4.d-Grover's Algorithm.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Grover's Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Useful additional packages\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from math import pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute\n",
    "from qiskit import Aer, IBMQ\n",
    "from qiskit.compiler import transpile, assemble\n",
    "from qiskit.visualization import *\n",
    "from qiskit.providers.aer import UnitarySimulator\n",
    "from qiskit.tools.visualization import circuit_drawer\n",
    "from qiskit.quantum_info import state_fidelity\n",
    "from qiskit import BasicAer\n",
    "\n",
    "\n",
    "backend = BasicAer.get_backend('unitary_simulator')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![img](img/ga.gif)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fundamental Gates used in Grover's Algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### H - Hadamard gate\n",
    "\n",
    "$$\n",
    "H = \n",
    "\\frac{1}{\\sqrt{2}}\n",
    "\\begin{pmatrix}\n",
    "1 & 1\\\\\n",
    "1 & -1\n",
    "\\end{pmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### $X$ -  Bit-flip gate\n",
    "\n",
    "$$\n",
    "X   =  \n",
    "\\begin{pmatrix}\n",
    "0 & 1\\\\\n",
    "1 & 0\n",
    "\\end{pmatrix}= u3(\\pi,0,\\pi)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####  $C_z$ - Controlled Phase gate\n",
    "\n",
    "$$\n",
    "C_Z = \n",
    "\\begin{pmatrix}\n",
    "1 & 0 & 0 & 0\\\\\n",
    "0 & 1 & 0 & 0\\\\\n",
    "0 & 0 & 1 & 0\\\\\n",
    "0 & 0 & 0 & -1\n",
    "\\end{pmatrix}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### $Z$: Phase-flip gate\n",
    "\n",
    "$$\n",
    "Z = \n",
    "\\begin{pmatrix}\n",
    "1 & 0\\\\\n",
    "0 & -1\n",
    "\\end{pmatrix}=u1(\\pi)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  1. Implementing Grover's Algorithm in two qubits database"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "qr = QuantumRegister(2)\n",
    "cr = ClassicalRegister(2)\n",
    "groverCircuit = QuantumCircuit(qr,cr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.1 Apply Hadamard gate to both qubit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 240.8x258.86 with 1 Axes>"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "groverCircuit.h(qr)\n",
    "groverCircuit.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.1.1. Matrix element "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- H operator in product space, $H_2 = H_1 \\otimes H_1$ :\n",
    "\n",
    "$\\frac{1}{\\sqrt{2}}\\begin{bmatrix}\n",
    "    1  &  1 \\\\\n",
    "    1  & -1\n",
    "\\end{bmatrix} \\otimes \\frac{1}{\\sqrt{2}}\\begin{bmatrix}\n",
    "    1  &  1 \\\\\n",
    "    1  & -1\n",
    "\\end{bmatrix} = \\frac{1}{2} \\begin{bmatrix}\n",
    "    1  &  1  &  1  &  1 \\\\\n",
