QuantumSimSudokuSolver.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# QuantumSim - 2 x 2 Sudoku Solver\n",
    "Author: Nico Kuijpers<br>\n",
    "Date: January 3, 2025\n",
    "\n",
    "In this notebook we use Grover's search algorithm to solve a $2 \\times 2$ Sudoku puzzle with and without known values.\n",
    "\n",
    "The notebook is based on the following notebook and blog post, but uses QuantumSim instead of Qiskit:\n",
    "\n",
    "https://github.com/Qiskit/textbook/blob/main/notebooks/ch-algorithms/grover.ipynb\n",
    "\n",
    "https://blog.theodo.com/2022/10/quantum-sudoku/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from quantumsim import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assume a $2 \\times 2$ by Sudoku puzzle. Four values have to be filled in, let's call them $v_0$, $v_1$, $v_2$, and $v_3$.\n",
    "\n",
    "|  $v_0$  |  $v_1$  | \n",
    "|---------|---------|\n",
    "|  $v_2$  |  $v_3$  | \n",
    "\n",
    "Since it is a $2 \\times 2$ Sudoku puzzle, the only values allowed are $0$ and $1$.\n",
    "\n",
    "A correct solution satisfies the following constraints:\n",
    "1. $v_0 \\neq v_1$\n",
    "2. $v_0 \\neq v_2$\n",
    "3. $v_1 \\neq v_3$\n",
    "4. $v_2 \\neq v_3$\n",
    "\n",
    "These constraints are coded in the *clause_list* below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Constraints for a 2 x 2 Sudoku puzzle\n",
    "clause_list = [[0,1],\n",
    "               [0,2],\n",
    "               [1,3],\n",
    "               [2,3]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To check these constraints, an exclusive OR (XOR) gate is used. \n",
    "The XOR operation of two binary values $A$ and $B$ is denoted by $A \\oplus B$ and\n",
    "is defined by the following truth table\n",
    "\n",
    "| $A$ | $B$ | $A \\oplus B$ |\n",
    "|:---:|:---:|:------------:|\n",
    "|  0  |  0  |       0      |\n",
    "|  0  |  1  |       1      |\n",
    "|  1  |  0  |       1      |\n",
    "|  1  |  1  |       0      |\n",
    "\n",
    "Thus $A \\oplus B = 1$ if and only if $A \\neq B$. \n",
    "\n",
    "In quantum computing, a XOR gate can be realized by two CNOT gates with control qubits $a$ and $b$ and target qubit the output qubit.\n",
    "\n",
    "Below a function *XOR* is defined which extends a quantum circuit with an XOR operation. Qubits $a$ and $b$ are input qubits and\n",
    "$c$ is the output qubit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def XOR(circuit:Circuit, a:int, b:int, c:int):\n",
    "    circuit.cnot(a, c)\n",
    "    circuit.cnot(b, c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the clause list and the XOR operation, an oracle can be created for the $2 \\times 2$ Sudoku puzzle. \n",
    "The first $4$ qubits represent $v_0$, $v_1$, $v_2$, and $v_3$ and are called *value_qubits*. \n",
    "The next $4$ qubits will be used to check the constraints and are called *clause_qubits*.\n",
    "An extra qubit is added which will be in state $|1\\rangle$ when the solution is valid. This qubit is called the *output* qubit.\n",
    "\n",
    "The oracle is constructed as follows:\n",
    "\n",
    "1. Determine the number of qubits and create a circuit.\n",
    "2. For each clause in the *clause_list* add an XOR operation with the value qubits as input and the respective clause qubit as output.\n",
    "3. Apply a multi-controlled Pauli X operation with all clause qubits as control and the *output* qubit as target.\n",
    "4. Repeat step 2 to reset the clause qubits.\n",
    "\n",
    "Below a function is defined to create a Sudoku oracle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_sudoku_oracle(clause_list:list[int,int], nr_value_qubits:int) -> Circuit:\n",
    "\n",
    "    # Determine the number of qubits and create a circuit\n",
    "    nr_clause_qubits = len(clause_list)\n",
    "    nr_qubits = nr_value_qubits + nr_clause_qubits + 1\n",
    "    circuit = Circuit(nr_qubits)\n",
    "\n",
    "    # Set the values for the clause qubits\n",
    "    q = nr_value_qubits\n",
    "    for clause in clause_list:\n",
    "        XOR(circuit, clause[0], clause[1], q)\n",
    "        q = q + 1\n",
    "\n",
    "    # Flip 'output' qubit if all clauses are satisfied\n",
    "    clause_circuit = Circuit(nr_clause_qubits + 1)\n",
    "    clause_circuit.multi_controlled_pauli_x()\n",
    "    circuit.append_circuit_general(clause_circuit, nr_value_qubits)\n",
    "\n",
    "    # Reset the clause qubits\n",
    "    q = nr_value_qubits\n",
