 x_2^2 + 12 x_2*x_3 + 12 x_2*x_4 + 6 x_3^2 + 12 x_3*x_4\n", + " + 6 x_4^2 ] + 24;\n", + " \n", + "subject to {\n", + "\n", + "}\n" + ] + } + ], + "source": [ + "problem = Problem()\n", + "qubo = FromDocplex2IsingModel(problem)\n", + "\n", + "# Ising encoding of the QUBO problem for binpacking problem\n", + "ising_encoding = qubo.ising_model\n", + "\n", + "# Docplex encoding of the QUBO problem for binpacking problem\n", + "mdl_qubo_docplex = qubo.qubo_docplex\n", + "\n", + "mdl_qubo_docplex.prettyprint()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 363 + }, + "id": "5xBd6VY7u1z6", + "outputId": "7bca826e-429b-44e6-d509-59f0c0691a00" + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "
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solutions_bitstringsbitstrings_energiesprobabilities
010001-3.00.087510
111000-3.00.087510
210100-3.00.087510
310010-2.00.156561
401001-2.00.020661
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solutions_bitstringsbitstrings_energiesprobabilities
010001-3.00.05
110100-3.00.05
211000-3.00.20
310010-2.00.10
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If you want to know more about OpenQAOA or ask them questions directly, check out their [discord channel](discord.gg/ana76wkKBd).\n", + "\n", + "🎉🎉🎉" + ] + } + ], + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "display_name": "mitiq-qaoa", + "language": "python", + "name": "mitiq-qaoa" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.8" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/hackathon/QuantumVoyagers/Q_BattleShip_2.ipynb b/hackathon/QuantumVoyagers/Q_BattleShip_2.ipynb new file mode 100644 index 0000000..bdd0071 --- /dev/null +++ b/hackathon/QuantumVoyagers/Q_BattleShip_2.ipynb @@ -0,0 +1,789 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "## Código" + ], + "metadata": { + "id": "YooIMoDE5cp1" + }, + "id": "YooIMoDE5cp1" + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "FyCBkHkDom6j", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "2f16b82c-e091-4e08-99f3-d5721a14a3a5" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m6.3/6.3 MB\u001b[0m \u001b[31m39.2 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m2.0/2.0 MB\u001b[0m \u001b[31m76.0 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m49.6/49.6 kB\u001b[0m \u001b[31m4.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m115.3/115.3 kB\u001b[0m \u001b[31m11.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K 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"!pip install pylatexenc --quiet\n", + "!pip install -U qiskit-aer --quiet" + ], + "id": "Yv2p1wdao9Xv" + }, + { + "cell_type": "markdown", + "source": [ + "Importación de paquetes" + ], + "metadata": { + "id": "lqVHgBZg5b2Q" + }, + "id": "lqVHgBZg5b2Q" + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "a56a63b5" + }, + "outputs": [], + "source": [ + "from qiskit import *\n", + "from qiskit.visualization import plot_histogram\n", + "\n", + "from qiskit.quantum_info import Statevector\n", + "from qiskit.visualization import array_to_latex, plot_bloch_multivector\n", + "from qiskit.extensions import UnitaryGate\n", + "\n", + "from qiskit.providers.aer import AerSimulator\n", + "from qiskit.providers.fake_provider import FakeYorktown\n", + "\n", + "from qiskit import execute, Aer\n", + "\n", + "from qiskit import transpile" + ], + "id": "a56a63b5" + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "L8vacay5pz_-" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import math\n", + "import matplotlib.pyplot as plt\n", + "\n", + "import getpass\n", + "\n", + "import random\n", + "import re" + ], + "id": "L8vacay5pz_-" + }, + { + "cell_type": "markdown", + "source": [ + "Declaración de variables iniciales" + ], + "metadata": { + "id": "J8EA8Quj7QSe" + }, + "id": "J8EA8Quj7QSe" + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "DyuWyqKo7Blv" + }, + "outputs": [], + "source": [ + "n = 4\n", + "tablero1 = np.empty([n, n], dtype=\"