7 - Programming a Quantum Search Algorithm (key).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "18e084c4",
   "metadata": {},
   "source": [
    "# Programming a Quantum Search Algorithm\n",
    "\n",
    "(Grover's Algorithm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a072850a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\n+-----------+\\n|00|01|10|11|\\n+-----------+\\n          xx\\n'"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's search a set of four numbers, looking for 'xx'. How do I find it?\n",
    "\n",
    "\"\"\"\n",
    "+-----------+\n",
    "|00|01|10|11|\n",
    "+-----------+\n",
    "          xx\n",
    "\"\"\"\n",
    "\n",
    "# Classically, this will take N=2 steps maximum. But the grover's algorithm takes sqrt(N)!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1376c6b",
   "metadata": {},
   "source": [
    "import the necessary libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "456936ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "#initialization\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import math\n",
    "\n",
    "# importing Qiskit\n",
    "from qiskit import IBMQ, Aer, transpile, execute\n",
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister\n",
    "from qiskit.providers.ibmq import least_busy\n",
    "\n",
    "# import basic plot tools\n",
    "from qiskit.visualization import plot_histogram\n",
    "\n",
    "def initialize_s(qc, qubits):\n",
    "    \"\"\"Apply a H-gate to 'qubits' in qc\"\"\"\n",
    "    for q in qubits:\n",
    "        qc.h(q)\n",
    "    return qc"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25dfd715",
   "metadata": {},
   "source": [
    "constructing the grover circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "d7a83e6b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# first, initialize the qbits\n",
    "n = 2\n",
    "grover_circuit = QuantumCircuit(n)\n",
    "grover_circuit = initialize_s(grover_circuit, [0,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e701d8c",
   "metadata": {},
   "source": [
    "build the oracle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "b6d2dd59",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐   \n",
       "q_0: ┤ H ├─■─\n",
       "     ├───┤ │ \n",
       "q_1: ┤ H ├─■─\n",
       "     └───┘   </pre>"
      ],
      "text/plain": [
       "     ┌───┐   \n",
       "q_0: ┤ H ├─■─\n",
       "     ├───┤ │ \n",
       "q_1: ┤ H ├─■─\n",
       "     └───┘   "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grover_circuit.cz(0,1)\n",
    "grover_circuit.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05771554",
   "metadata": {},
   "source": [
    "build the diffuser"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "abe109f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐   ┌───┐┌───┐   ┌───┐\n",
       "q_0: ┤ H ├─■─┤ H ├┤ Z ├─■─┤ H ├\n",
       "     ├───┤ │ ├───┤├───┤ │ ├───┤\n",
       "q_1: ┤ H ├─■─┤ H ├┤ Z ├─■─┤ H ├\n",
       "     └───┘   └───┘└───┘   └───┘</pre>"
      ],
      "text/plain": [
       "     ┌───┐   ┌───┐┌───┐   ┌───┐\n",
       "q_0: ┤ H ├─■─┤ H ├┤ Z ├─■─┤ H ├\n",
       "     ├───┤ │ ├───┤├───┤ │ ├───┤\n",
       "q_1: ┤ H ├─■─┤ H ├┤ Z ├─■─┤ H ├\n",
       "     └───┘   └───┘└───┘   └───┘"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grover_circuit.h([0,1])\n",
    "grover_circuit.z([0,1])\n",
    "grover_circuit.cz(0,1)\n",
    "grover_circuit.h([0,1])\n",
    "grover_circuit.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec2c7220",
   "metadata": {},
   "source": [
    "place a marker at 11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a89f7dca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\n",
       "|\\psi\\rangle =\n",
       "\\begin{bmatrix}\n",
       "0 & 0 & 0 & 1  \\\\\n",
       " \\end{bmatrix}\n",
       "$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sv_sim = Aer.get_backend('statevector_simulator')\n",
    "result = sv_sim.run(grover_circuit).result()\n",
    "statevec = result.get_statevector()\n",
    "from qiskit.visualization import array_to_latex\n",
    "array_to_latex(statevec, prefix=\"|\\\\psi\\\\rangle =\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "6f39c340",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grover_circuit.measure_all()\n",
    "\n",
    "qasm_sim = Aer.get_backend('qasm_simulator')\n",
    "result = qasm_sim.run(grover_circuit).result()\n",
    "counts = result.get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f7eed8b1",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}