diff --git a/challenges/QOSF challenge/challenge_qosf.ipynb b/challenges/QOSF challenge/challenge_qosf.ipynb new file mode 100644 index 0000000..5629c45 --- /dev/null +++ b/challenges/QOSF challenge/challenge_qosf.ipynb @@ -0,0 +1,494 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "id": "ACyKwaAoFvVD" + }, + "outputs": [], + "source": [ + "%%capture\n", + "!pip install qiskit\n", + "!pip install pylatexenc\n", + "!pip install qiskit-aer\n", + "!pip install qiskit_optimization" + ] + }, + { + "cell_type": "markdown", + "source": [ + "# Members / Integrantes\n", + "\n", + "- Edgar Mencia\n", + "- Axel Jamil León Arteaga\n", + "- Sergio Paulo Rubén Avila Concepción\n", + "\n", + "\n", + "Equipo8\n" + ], + "metadata": { + "id": "zumLARbllRT7" + } + }, + { + "cell_type": "markdown", + "source": [ + "# Propuesta de solución para el challenge de la QOSF" + ], + "metadata": { + "id": "uBUy92O-PDLT" + } + }, + { + "cell_type": "markdown", + "source": [ + "## Challenge / Desafio\n", + "English: For this problem you have the following situation: you are playing a game of tic-tac-toe, and you find the situation in the figure below, next is your turn, develop a quantum algorithm to be able to find the best decisions with higher probability.\n", + "\n", + "Español: Para este problema tienes la siguiente situación: estás jugando un juego de tres en línea (tatetí), y te encuentras con la situación en la figura a continuación, a continuación es tu turno, desarrolla un algoritmo cuántico para poder encontrar las mejores decisiones con mayor probabilidad.\n", + "\n", + "\n", + "
Gráfica de Alberto Maldonado
" + ], + "metadata": { + "id": "6lUxzwvXgb51" + } + }, + { + "cell_type": "code", + "source": [ + "tic_tac_toe_board = [\n", + " ['1', '2', '2'],\n", + " ['1', '0', '0'],\n", + " ['2', '0', '0']\n", + "]\n", + "\n", + "flattened_list = [item for row in tic_tac_toe_board for item in row]\n", + "print(flattened_list)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "3CYvYu-0h4oM", + "outputId": "945fdba5-c8ba-4286-c6c8-45f84cecd333" + }, + "execution_count": 2, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "['1', '2', '2', '1', '0', '0', '2', '0', '0']\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "\n", + "## Solution Proposal /Propuesta de solución\n", + "\n", + "English: Given the current situation and the challenges we face, the strategy does not focus on the rules of the game itself, but rather on identifying those variables that increase our chances of success within it. The goal is to discover specific states that, with a high probability, will lead us to victory. In this context, the decision was made to implement Grover's algorithm. This choice is due to its ability to efficiently search within a set of possible solutions, reducing the required time to approximately\n", + "$O(\\sqrt{N})$, which makes it considerably fast for this purpose.\n", + "\n", + "Español: Dada la situación presente y los retos que enfrentamos, la estrategia no se centra en las reglas del juego en sí, sino en identificar aquellas variables que aumenten nuestras chances de éxito dentro del mismo. El objetivo es descubrir estados específicos que, con alta probabilidad, nos conduzcan a la victoria. En este contexto, se optó por implementar el algoritmo de Grover. Esta elección se debe a su capacidad de realizar búsquedas dentro de un conjunto de posibles soluciones de manera eficiente, reduciendo el tiempo requerido a aproximadamente el $O(\\sqrt{N})$, lo que lo hace considerablemente rápido para este propósito.\n", + "\n", + "\n", + "A classic solution includes $O({N})$ / Una solución clasica incluye $O({N})$\n", + "```\n", + "def busqueda_lineal(arreglo, objetivo):\n", + "\n", + " for indice, elemento in enumerate(arreglo):\n", + " if elemento == objetivo:\n", + " return indice # Elemento encontrado, retorna la posición\n", + " return -1 # El elemento no está en el arreglo\n", + "\n", + "# Ejemplo de uso\n", + "arreglo = [3, 5, 2, 1, 4]\n", + "objetivo = 1\n", + "\n", + "# Llamada a la función\n", + "indice_objetivo = busqueda_lineal(arreglo, objetivo)\n", + "\n", + "if indice_objetivo != -1:\n", + " print(f\"Elemento encontrado en el índice {indice_objetivo}.