{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import modules\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Parameters\n",
    "N = 64\n",
    "steps = 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.015625 0.015625 0.015625 ... 0.015625 0.015625 0.015625]\n",
      " [0.015625 0.015625 0.015625 ... 0.015625 0.015625 0.015625]\n",
      " [0.015625 0.015625 0.015625 ... 0.015625 0.015625 0.015625]\n",
      " ...\n",
      " [0.015625 0.015625 0.015625 ... 0.015625 0.015625 0.015625]\n",
      " [0.015625 0.015625 0.015625 ... 0.015625 0.015625 0.015625]\n",
      " [0.015625 0.015625 0.015625 ... 0.015625 0.015625 0.015625]]\n"
     ]
    }
   ],
   "source": [
    "# Initial state\n",
    "psi = np.zeros((N,N))\n",
    "for i in range(N):\n",
    "    for j in range(N):\n",
    "        psi[i][j] = 1/np.sqrt(N*N)\n",
    "print(psi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Specify the marked vertex\n",
    "a = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create an array to store the probabilities.\n",
    "prob = np.zeros(steps+1)\n",
    "\n",
    "# Print the probability at the marked vertex\n",
    "prob[0] = np.sum(np.square(psi[a][:]));\n",
    "#print(0,\"\\t\",prob[0])\n",
    "\n",
    "for t in range(steps):\n",
    "    # Query the oracle.\n",
    "    for i in range(N):\n",
    "        psi[a][i] *= -1\n",
    "    \n",
    "    # Temporary variable.\n",
    "    tmp = np.zeros((N,N))\n",
    "\n",
    "    # Apply the Grover coin\n",
    "    for i in range(N):\n",
    "        # Calculate the average amplitude at this vertex.\n",
    "        avg = 0\n",
    "        for j in range(N):\n",
    "            avg += psi[i][j]\n",
    "        avg /= N\n",
    "    \n",
    "        # Invert each amplitude about this average.\n",
    "        for j in range(N):\n",
    "            tmp[i][j] = 2*avg - psi[i][j]\n",
    "    \n",
    "    # Flip-Flop Shift\n",
    "    for i in range(N):\n",
    "        for j in range(N):\n",
    "            psi[i][j] = tmp[j][i]\n",
    "            \n",
    "    # Print the probability at the marked vertex\n",
    "    prob[t+1] =  np.sum(np.square(psi[a][:]))\n",
    "    #print(t+1,\"\\t\",prob[t+1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f13dc453730>]"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(prob)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.9.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}