    "    1  &  -1  &  1  &  -1 \\\\\n",
    "    1  &  1  &  -1  &  -1 \\\\\n",
    "    1  &  -1  &  -1  &  1 \\\\\n",
    "\\end{bmatrix}$\n",
    "\n",
    "- Basis States in product space, $|q_1q_2> = q_1 \\otimes q_2$ : \n",
    "\n",
    "|00> = $\\begin{bmatrix}\n",
    "    1  \\\\\n",
    "    0 \\\\\n",
    "    0\\\\\n",
    "    0\n",
    "\\end{bmatrix}$ ; |01> = $\\begin{bmatrix}\n",
    "    0\\\\\n",
    "    1\\\\\n",
    "    0\\\\\n",
    "    0\n",
    "\\end{bmatrix}$ ; |10> = $\\begin{bmatrix}\n",
    "    0  \\\\\n",
    "    0 \\\\\n",
    "    1\\\\\n",
    "    0\n",
    "\\end{bmatrix}$ ; |11> = $\\begin{bmatrix}\n",
    "    0\\\\\n",
    "    0\\\\\n",
    "    0\\\\\n",
    "    1\n",
    "\\end{bmatrix}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.5+0.j,  0.5+0.j,  0.5+0.j,  0.5+0.j],\n",
       "       [ 0.5+0.j, -0.5+0.j,  0.5+0.j, -0.5+0.j],\n",
       "       [ 0.5+0.j,  0.5+0.j, -0.5+0.j, -0.5+0.j],\n",
       "       [ 0.5+0.j, -0.5+0.j, -0.5+0.j,  0.5+0.j]])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "job = execute(groverCircuit, backend)\n",
    "job.result().get_unitary(groverCircuit, decimals=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.1.2. Manual approach\n",
    "\n",
    "---------\n",
    "- Initial state: |00>\n",
    "- After Hadamard Gate on first qubit: $\\frac{1}{\\sqrt{2}}|00> + \\frac{1}{\\sqrt{2}}|10>$\n",
    "- After Hadamard Gate on second qubit: $\\frac{1}{{2}}|00> + \\frac{1}{{2}}|01>  +  \\frac{1}{{2}}|10> + \\frac{1}{{2}}|11>$\n",
    "\n",
    "---------\n",
    "- This is tensor product of two Hedamard transform:\n",
    "$H|0>_A \\otimes H|0>_B$\n",
    "- i.e., $(\\frac{1}{\\sqrt{2}}|0> + \\frac{1}{\\sqrt{2}}|1>) \\otimes (\\frac{1}{\\sqrt{2}}|0> + \\frac{1}{\\sqrt{2}}|1>) = \\frac{1}{{2}}|00> + \\frac{1}{{2}}|01>  +  \\frac{1}{{2}}|10> + \\frac{1}{{2}}|11>$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.1.3 Measurement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 481.6x258.86 with 1 Axes>"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "groverCircuit.measure(qr,cr)\n",
    "groverCircuit.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "result = execute(groverCircuit, simulator).result()\n",
    "counts = result.get_counts(groverCircuit)\n",
    "plot_histogram(counts, title='Grover Intermediate measurement')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.2 Apply Oracle for $ w = |00>$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 421.4x258.86 with 1 Axes>"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qr = QuantumRegister(2)\n",
    "cr = ClassicalRegister(2)\n",
    "groverCircuit = QuantumCircuit(qr,cr)\n",
    "groverCircuit.h(qr)\n",
    "\n",
    "'''oracle w = |00>'''\n",
    "groverCircuit.x(qr)\n",
    "groverCircuit.cz(qr[0],qr[1])\n",