\")\n", + "else:\n", + " print(\"Elemento no encontrado.\")\n", + "\n", + "```" + ], + "metadata": { + "id": "sGTdtbPemia3" + } + }, + { + "cell_type": "markdown", + "source": [ + "## Implementation / Implementación" + ], + "metadata": { + "id": "jI9INqYUzzaB" + } + }, + { + "cell_type": "code", + "source": [ + "from qiskit import QuantumCircuit\n", + "from qiskit import Aer\n", + "from qiskit import execute\n", + "from qiskit.visualization import plot_histogram\n", + "from qiskit.quantum_info import Statevector\n", + "from qiskit.circuit.library import C3XGate, C4XGate\n", + "\n", + "qubits = 10\n", + "qc = QuantumCircuit(qubits, 4) # 8 bits clásicos para las 8 posibles líneas de victoria\n", + "\n", + "# Qubits de Entrada\n", + "qc.x(0)\n", + "qc.x(3)\n", + "for i in [4, 5, 7, 8]:\n", + " qc.h(i)\n", + "qc.h(qubits-1)\n", + "qc.z(qubits-1)\n", + "qc.barrier()\n", + "qc.x(7)\n", + "qc.x(8)\n", + "qc.h(9)\n", + "\n", + "qc.append(C4XGate(), [4, 5, 7, 8, 9])\n", + "qc.x(7)\n", + "qc.x(8)\n", + "qc.h(9)\n", + "qc.barrier()\n", + "qc.x(5)\n", + "qc.x(7)\n", + "qc.h(9)\n", + "qc.append(C4XGate(), [4, 5, 7, 8, 9])\n", + "qc.x(5)\n", + "qc.x(7)\n", + "qc.h(9)\n", + "qc.barrier()\n", + "\n", + "for i in [4, 5, 7, 8]:\n", + " qc.h(i)\n", + "\n", + "for i in [4, 5, 7, 8]:\n", + " qc.x(i)\n", + "qc.h(8)\n", + "qc.append(C3XGate(), [4, 5, 7, 8])\n", + "qc.h(8)\n", + "for i in [4, 5, 7, 8]:\n", + " qc.x(i)\n", + "for i in [4, 5, 7, 8]:\n", + " qc.h(i)\n", + "qc.barrier()\n", + "\n", + "qc.measure(4, 0)\n", + "qc.measure(5, 1)\n", + "qc.measure(7, 2)\n", + "qc.measure(8, 3)\n", + "# Dibujar el circuito\n", + "qc.draw('mpl')\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 822 + }, + "id": "U8L2HkkkGrjp", + "outputId": "e3e4b50a-9b5e-4ffa-f17c-565596a97700" + }, + "execution_count": 3, + "outputs": [ + { + "output_type": "stream", + "name": "stderr", + "text": [ + "/usr/local/lib/python3.10/dist-packages/qiskit/visualization/circuit/matplotlib.py:266: FutureWarning: The default matplotlib drawer scheme will be changed to \"iqp\" in a following release. To silence this warning, specify the current default explicitly as style=\"clifford\", or the new default as style=\"iqp\".\n", + " self._style, def_font_ratio = load_style(self._style)\n" + ] + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "
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+ }, + "metadata": {}, + "execution_count": 3 + } + ] + }, + { + "cell_type": "code", + "source": [ + "simulator = Aer.get_backend('qasm_simulator')\n", + "job = execute(qc, simulator, shots=1000)\n", + "result = job.result()\n", + "counts = result.get_counts(qc)\n", + "plot_histogram(counts)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 483 + }, + "id": "g5UC_fwiHhNf", + "outputId": "817dcf34-69d5-4b1e-a844-08b68f38e0db" + }, + "execution_count": 4, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {}, + "execution_count": 4 + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "Explanation of the Circuit /Explicación del circuito.\n", + "\n", + "English: In the circuit, we have started with 10 qubits, 9 to represent the number of elements of the flattened vector. However, all those states that are already occupied are maintained only in those states; this is done to represent the complete state of the system and to explore its possible solutions. To optimize the number of qubits, a circuit should be built that includes only those available spaces. In this example, there are only 4. From there, the implementation of Grover's algorithm is applied. The first step is to put the empty states into a state of superposition. Subsequently, the oracle indicates the states that allow obtaining a winning solution, which in this case are the states |1001> and |1100>, which represent the sequence of the empty spaces.