Visualization of Grovers quantum algorithm for unstructured search

Grover.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook visualizes an execution of Grover's algorithm for unstructured search on a quantum computer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Some imports\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "# The number of qubits involved\n",
    "n = 3\n",
    "# The size of the search space\n",
    "N = 2**n\n",
    "# The element we are looking for - this is chosen arbitrarily \n",
    "hit = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# \n",
    "# This function models the function P in Grover's algorithm. It is one if and only if the argument matches the \n",
    "# element we are looking for\n",
    "#\n",
    "def P(x):\n",
    "    if (x == hit):\n",
    "        return 1\n",
    "    return 0\n",
    "\n",
    "\n",
    "#\n",
    "# Given a superposition, modeled as an array of length N, this function returns a new array which\n",
    "# is the result of a conditional phase shift \n",
    "# \n",
    "def S(psi):\n",
    "    R = np.zeros(N)\n",
    "    for i in range(N):\n",
    "        if (P(i) == 1):\n",
    "            R[i] = - psi[i]\n",
    "        else:\n",
    "            R[i] = psi[i]\n",
    "    return R\n",
    "\n",
    "\n",
    "#\n",
    "# Given a superposition, modeled as an array of length N, this function returns a new array which\n",
    "# is the result of inversion around the average (the diffusion matrix D)\n",
    "# \n",
    "def D(psi):\n",
    "    return (2*np.mean(psi) - psi)\n",
    "\n",
    "#\n",
    "# Create the initial state which is the result of applying the Hadamard-Walsh transformation\n",
    "# to the zero state\n",
    "#\n",
    "def init():\n",
    "    return np.ones(N)*(1/np.sqrt(N))\n",
    "\n",
    "\n",
    "#\n",
    "# Given a state, modelled as an array of length N, and an axis, plot the state\n",
    "#\n",
    "def plot(ax, psi):\n",
    "    ax.bar(range(N),psi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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wjB6ITe4vJ6feFWuViHaBOM8feFr8ynteT7j96bJDl+WggGAAAAsBOcOPtSjtxxbSFYa2stP9AV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\nYRLtCn0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f99780910f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#\n",
    "# Parameters\n",
    "#\n",
    "plots = 3\n",
    "size = 1\n",
    "#\n",
    "# Create the initial state and plot it\n",
    "# \n",
    "psi = init()\n",
    "fig = plt.figure(figsize=(30,30))\n",
    "ax = fig.add_subplot(plots+2,1,1)\n",
    "ax.set_ylim(-size,size)\n",
    "plot(ax, psi)\n",
    "#\n",
    "# Now apply a number of iterations of the algorithm and plot the result\n",
    "#\n",
    "for i in range(plots):\n",
    "    psi = D(S(psi))\n",
    "    ax = fig.add_subplot(plots+2,1,i+2)\n",
    "    ax.set_ylim(-size,size)\n",
    "    plot(ax,psi)\n",
    "\n",
    "#\n",
    "# We now reset everything and run the algorithm for a few iterations. We measure the quality of the outcome by\n",
    "# comparing the absolute value of psi(hit) with the max across all other amplitudes and plot the resulting curve\n",
    "#\n",
    "psi = init()\n",
    "trials = 100\n",
    "X = np.zeros(trials)\n",
    "for i in range(trials):\n",
    "    psi = D(S(psi))\n",
    "    check = np.copy(psi)\n",
    "    check[hit] = 0\n",
    "    X[i] = abs(psi[hit]) / np.max(abs(check))\n",
    "ax = fig.add_subplot(plots+2,1,plots+2)\n",
    "ax.plot(range(trials),X)\n",
    "#\n",
    "# Show everything\n",
    "#\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}