    "groverCircuit.x(qr)\n",
    "\n",
    "groverCircuit.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.2.1. Matrix element"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\n",
    "(X \\otimes X)   =  \n",
    "\\begin{pmatrix}\n",
    "0 & 1\\\\\n",
    "1 & 0\n",
    "\\end{pmatrix} \\otimes \\begin{pmatrix}\n",
    "0 & 1\\\\\n",
    "1 & 0\n",
    "\\end{pmatrix} = \\begin{pmatrix}\n",
    "0 & 0 & 0 & 1\\\\\n",
    "0 & 0 & 1 & 0\\\\\n",
    "0 & 1 & 0 & 0\\\\\n",
    "1 & 0 & 0 & 0\\\\\n",
    "\\end{pmatrix}\n",
    "$, $C_Z = \n",
    "\\begin{pmatrix}\n",
    "1 & 0 & 0 & 0\\\\\n",
    "0 & 1 & 0 & 0\\\\\n",
    "0 & 0 & 1 & 0\\\\\n",
    "0 & 0 & 0 & -1\n",
    "\\end{pmatrix}$\n",
    "\n",
    "------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### ORACLE\n",
    "$= (X \\otimes X) \\times C_z \\times (X \\otimes X)$\n",
    "\n",
    "$= \\begin{pmatrix}\n",
    "0 & 0 & 0 & 1\\\\\n",
    "0 & 0 & 1 & 0\\\\\n",
    "0 & 1 & 0 & 0\\\\\n",
    "1 & 0 & 0 & 0\\\\\n",
    "\\end{pmatrix}\n",
    "\\times\n",
    "\\begin{pmatrix}\n",
    "1 & 0 & 0 & 0\\\\\n",
    "0 & 1 & 0 & 0\\\\\n",
    "0 & 0 & 1 & 0\\\\\n",
    "0 & 0 & 0 & -1\n",
    "\\end{pmatrix}\n",
    "\\times \n",
    "\\begin{pmatrix}\n",
    "0 & 0 & 0 & 1\\\\\n",
    "0 & 0 & 1 & 0\\\\\n",
    "0 & 1 & 0 & 0\\\\\n",
    "1 & 0 & 0 & 0\\\\\n",
    "\\end{pmatrix}\n",
    "= \\begin{pmatrix}\n",
    "-1 & 0 & 0 & 0\\\\\n",
    "0 & 1 & 0 & 0\\\\\n",
    "0 & 0 & 1 & 0\\\\\n",
    "0 & 0 & 0 & 1\\\\\n",
    "\\end{pmatrix}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-----------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### CIRCUIT with ORCL and INIT\n",
    "\n",
    "$= ORCL \\times INIT $\n",
    "\n",
    "$= \n",
    "\\begin{pmatrix}\n",
    "-1 & 0 & 0 & 0\\\\\n",
    "0 & 1 & 0 & 0\\\\\n",
    "0 & 0 & 1 & 0\\\\\n",
    "0 & 0 & 0 & 1\\\\\n",
    "\\end{pmatrix}\n",
    "\\times\n",
    "\\frac{1}{2} \\begin{pmatrix}\n",
    "    1  &  1  &  1  &  1 \\\\\n",
    "    1  &  -1  &  1  &  -1 \\\\\n",
    "    1  &  1  &  -1  &  -1 \\\\\n",
    "    1  &  -1  &  -1  &  1 \\\\\n",
    "\\end{pmatrix}\n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.5+0.j, -0.5+0.j, -0.5+0.j, -0.5+0.j],\n",
       "       [ 0.5+0.j, -0.5+0.j,  0.5+0.j, -0.5+0.j],\n",
       "       [ 0.5+0.j,  0.5+0.j, -0.5+0.j, -0.5+0.j],\n",
       "       [ 0.5+0.j, -0.5+0.j, -0.5+0.j,  0.5+0.j]])"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "job = execute(groverCircuit, backend)\n",
    "job.result().get_unitary(groverCircuit, decimals=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1  0  0  0]\n",
      " [ 0  1  0  0]\n",
      " [ 0  0  1  0]\n",
      " [ 0  0  0  1]]\n"
     ]
    }
   ],
   "source": [
    "INIT = 0.5*np.array([[1,1,1,1],[1,-1,1,-1],[1,1,-1,-1],[1,-1,-1,1]])\n",