\n", + "\n", + "Español: En el circuito se ha comenzado con 10 qubits, 9 para representar la cantidad de elementos del vector aplanado. Sin embargo, todos aquellos estados que ya están ocupados se mantienen únicamente en dichos estados; esto se hace para representar el estado completo del sistema y explorar sus posibles soluciones. Para optimizar el número de qubits, se debería construir un circuito que incluya solamente aquellos espacios disponibles. En este ejemplo, son solo 4. A partir de ahí, se aplica la implementación del algoritmo de Grover. El primer paso es poner en estado de superposición los estados vacíos. Posteriormente, el oráculo señala los estados que permiten obtener una solución ganadora, que en este caso son los estados |1001> y |1100>, los cuales representan la secuencia de los espacios vacíos.\n", + "\n", + "```\n", + "['1', '2', '2', '1', '0', '0', '2', '0', '0']\n", + "# index of the empty spaces / índice de los espacios vacios\n", + "[4,5,7,8]\n", + "#translate those spaces into /traducir esos espacios en\n", + "[0,1,2,3]\n", + "#Which are the spaces that are the solution space that ranges from |0000> to |1111> / Que son los espacios que es el espacios de soluciones que va desde |0000> a |1111>\n", + "```\n", + "\n", + "English: As for the ancilla qubit, we use it as part of the implementation of Grover's algorithm to mark the states of interest.\n", + "\n", + "Español: En cuanto al qubit ancila, lo utilizamos como parte de la implementación del algoritmo de Grover para marcar los estados de interés." + ], + "metadata": { + "id": "8TLluAFFuzgt" + } + }, + { + "cell_type": "markdown", + "source": [ + "## Bonus" + ], + "metadata": { + "id": "KHoV12C90S3u" + } + }, + { + "cell_type": "markdown", + "source": [ + "## Challenges / Desafio\n", + "\n", + "English: What if we start one step earlier and your opponent has not chosen yet, as shown in the following image, it shows with higher probability the chances of you winning. Please refer to the above considerations.\n", + "\n", + "Español: Qué tal si comenzamos un paso antes y tu oponente aún no ha elegido, como se muestra en la siguiente imagen, esta muestra con mayor probabilidad las chances de que tú ganes. Por favor, ten en cuenta las consideraciones anteriores.\n", + "\n", + "\n" + ], + "metadata": { + "id": "lLUYlfWzRBJi" + } + }, + { + "cell_type": "code", + "source": [ + "tic_tac_toe_board = [\n", + " ['1', '2', '2'],\n", + " ['1', '0', '0'],\n", + " ['0', '0', '0']\n", + "]\n", + "\n", + "flattened_list = [item for row in tic_tac_toe_board for item in row]\n", + "print(flattened_list)" + ], + "metadata": { + "id": "i9S10x00RifE", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "6e62e722-14fc-45a0-84a0-e89e782648f2" + }, + "execution_count": 5, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "['1', '2', '2', '1', '0', '0', '0', '0', '0']\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "## Solution Proposal / Propuesta de solución\n", + "English: In the game of tic-tac-toe, the goal is to align three of your symbols, either circles or crosses, in a horizontal, vertical, or diagonal line. The first to achieve this wins the game. Currently, it is the opponent's turn. The strategy involves anticipating and countering their move, which will likely aim to prevent my victory. By analyzing the state of the game, it is foreseeable that the opponent's most obvious move would be to place their symbol in the third row, first column, thus blocking my potentially winning line\n", + "\n", + "Español: En el juego de tateti, también conocido tic-tac-toe, el objetivo es alinear tres de tus propias marcas, ya sean círculos o cruces, en una fila, columna o diagonal. Quien logra esto primero es el ganador. En la situación actual, le toca jugar a mi oponente. La estrategia a seguir implica anticipar y bloquear su jugada, la cual probablemente estará dirigida a obstaculizar mi posibilidad de