    "    for clause in clause_list:\n",
    "        XOR(circuit, clause[0], clause[1], q)\n",
    "        q = q + 1\n",
    "    \n",
    "    return circuit\n",
    "   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next step is to constuct a diffusion operator, or *diffuser*. The diffuser acts on the value qubits only. \n",
    "For the $2 \\times 2$ Sudoku solver, it is taken into account that some of the values $v_0$, $v_1$, $v_2$, and $v_3$ may be known.\n",
    "\n",
    "For an explanation of the role of the diffuser in Grover's algorithm, we refer to this Qiskit notebook:\n",
    "\n",
    "https://github.com/Qiskit/textbook/blob/main/notebooks/ch-algorithms/grover.ipynb\n",
    "\n",
    "For an intuitive explanation of a diffuser which takes the known values into account, \n",
    "we refer to this blog by Ivan Popkov:\n",
    "\n",
    "https://blog.theodo.com/2022/10/quantum-sudoku/\n",
    "\n",
    "Below a function is described to create a diffuser to solve a $2 \\times 2$ Sudoku puzzle. Input parameters are the number of value qubits\n",
    "*nr_value_qubits* and a list of qubits for which the values have to be filled in, the *unknown_qubits*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_diffuser(nr_value_qubits:int, unknown_qubits:list[int]) -> Circuit:\n",
    "\n",
    "    # Create a circuit for the diffuser\n",
    "    circuit = Circuit(nr_value_qubits)\n",
    "\n",
    "    # Apply transformation |s> -> |00..0> (using H-gates)\n",
    "    for q in unknown_qubits:\n",
    "        circuit.hadamard(q)\n",
    "\n",
    "    # Apply transformation |00..0> -> |11..1> (using X-gates)\n",
    "    for q in unknown_qubits:\n",
    "        circuit.pauli_x(q)\n",
    "\n",
    "    # Apply a multi-controlled Z gate (using H-gates and a Toffoli gate)\n",
    "    controls = [q for q in range(nr_value_qubits-1) if q in unknown_qubits]\n",
    "    target = nr_value_qubits - 1\n",
    "    circuit.hadamard(target)\n",
    "    circuit.generic_toffoli(controls, target)\n",
    "    circuit.hadamard(target)\n",
    "\n",
    "    # Apply transformation |11..1> -> |00..0> (using X-gates)\n",
    "    for q in unknown_qubits:\n",
    "        circuit.pauli_x(q)\n",
    "\n",
    "    # Apply transformation |00..0> -> |s> (using H-gates)\n",
    "    for q in unknown_qubits:\n",
    "        circuit.hadamard(q)\n",
    "\n",
    "    return circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, a function is defined to create the Grover circuit. This function has as input parameters *clause_list*, *known_values*, *nr_values*, and *nr_iterations*.\n",
    "Parameter *known_values* is a dictionary with entry numbers ($0$, $1$, $2$ or $3$) as key and the known value ($0$ or $1$) as value. \n",
    "Parameter *nr_iterations* determines how many times the oracle and the diffuser are repeated in the Grover circuit.\n",
    "\n",
    "Using Hadamard gates, the unknown value qubits (*unknown_qubits*) are brought into superposition. \n",
    "The known value qubits (*known_qubits*) are brought into states $|0\\rangle$ or $|1\\rangle$\n",
    "depending on the values in the *known_values* dictionary.\n",
    "The clause qubits have initial state $|0\\rangle$.\n",
    "\n",
    "Below a function is defined to create a Grover circuit to solve a $2 \\times $ Sudoku puzzle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_grover_circuit(clause_list:list[int,int], known_values:dict, nr_values:int, nr_iterations:int) -> Circuit:\n",
    "    \n",
    "    # List of qubits for which values are already known\n",
    "    known_qubits = list(known_values.keys())\n",
    "    \n",
    "    # List of qubits for which values will be be calculated\n",
    "    unknown_qubits = [q for q in range(nr_values) if q not in known_qubits]\n",
    "\n",
    "    # Create the Sudoku oracle for the 2 x 2 Sudoku puzzle\n",
    "    sudoku_oracle = create_sudoku_oracle(clause_list, nr_values)\n",
    "\n",
    "    # Create the Grover circuit with same number of qubits\n",
    "    circuit = Circuit(sudoku_oracle.N)\n",
    "\n",
    "    # Initialize the output qubit in state |->\n",
    "    output_qubit = nr_values + len(clause_list)\n",
    "    circuit.pauli_x(output_qubit)\n",
    "    circuit.hadamard(output_qubit)\n",
    "\n",
    "    # Initialize the value qubits\n",
    "    for q in range(nr_values):\n",
    "        if q in known_qubits:\n",
    "            # Qubits are in the |0> state by default\n",
    "            # If the value of the known qubit is 1, the state is \n",