    "CZ = np.array([[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,-1]])\n",
    "XX = np.array([[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]])\n",
    "\n",
    "'''Oracle'''\n",
    "ORCL = np.dot(XX,np.dot(CZ,XX))\n",
    "print(ORCL)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.5, -0.5, -0.5, -0.5],\n",
       "       [ 0.5, -0.5,  0.5, -0.5],\n",
       "       [ 0.5,  0.5, -0.5, -0.5],\n",
       "       [ 0.5, -0.5, -0.5,  0.5]])"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'''FUll circuit matrix so far'''\n",
    "np.dot(ORCL,INIT)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.2.2 Manual Approach\n",
    "\n",
    "---------\n",
    "- Initial state: |00>\n",
    "- After Hadamard Gate on first qubit: $\\frac{1}{\\sqrt{2}}|00> + \\frac{1}{\\sqrt{2}}|10>$\n",
    "- After Hadamard Gate on second qubit: $\\frac{1}{{2}}|00> + \\frac{1}{{2}}|01>  +  \\frac{1}{{2}}|10> + \\frac{1}{{2}}|11>$\n",
    "- After Application of Oracle: $-\\frac{1}{{2}}|00> + \\frac{1}{{2}}|01>  +  \\frac{1}{{2}}|10> + \\frac{1}{{2}}|11>$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 662.2x258.86 with 1 Axes>"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "groverCircuit.measure(qr,cr)\n",
    "groverCircuit.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "result = execute(groverCircuit, simulator).result()\n",
    "counts = result.get_counts(groverCircuit)\n",
    "plot_histogram(counts, title='Grover Intermediate measurement')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.3 Apply Grover Transform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 662.2x258.86 with 1 Axes>"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qr = QuantumRegister(2)\n",
    "cr = ClassicalRegister(2)\n",
    "groverCircuit = QuantumCircuit(qr,cr)\n",
    "groverCircuit.h(qr)\n",
    "\n",
    "'''oracle w = |00>'''\n",
    "groverCircuit.x(qr)\n",
    "groverCircuit.cz(qr[0],qr[1])\n",
    "groverCircuit.x(qr)\n",
    "\n",
    "'''Grover Transform'''\n",
    "groverCircuit.h(qr)\n",
    "'''Reflection'''\n",
    "groverCircuit.z(qr)\n",
    "groverCircuit.cz(qr[0],qr[1])\n",
    "'''end of Reflection'''\n",
    "groverCircuit.h(qr)\n",
    "'''end of Grover Transform'''\n",
    "\n",
    "\n",
    "\n",
    "groverCircuit.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.3.1 Matrix Element"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- $Z$: phase-flip gate\n",
    "\n",
    "$\n",
    "(Z \\otimes Z)   =  \n",
    "\\begin{pmatrix}\n",
    "1 & 0\\\\\n",
    "0 & -1\n",
    "\\end{pmatrix} \\otimes \\begin{pmatrix}\n",
    "1 & 0\\\\\n",
    "0 & -1\n",
    "\\end{pmatrix} = \\begin{pmatrix}\n",
    "1 & 0 & 0 & 0\\\\\n",
    "0 & -1 & 0 & 0\\\\\n",
    "0 & 0 & -1 & 0\\\\\n",
    "0 & 0 & 0 & 1\\\\\n",
    "\\end{pmatrix}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### GROVER TRANSFORM (GT) \n",
