grovers.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Grover's Algorithm Implementation in Qiskit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import QuantumCircuit, Aer, execute\n",
    "from qiskit.visualization import plot_histogram\n",
    "from qiskit.quantum_info import Operator\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# First we define the Oracle for a specific example the solution is a particular bit string, say 101 for a\n",
    "# 3 qubit system\n",
    "\n",
    "def grover_oracle(n, solution):\n",
    "    # Create a quantum circuit\n",
    "    qc = QuantumCircuit(n)\n",
    "\n",
    "    # Apply X-gates to the qubits that correspond to '0' in the solution\n",
    "    for qubit in range(n):\n",
    "        if solution[qubit] == '0':\n",
    "            qc.x(qubit)\n",
    "\n",
    "    # Apply a multi-controlled Z-gate\n",
    "    qc.h(n-1)\n",
    "    qc.mct(list(range(n-1)), n-1)  # multi-controlled-toffoli\n",
    "    qc.h(n-1)\n",
    "\n",
    "    # Apply X-gates again\n",
    "    for qubit in range(n):\n",
    "        if solution[qubit] == '0':\n",
    "            qc.x(qubit)\n",
    "\n",
    "    # Convert to gate\n",
    "    oracle_gate = qc.to_gate()\n",
    "    oracle_gate.name = \"Oracle\"\n",
    "    return oracle_gate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Implementation for a diffuser to amplify the probability of the solution state\n",
    "\n",
    "def grover_diffuser(n):\n",
    "    qc = QuantumCircuit(n)\n",
    "    \n",
    "    # Apply transformation |s> -> |00..0> (H-gates)\n",
    "    qc.h(range(n))\n",
    "    \n",
    "    # Apply transformation |00..0> -> |11..1> (X-gates)\n",
    "    qc.x(range(n))\n",
    "    \n",
    "    # Do multi-controlled-Z gate\n",
    "    qc.h(n-1)\n",
    "    qc.mct(list(range(n-1)), n-1)  # multi-controlled-toffoli\n",
    "    qc.h(n-1)\n",
    "    \n",
    "    # Apply transformation |11..1> -> |00..0>\n",
    "    qc.x(range(n))\n",
    "    \n",
    "    # Apply transformation |00..0> -> |s>\n",
    "    qc.h(range(n))\n",
    "\n",
    "    # Convert to gate\n",
    "    diffuser_gate = qc.to_gate()\n",
    "    diffuser_gate.name = \"Diffuser\"\n",
    "    return diffuser_gate\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "81\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/zn/g_jfcp8s505gzx7nk3gggjnr0000gn/T/ipykernel_95022/1069033121.py:15: DeprecationWarning: The method ``qiskit.circuit.quantumcircuit.QuantumCircuit.mct()`` is deprecated as of qiskit 0.45.0. It will be removed no earlier than 3 months after the release date. Use QuantumCircuit.mcx as direct replacement.\n",
      "  qc.mct(list(range(n-1)), n-1)  # multi-controlled-toffoli\n",
      "/var/folders/zn/g_jfcp8s505gzx7nk3gggjnr0000gn/T/ipykernel_95022/3764361831.py:14: DeprecationWarning: The method ``qiskit.circuit.quantumcircuit.QuantumCircuit.mct()`` is deprecated as of qiskit 0.45.0. It will be removed no earlier than 3 months after the release date. Use QuantumCircuit.mcx as direct replacement.\n",
      "  qc.mct(list(range(n-1)), n-1)  # multi-controlled-toffoli\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x1575ad750>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Bringing the circuit together\n",
    "\n",
    "solution = '101101101101101101101101101101101101101101101101101101101101101101101101101101101'  # The solution string\n",
    "n = len(solution)  # Number of qubits\n",
    "print(n)\n",
    "qc = QuantumCircuit(n, n)\n",
    "\n",
    "# Apply Hadamard gates\n",
    "qc.h(range(n))\n",
    "\n",
    "# Add the oracle\n",
    "oracle_gate = grover_oracle(n, solution)\n",
    "qc.append(oracle_gate, range(n))\n",
    "\n",
    "# Add the diffuser\n",
    "diffuser_gate = grover_diffuser(n)\n",
    "qc.append(diffuser_gate, range(n))\n",
    "\n",
    "# Measure the qubits\n",
    "qc.measure(range(n), range(n))\n",
    "\n",
    "# qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Counts(ideal): {'000': 19, '010': 33, '110': 33, '100': 34, '001': 22, '111': 24, '011': 34, '101': 825}\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Running the circuit\n",
    "from qiskit_aer import AerSimulator\n",
    "\n",
    "# we will use Aer's qasm_simulator\n",
    "aersim = AerSimulator()\n",
    "\n",
    "# get the results and the counts and plot a histogram\n",
    "result_ideal = aersim.run(qc.decompose(), shots = 1024).result()\n",
    "counts_ideal = result_ideal.get_counts(0)\n",
    "print('Counts(ideal):', counts_ideal)\n",
    "\n",
    "plot_histogram(counts_ideal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Counts(noise): {'010': 20, '000': 33, '011': 32, '111': 45, '001': 67, '100': 131, '110': 37, '101': 659}\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.providers.fake_provider import FakeManilaV2\n",
    "\n",
    "# Construct a noisy simulator backend from an IBMQ backend\n",
    "# This simulator backend will be automatically configured\n",
    "# using the device configuration and noise model\n",
    "backend = FakeManilaV2()\n",
    "aersim_backend = AerSimulator.from_backend(backend)\n",
    "\n",
    "# Perform noisy simulation\n",
    "result_noise = aersim_backend.run(qc.decompose(), shots = 1024).result()\n",
    "counts_noise = result_noise.get_counts(0)\n",
    "\n",
    "print('Counts(noise):', counts_noise)\n",
    "\n",
    "plot_histogram(counts_noise)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Execution Time')"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot for scalability of circuit\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "num_qubits = [2, 10, 50, 80]\n",
    "exec_time = [0.0, 0.0, 1.1, 3.6]\n",
    "\n",
    "plt.scatter(num_qubits, exec_time)\n",
    "plt.xlabel(\"Number of Qubits\")\n",
    "plt.ylabel(\"Execution Time\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.11.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}