    "            # changed to |1> by applying a Pauli X gate\n",
    "            if known_values[q] == 1:\n",
    "                circuit.pauli_x(q)\n",
    "        if q in unknown_qubits:\n",
    "            # Unknown qubits are initialized in the |+> state with a Hadamard gate\n",
    "            circuit.hadamard(q)    \n",
    "        \n",
    "    # Create the diffuser\n",
    "    diffuser = create_diffuser(nr_values, unknown_qubits)\n",
    "\n",
    "    # Add the Sudoku oracle and diffuser nr_iterations times\n",
    "    for i in range(nr_iterations):\n",
    "        # Apply the Sudoku oracle\n",
    "        circuit.append_circuit(sudoku_oracle)\n",
    "\n",
    "        # Apply the diffuser\n",
    "        circuit.append_circuit_general(diffuser, 0)\n",
    "\n",
    "    # Bring the output qubit to one of the basis states |0> or |1>\n",
    "    circuit.hadamard(output_qubit)\n",
    "\n",
    "    return circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, a Grover circuit with no known qubits is created. In this case, two solutions are possible:\n",
    "\n",
    "|  $v_0 = 0$  |  $v_1 = 1$  | \n",
    "|-------------|-------------|\n",
    "|  $v_2 = 1$  |  $v_3 = 0$  | \n",
    "\n",
    "and\n",
    "\n",
    "|  $v_0 = 1$  |  $v_1 = 0$  | \n",
    "|-------------|-------------|\n",
    "|  $v_2 = 0$  |  $v_3 = 1$  |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nr_values = 4\n",
    "nr_iterations = 2\n",
    "# Case 1: no known values => 2 possible solutions: 0110 and 1001\n",
    "known_values = {}\n",
    "circuit = create_grover_circuit(clause_list, known_values, nr_values, nr_iterations)\n",
    "result = QuantumUtil.measure_circuit(circuit, 10000)\n",
    "QuantumUtil.histogram_of_classical_states(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two most occurring classical states are $|011000001\\rangle$ and $|100100001\\rangle$. \n",
    "Indeed, these states represent the two possible solutions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, a function is defined to print the solutions found by the Grover circuit. \n",
    "It is assumed that all classical states occurring more than $1000$ times are valid solutions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import Counter\n",
    "\n",
    "def print_solutions(result:list[str]):\n",
    "    counts = Counter(result)\n",
    "    frequent_strings = [string for string, count in counts.items() if count > 1000]\n",
    "    print(\"Solutions found:\")\n",
    "    for string in frequent_strings:\n",
    "        solution = string[1:5]\n",
    "        print(\"\")\n",
    "        print(\"---------\")\n",
    "        print(f\"| {solution[0]} | {solution[1]} |\")\n",
    "        print(\"---------\")\n",
    "        print(f\"| {solution[2]} | {solution[3]} |\")\n",
    "        print(\"---------\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solutions found:\n",
      "\n",
      "---------\n",
      "| 0 | 1 |\n",
      "---------\n",
      "| 1 | 0 |\n",
      "---------\n",
      "\n",
      "---------\n",
      "| 1 | 0 |\n",
      "---------\n",
      "| 0 | 1 |\n",
      "---------\n"
     ]
    }
   ],
   "source": [
    "print_solutions(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, a function is defined to create, execute and measure a Grover circuit for given known values. A histogram of measurements is created and the solutions are printed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_solutions(known_values:dict):\n",
    "    circuit = create_grover_circuit(clause_list, known_values, nr_values=4, nr_iterations=2)\n",
    "    result = QuantumUtil.measure_circuit(circuit, 10000)\n",
    "    QuantumUtil.histogram_of_classical_states(result)\n",
    "    print_solutions(result)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's make $v_0$ known to be $0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solutions found:\n",
      "\n",
      "---------\n",
      "| 0 | 1 |\n",
      "---------\n",
      "| 1 | 0 |\n",
      "---------\n"
     ]
    }
   ],
   "source": [
    "known_values = {0:0}\n",
    "find_solutions(known_values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's make $v_3$ known to be $1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solutions found:\n",
      "\n",
      "---------\n",
      "| 1 | 0 |\n",
      "---------\n",
      "| 0 | 1 |\n",
      "---------\n"
     ]
    }
   ],
   "source": [
    "known_values = {3:1}\n",
    "find_solutions(known_values)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}