    "\n",
    "$= (H \\otimes H) \\times Cz \\times (Z \\otimes Z)  \\times (H \\otimes H)$\n",
    "\n",
    "$ =  \n",
    "\\frac{1}{2} \\begin{pmatrix}\n",
    "    1  &  1  &  1  &  1 \\\\\n",
    "    1  &  -1  &  1  &  -1 \\\\\n",
    "    1  &  1  &  -1  &  -1 \\\\\n",
    "    1  &  -1  &  -1  &  1 \\\\\n",
    "\\end{pmatrix}\n",
    "\\times\n",
    "\\begin{pmatrix}\n",
    "1 & 0 & 0 & 0\\\\\n",
    "0 & 1 & 0 & 0\\\\\n",
    "0 & 0 & 1 & 0\\\\\n",
    "0 & 0 & 0 & -1\n",
    "\\end{pmatrix}\n",
    "\\times\n",
    "\\begin{pmatrix}\n",
    "1 & 0 & 0 & 0\\\\\n",
    "0 & -1 & 0 & 0\\\\\n",
    "0 & 0 & -1 & 0\\\\\n",
    "0 & 0 & 0 & 1\\\\\n",
    "\\end{pmatrix}\n",
    "\\times\n",
    "\\frac{1}{2} \\begin{pmatrix}\n",
    "    1  &  1  &  1  &  1 \\\\\n",
    "    1  &  -1  &  1  &  -1 \\\\\n",
    "    1  &  1  &  -1  &  -1 \\\\\n",
    "    1  &  -1  &  -1  &  1 \\\\\n",
    "\\end{pmatrix}$\n",
    "\n",
    "$= \\begin{pmatrix}\n",
    "    -\\frac{1}{2}  &  \\frac{1}{2}  &  \\frac{1}{2}  &  \\frac{1}{2} \\\\\n",
    "    \\frac{1}{2}  &  -\\frac{1}{2}  &  \\frac{1}{2}  &  \\frac{1}{2} \\\\\n",
    "    \\frac{1}{2}  &  \\frac{1}{2}  &  -\\frac{1}{2}  &  \\frac{1}{2} \\\\\n",
    "    \\frac{1}{2}  &  \\frac{1}{2}  &  \\frac{1}{2}  &  -\\frac{1}{2} \\\\\n",
    "\\end{pmatrix}\n",
    "$\n",
    "\n",
    "--------------\n",
    "\n",
    "##### CIRCUIT with GT, ORCL and INIT\n",
    "$ = GT \\times ORCL \\times INIT$\n",
    "\n",
    "$ = \\begin{pmatrix}\n",
    "    -\\frac{1}{2}  &  \\frac{1}{2}  &  \\frac{1}{2}  &  \\frac{1}{2} \\\\\n",
    "    \\frac{1}{2}  &  -\\frac{1}{2}  &  \\frac{1}{2}  &  \\frac{1}{2} \\\\\n",
    "    \\frac{1}{2}  &  \\frac{1}{2}  &  -\\frac{1}{2}  &  \\frac{1}{2} \\\\\n",
    "    \\frac{1}{2}  &  \\frac{1}{2}  &  \\frac{1}{2}  &  -\\frac{1}{2} \\\\\n",
    "\\end{pmatrix}\n",
    "\\times \n",
    "\\begin{pmatrix}\n",
    "-1 & 0 & 0 & 0\\\\\n",
    "0 & 1 & 0 & 0\\\\\n",
    "0 & 0 & 1 & 0\\\\\n",
    "0 & 0 & 0 & 1\\\\\n",
    "\\end{pmatrix}\n",
    "\\times\n",
    "\\frac{1}{2} \\begin{pmatrix}\n",
    "    1  &  1  &  1  &  1 \\\\\n",
    "    1  &  -1  &  1  &  -1 \\\\\n",
    "    1  &  1  &  -1  &  -1 \\\\\n",
    "    1  &  -1  &  -1  &  1 \\\\\n",
    "\\end{pmatrix}$\n",
    "\n",
    "$=\\begin{pmatrix}\n",
    "1 & 0 & 0 & 0\\\\\n",
    "0 & 0 & -1 & 0\\\\\n",
    "0 & -1 & 0 & 0\\\\\n",
    "0 & 0 & 0 & -1\\\\\n",
    "\\end{pmatrix}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n",
       "       [ 0.+0.j,  0.+0.j, -1.+0.j,  0.+0.j],\n",
       "       [ 0.+0.j, -1.+0.j,  0.+0.j,  0.+0.j],\n",
       "       [ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j]])"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "job = execute(groverCircuit, backend)\n",