ganar. Con base en el análisis del tablero, el movimiento más previsible para el oponente sería colocar su marca en la fila tres, columna uno, para interrumpir mi secuencia ganadora. A partir de su movimiento más previsible. Tengo dos jugadas ganadores explicadas ya en el circuito anterior." + ], + "metadata": { + "id": "9rpA9diJR6fU" + } + }, + { + "cell_type": "code", + "source": [ + "from qiskit import QuantumCircuit\n", + "from qiskit import Aer\n", + "from qiskit import execute\n", + "from qiskit.visualization import plot_histogram\n", + "from qiskit.quantum_info import Statevector\n", + "\n", + "from qiskit.circuit.library import MCXGate, C4XGate\n", + "\n", + "qubits = 10\n", + "qc = QuantumCircuit(qubits, 5) # 8 bits clásicos para las 8 posibles líneas de victoria\n", + "\n", + "# Qubits de Entrada\n", + "qc.x(0)\n", + "qc.x(3)\n", + "for i in [4, 5, 6 ,7, 8]:\n", + " qc.h(i)\n", + "qc.h(qubits-1)\n", + "qc.z(qubits-1)\n", + "qc.barrier()\n", + "\n", + "qc.x([4,5,7,8])\n", + "qc.h(9)\n", + "\n", + "\n", + "gate = MCXGate(5)\n", + "qc.append(gate, [4, 5, 6,7, 8, 9])\n", + "\n", + "qc.x([4,5,7,8])\n", + "qc.h(9)\n", + "\n", + "qc.barrier()\n", + "\n", + "for i in [4, 5, 6 ,7, 8]:\n", + " qc.h(i)\n", + "\n", + "for i in [4, 5, 6 ,7, 8]:\n", + " qc.x(i)\n", + "qc.h(8)\n", + "qc.append(C4XGate(), [4, 5, 6, 7, 8])\n", + "qc.h(8)\n", + "for i in [4, 5,6 ,7, 8]:\n", + " qc.x(i)\n", + "for i in [4, 5,6, 7, 8]:\n", + " qc.h(i)\n", + "qc.barrier()\n", + "\n", + "\n", + "\n", + "qc.measure(4, 0)\n", + "qc.measure(5, 1)\n", + "qc.measure(6, 2)\n", + "qc.measure(7, 3)\n", + "qc.measure(8, 4)\n", + "# Dibujar el circuito\n", + "qc.draw('mpl')\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 769 + }, + "id": "uDAnPhsg0R72", + "outputId": "abf1c3b6-8c9f-4c4d-e51f-7787cc497a7b" + }, + "execution_count": 6, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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+ }, + "metadata": {}, + "execution_count": 6 + } + ] + }, + { + "cell_type": "code", + "source": [ + "simulator = Aer.get_backend('qasm_simulator')\n", + "job = execute(qc, simulator, shots=1000)\n", + "result = job.result()\n", + "counts = result.get_counts(qc)\n", + "\n", + "plot_histogram(counts)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 501 + }, + "id": "secRfGgF18jd", + "outputId": "363577e2-84a7-4caf-9830-8b4abfc15cb3" + }, + "execution_count": 7, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {}, + "execution_count": 7 + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "#Conclusions on Tic-Tac-Toe and Grover's Algorithm / Conclusiones del tictatoe y el algoritmo de Grover\n", + "\n", + "English: It is a relevant solution, considering that Grover's algorithm operates in a manner similar to the mental analysis performed during the game. When analyzing moves, the player does not iteratively review the possibilities of victory. Instead, they take a glance at all available options and, from that point, emphasize those that are identified according to the pattern. It is possible that some alternatives might be overlooked during this analysis, but through a global analysis approach, they are able to draw conclusions; that is, they highlight those plays that make achieving their goal easier.\n", + "\n", + "Español: Es una solución pertinente, considerando que el algoritmo de Grover opera de manera análoga al análisis mental realizado durante el juego. Al analizar los movimientos, el jugador no revisa iterativamente las posibilidades de victoria. Más bien, observa de un solo vistazo todas las opciones disponibles y, desde ese punto, realza aquellas que identifica conforme al patrón. Puede que durante este análisis se le pase por alto alguna alternativa, pero mediante un enfoque de análisis global, es capaz de extraer conclusiones; es decir, resalta aquellas jugadas que le faciliten la consecución de su objetivo." + ], + "metadata": { + "id": "2RNgS5sSUZJG" + } + } + ] +} \ No newline at end of file