    "job.result().get_unitary(groverCircuit, decimals=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.5  0.5  0.5  0.5]\n",
      " [ 0.5 -0.5  0.5  0.5]\n",
      " [ 0.5  0.5 -0.5  0.5]\n",
      " [ 0.5  0.5  0.5 -0.5]]\n"
     ]
    }
   ],
   "source": [
    "HH = 0.5*np.array([[1,1,1,1],[1,-1,1,-1],[1,1,-1,-1],[1,-1,-1,1]])\n",
    "ZZ = np.array([[1,0,0,0],[0,-1,0,0],[0,0,-1,0],[0,0,0,1]])\n",
    "\n",
    "'''Grover Transform'''\n",
    "GT =  np.dot(HH,np.dot(CZ,np.dot(ZZ,HH)))\n",
    "print(GT)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  0.,  0.,  0.],\n",
       "       [ 0.,  0., -1.,  0.],\n",
       "       [ 0., -1.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., -1.]])"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'''FUll circut matrix'''\n",
    "np.dot(INIT,np.dot(ORCL,GT))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.4 Manual Approach"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---------\n",
    "- Initial state: |00>\n",
    "- After Hadamard Gate on first qubit: $\\frac{1}{\\sqrt{2}}|00> + \\frac{1}{\\sqrt{2}}|10>$\n",
    "- After Hadamard Gate on second qubit: $\\frac{1}{{2}}|00> + \\frac{1}{{2}}|01>  +  \\frac{1}{{2}}|10> + \\frac{1}{{2}}|11>$\n",
    "- After Application of Oracle for $|00>$: $-\\frac{1}{{2}}|00> + \\frac{1}{{2}}|01>  +  \\frac{1}{{2}}|10> + \\frac{1}{{2}}|11>$\n",
    "- After Application of Grover Transformation$: $1.0|00> + 0.0|01>  +  0.0|10> + 0.0|11>$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.5. Measurement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No measurements in circuit \"circuit42\": count data will return all zeros.\n"
     ]
    },
    {
     "data": {
      "image/png": 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FBqgkSRUYoJIkVWCASpJUQVMBGhGHRMRHaua/ERHPRMRNETG864cnSVLf1Owe6JmrJiJiR+DvgH8F1gO+3XXDkiSpb2s2QLcEZpfTnwR+kpnnAacA+zbSQUScEBFPRsSrEfFQROzRQdvLIiLb+CyvaTOxnTbva3LbJElqWLMB+iqwUTm9L3BrOf1iTXm7IuJQ4ELgXGAccA9wY0SMbGeRrwDD6z6/B65to+12de0e73xzJEmqZt0m298JfDsi7gImAH9Vlm8DPN3A8qcAl2XmpeX8SRHxUeCLwOn1jTPzRYpwBiAidgNGA59to+/nMvOFRjdEkqQ10ewe6InACorgPD4z55fl+wM3dbRgRKwPjAdurqu6Gdi1wfV/AXgsM+9po256RCyIiNsiYu8G+5MkqZKm9kAz8xng422Un9zA4psBA4BFdeWLgP06WzgiBgOH8PY91QUUe7APAutT7J3eFhF7ZeadbfRzHHAcwPDhw3n44YcBaG1tZdCgQcyZMweAwYMHM3r0aGbMmAHAgAEDGDt2LLNnz2b58uIU7JgxY1iyZAmwaedbL0nqVosXL2bu3LkAtLS00NLSwqxZswAYOHAgY8aMYebMmaxcuRKAsWPHMm/ePJYuXQrA6NGjWbFiRcPri8xsaoARsQHwMeC9wPcyc1lEvBdYmplLOliuFXgW2Csz76gp/wZweGZu28l6v0RxpW9rR+sp204BXs/MT3TUbty4cTl16tSOmjTkaz8wQCWpt533uaVd0s+QIUMeyswJnbVrag80IramuHBoQ2AT4DpgGcUe4CbAsR0s/gLwBrB5XfnmwMIGVv8F4EedhWfpfuCwBtpJklRJs+dAL6A4Z7k58EpN+c+ADs87ZuYK4CFgUl3VJIqrcdsVER8CxgKXdtSuxg4Uh3YlSeoWzV6Fuyvw4cx8IyJqy+cBrQ0sfz5wRUQ8ANwNHF8udzFARFwOkJlH1i13HPB4Zt5e32FEnAw8BTxGcQ70COAg4FONbpQkSc1qNkCheOpQvZHU3G7Snsy8JiKGAmdQ3Kv5KHBAZs6t6Wc1EbERxeHYs9vpdn3gW8AWFHvFjwEHZuaUzsYjSVJVzQbozRT3cn6+nM+I2Bg4C/jfRjrIzIuAi9qpm9hG2UsU51zb6+884LxG1i1JUldpNkBPAaZFxGxgA+AaYGuKW1EO6eKxSZLUZzV7H+j8iNgB+DSwI8VFSJcAP8zMVzpcWJKkd5Cmz4GWQfn98iNJUr/UaYBGxMHAzzNzZTndrsz8cZeNTJKkPqyRPdDrgWHAc+V0e5LiUX2SJL3jdRqgmblOW9OSJPVnTQViROwZEW8L3YgYEBF7dt2wJEnq25rdo5wGDGmjfJOyTpKkfqHZAA2Kc531hgLL13w4kiStHRq6jSUiflZOJnBlRLxWUz0A+ACdPBBekqR3kkbvA11c/hvAUlZ/E8sK4C4af1OKJElrvYYCNDOPBoiIp4B/yUwP10qS+rVmH+V3VncNRJKktUkjTyL6DbBXZi6NiJm0fRERAJn5wa4cnCRJfVUje6A/AlZdNNTRk4gkSeo3GnkS0VltTUuS1J/5aD5Jkipo5Bxoh+c9a3kOVJLUXzT6NhZJklSjqXOgkiSp4DlQSZIq8D5QSZIq8D5QSZIq8D5QSZIqaOpZuKtExHuBMeXsbzPzia4bkiRJfV9TARoRQ4H/Aj4BvPmn4vgFcExmLm53YUmS3kGavQr3P4GtgT2ADcrPnsAofB+oJKkfafYQ7l8A+2bmvTVld0fE3wC3dt2wJEnq25rdA30eaOtl2i8DHr6VJPUbzQbo2cAFETFiVUE5/e2yTpKkfqHKw+RHAU9FxLPl/AjgVeDdFOdIJUl6x/Nh8pIkVeDD5CVJqsCHyUuSVEFTARoR60fEWRHxu4h4NSLeqP101yAlSeprmt0D/SfgcxRX3b4JfBX4d4pbWE7o2qFJktR3NRughwDHZ+b3gDeAn2bml4F/BCZ19eAkSeqrmg3QzYFZ5fQfgU3K6V8CH+mqQUmS1Nc1G6DzgNZyeg7Fo/0AdgFe6apBSZLU1zUboDcA+5bTFwJnRcSTwGX4EAVJUj/S1MPkM/P0munrI+IZYFfgd5n5i64enCRJfVWlF2qvkpn3Afd10VgkSVprNP0ghYjYMSIuj4jp5eeKiNixOwYnSVJf1eyDFA4HHgSGA1PKz+bAAxFxRNcPT5KkvqnZQ7jnAP+QmefWFkbE6cA/A1d21cAkSerLmj2E2wJc20b5dRSvM+tURJwQEU+WjwJ8KCL26KDtxIjINj7vq2v3qYiYFRGvlf9+sqmtkiSpSc0G6DRgYhvlE4FfdbZwRBxKcfvLucA44B7gxogY2cmi21EcNl71ebymz12Aa4AfAjuU/14XETt3Nh5Jkqpq5IXaB9fM3gh8MyIm8Kerbz8MHAyc2cD6TgEuy8xLy/mTIuKjwBeB09tfjOcy84V26k4GpmXmOeX8ORGxd1n+6QbGJElS06q+UPu48lPr34CL2uskItYHxgP/Uld1M8W9pB2ZHhHvoniM4D9n5rSaul3Kdde6CTixkz4lSaqskRdqd9U7QzcDBgCL6soXAfu1s8wCir3TB4H1gc8Ct0XEXpl5Z9lmWDt9Dmurw4h4K/yHDx/Oww8/DEBrayuDBg1izpw5AAwePJjRo0czY8YMAAYMGMDYsWOZPXs2y5cvB2DMmDEsWbIE2LTzrZckdavFixczd+5cAFpaWmhpaWHWrOLx7QMHDmTMmDHMnDmTlStXAjB27FjmzZvH0qVLARg9ejQrVqxoeH1r9CCF7paZs4HZNUX3RsRWFK9Ru7OtZRro8xLgEoBx48bljjuufgtrZ/PbbrvtavMjRoyoMgxJUhcbOnQoQ4cOXa2s/nf49ttvv9r8qFGjGDVqVKX1VXmQwoERcUdEvBARz0fEryLigAYWfYHiFWib15VvDixsYgj3A39eM7+wC/qUJKkpzT5I4ViKB8o/AXwdmAw8CdwQEcd0tGxmrgAe4u3vDZ1EcTVuo3agOLS7yr1d0KckSU1p9hDu14FTMvO7NWX/FREPUYTp9ztZ/nzgioh4ALgbOJ7i9WgXA0TE5QCZeWQ5fzLwFPAYxTnQI4CDgE/V9HkhcEdETAZ+AnwS2BvYvcltkySpYc0G6EiKl2fXu5G3X137Npl5TUQMBc6guJ/zUeCAzJxb03+t9YFvAVtQvG/0MeDAzJxS0+c9EXEYxZOQzqbYOz40M+9vZsMkSWpGswE6j+Lw6Jy68o8Ac9/e/O0y8yLaud0lMyfWzZ8HnNdAn9fT9u02kiR1i2YD9F+AfyvfvrLqHONuFLeXnNSVA5MkqS9r9oXa34uI54BTKZ4+BPBb4JDM/GlXD06SpL6q4QCNiHUpDtXekZk3dN+QJEnq+xq+jSUzXwd+DGzUfcORJGnt0OyDFH4NbN0dA5EkaW3SbICeCXw7Ig6KiPdExJDaTzeMT5KkPqnZq3D/t/z3x0DWlEc5P6ArBiVJUl/XbIDu3S2jkCRpLdNQgEbEIIonAh0ErAfcCny5g5dcS5L0jtboOdCzgKMoDuFeRfE0ov/opjFJktTnNXoI92Dg85l5NUBE/BC4OyIGZOYb3TY6SZL6qEb3QN9DzQusM/MB4HWKN6lIktTvNBqgA4AVdWWv0/xFSJIkvSM0GoABXBkRr9WUbQBcGhEvryrIzE905eAkSeqrGg3QH7RRdmVXDkSSpLVJQwGamUd390AkSVqbNPsoP0mShAEqSVIlBqgkSRUYoJIkVWCASpJUgQEqSVIFBqgkSRUYoJIkVWCASpJUgQEqSVIFBqgkSRUYoJIkVWCASpJUgQEqSVIFBqgkSRUYoJIkVWCASpJUgQEqSVIFBqgkSRUYoJIkVWCASpJUgQEqSVIFBqgkSRUYoJIkVWCASpJUgQEqSVIFBqgkSRUYoJIkVWCASpJUgQEqSVIFPR6gEXFCRDwZEa9GxEMRsUcHbQ+OiJsj4vmIeCki7o+IT9S1OSoiso3PBt2/NZKk/qpHAzQiDgUuBM4FxgH3ADdGxMh2FtkLmAocWLafAtzQRui+DAyv/WTmq12/BZIkFdbt4fWdAlyWmZeW8ydFxEeBLwKn1zfOzK/UFZ0VEQcCBwF3rt40F3bHgCVJakuP7YFGxPrAeODmuqqbgV2b6GojYGld2cCImBsRz0TELyJi3BoMVZKkTvXkHuhmwABgUV35ImC/RjqIiC8BWwBX1BTPBo4Bfk0Rrl8B7o6IsZn5eBt9HAccBzB8+HAefvhhAFpbWxk0aBBz5swBYPDgwYwePZoZM2YAMGDAAMaOHcvs2bNZvnw5AGPGjGHJkiXApo0MX5LUjRYvXszcuXMBaGlpoaWlhVmzZgEwcOBAxowZw8yZM1m5ciUAY8eOZd68eSxdWuyTjR49mhUrVjS8vsjMLt6EdlYU0Qo8C+yVmXfUlH8DODwzt+1k+U9RBOehmfnzDtoNAB4BpmXmlzvqc9y4cTl16tQmtqJtX/uBASpJve28z9UfnKxmyJAhD2XmhM7a9eRFRC8AbwCb15VvDnR4/jIi/ooiPI/sKDwBMvMNYDrw59WHKklSx3osQDNzBfAQMKmuahLF1bhtiohDKMLzqMy8vrP1REQAHwQWVB+tJEkd6+mrcM8HroiIB4C7geOBVuBigIi4HCAzjyznD6MIz9OAOyJiWNnPisxcUrb5R+A+4HFgY+DLFAH6xR7aJklSP9SjAZqZ10TEUOAMivs1HwUOyMy5ZZP6+0GPpxjjBeVnlV8BE8vpTYBLgGHAi8AMYM/MfKA7tkGSJOj5PVAy8yLgonbqJnY0384yfwv8bVeMTZKkRvksXEmSKjBAJUmqwACVJKkCA1SSpAoMUEmSKjBAJUmqwACVJKkCA1SSpAoMUEmSKjBAJUmqwACVJKkCA1SSpAoMUEmSKjBAJUmqwACVJKkCA1SSpAoMUEmSKjBAJUmqwACVJKkCA1SSpAoMUEmSKjBAJUmqwACVJKkCA1SSpAoMUEmSKjBAJUmqwACVJKkCA1SSpAoMUEmSKjBAJUmqwACVJKkCA1SSpAoMUEmSKjBAJUmqwACVJKkCA1SSpAoMUEmSKjBAJUmqwACVJKkCA1SSpAoMUEmSKjBAJUmqwACVJKkCA1SSpAoMUEmSKujxAI2IEyLiyYh4NSIeiog9Omm/V9nu1Yj4fUQcv6Z9SpK0pno0QCPiUOBC4FxgHHAPcGNEjGyn/ShgStluHPBN4N8i4lNV+5QkqSv09B7oKcBlmXlpZv42M08CFgBfbKf98cD8zDypbH8p8APgtDXoU5KkNdZjARoR6wPjgZvrqm4Gdm1nsV3aaH8TMCEi1qvYpyRJa6wn90A3AwYAi+rKFwHD2llmWDvt1y37q9KnJElrbN3eHkBPi4jjgOPK2T8OGTJkdm+OR+pDNgNe6O1BSFX95992WVdbNtKoJwP0BeANYPO68s2Bhe0ss7Cd9q+X/UWzfWbmJcAlDY9a6iciYnpmTujtcUhrix47hJuZK4CHgEl1VZMorpxty73ttJ+emSsr9ilJ0hrr6UO45wNXRMQDwN0UV9m2AhcDRMTlAJl5ZNn+YuDEiLgA+B6wG3AU8OlG+5QkqTv0aIBm5jURMRQ4AxgOPAockJlzyyYj69o/GREHAN+huC1lPvDlzPxRE31KaoynNqQmRGb29hgkSVrr+CxcSZIqMEAlSarAAJUkqQIDVJKkCvrdk4gkFSJiC2BrigeSvAnMzsz2HmoiqY5X4Ur9UER8ETgGGAssB+YAzwD3AT/JzNkRsU5mvtmLw5T6NA/hSv1Med/0ucBPKe6d3oXiNYFvAEcC/xoR78/MNyMiem+kUt/mHqjUz0TEScARmblzG3W7U7y4fgTwocz04fJSO9wDlfqfFcBGEfEBgIh4V/luXTLzLuBw4FXgI703RKnvM0Cl/ud6iouGTo6IjTLztcxcERHrAGTmPGAZsEVvDlLq6wxQqR8pz2kuoXh29CRgfkT8V0SML+tHRsQRwPbAtb03Uqnv8xyo1A9FxCYUL2/YFfgkxZuOoHiPbgBXZOaZvTM6ae1ggEr9RES8G/gscCrFC+lfoThUexfF7SvrUdwX+svM/F1vjVNaWxigUj9Dh80CAAABD0lEQVQREZcB2wE/pziMO4TiUO02wHPAGZl5f68NUFrLGKBSP1Ce+3yJ4l25d9SUjQR2Bo4FRgOHZObDvTZQaS3iRURS//B+4EmKW1gAyMLczLwW+DjF4dy/7qXxSWsdA1TqH35PcZj2OxHx56tuWVklM1+jeBrR/r0xOGltZIBK/UBmvgL8PTAQuBw4MiLeExEbAkTEIGAv4NHeG6W0dvEcqNSPlE8f+gfgExQPkb8XeB7YD1gAHJuZM3tvhNLawwCV+qHylpYDgYMoHtv3KHBdZv5frw5MWosYoFI/52vLpGoMUEmSKvAiIkmSKjBAJUmqwACVJKkCA1SSpAoMUEmSKjBAJUmqwACVJKmC/w8HHntHvrDiqQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "result = execute(groverCircuit, simulator).result()\n",
    "counts = result.get_counts(groverCircuit)\n",
    "plot_histogram(counts, title='Grover Intermediate measurement')"
   ]
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}