3.a-Bell-State.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bell States\n",
    "\n",
    "\n",
    "Bell state is constructed with application of $\\textbf{Hadamard}$ and $\\textbf{CNOT}$ gates in two qubit system.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import *\n",
    "from math import pi\n",
    "import numpy as np\n",
    "from qiskit.visualization import *\n",
    "import matplotlib.pyplot as plt\n",
    "from qutip import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Bell State Circuit ($\\beta_{00}$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 418.992x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2)\n",
    "qc.barrier()\n",
    "qc.h(0)\n",
    "qc.cx(0, 1)\n",
    "qc.barrier()\n",
    "qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.2. Two qubit system (state vector)\n",
    " <ul>\n",
    "        <li> Initial state = |00> </li>\n",
    "        <li> After application of Hadamard Gate: $\\frac{1}{\\sqrt{2}}|00\\rangle + \\frac{1}{\\sqrt{2}}|01\\rangle $ </li>\n",
    "        <li> After application of CNOT Gate: $\\frac{1}{\\sqrt{2}}|00 \\rangle + \\frac{1}{\\sqrt{2}}|11 \\rangle $ </li>\n",
    "</ul>\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.70710678+0.j 0.        +0.j 0.        +0.j 0.70710678+0.j]\n"
     ]
    }
   ],
   "source": [
    "backend = Aer.get_backend('statevector_simulator')\n",
    "out = execute(qc,backend).result().get_statevector()\n",
    "print(out)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.3 Single qubit states (tensor product)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-danger\">\n",
    "$\\textbf{Question:}$ Can you write Bell state as a tensor product of single qubit state?\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\textbf{Answer}$: No, it is not possible. It is hard to realise.\n",
    "    \n",
    "  $\\begin{bmatrix}\n",
    "    p   \\\\\n",
    "    q \n",
    "\\end{bmatrix} \\otimes \\begin{bmatrix}\n",
    "    r   \\\\\n",
    "    s \n",
    "\\end{bmatrix} = c \\begin{bmatrix}\n",
    "    m   \\\\\n",
    "    0 \\\\\n",
    "    0 \\\\\n",
    "    n\n",
    "\\end{bmatrix}$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4. Matrix element (tensor product)\n",
    "\n",
    "<div class=\"alert alert-block alert-danger\">\n",
    "$\\textbf{Question:}$ Can we write matrix represented by the Bell circuit as a  tensor product of fundamental gate matrices?\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on above Bell circuit, lets construct the matrix representation of the circuit using fundamental gates matrices involved in the circuit.\n",
    "\n",
    "$H = \\frac{1}{\\sqrt{2}} \\begin{bmatrix}\n",
    "    1  & 1 \\\\\n",
    "    1 & -1\n",
    "\\end{bmatrix}; I = \\frac{1}{\\sqrt{2}} \\begin{bmatrix}\n",
    "    1  & 0 \\\\\n",
    "    0 &  1\n",
    "\\end{bmatrix}; \\text{CNOT} = \\begin{bmatrix} 1 & 0 & 0 & 0 \\\\\n",
    "                              0 & 0 & 0 & 1 \\\\\n",
    "                              0 & 0 & 1 & 0 \\\\\n",
    "                              0 & 1 & 0 & 0 \\\\\n",
    "\\end{bmatrix}$\n",
    "\n",
    "- Before first barrier\n",
    "\n",
    "$I \\otimes H$ = $ \\begin{bmatrix}\n",
    "    H  & 0 \\\\\n",
    "    0 & H\n",
    "\\end{bmatrix}$\n",
    "\n",
    "- After first barrier\n",
    "\n",
    "$\\text{CNOT}$ \n",
    "\n",
    "- Net operation before measurement\n",
    "\n",
    "$U = \\text{CNOT} \\times (I \\otimes H)   $\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets express ``U`` matrix using ``numpy`` library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.70710678  0.70710678  0.          0.        ]\n",
      " [ 0.          0.          0.70710678 -0.70710678]\n",
      " [ 0.          0.          0.70710678  0.70710678]\n",
      " [ 0.70710678 -0.70710678  0.          0.        ]]\n"
     ]
    }
   ],
   "source": [
    "I = np.eye(2,2)\n",
    "H = 1/np.sqrt(2)*np.array([[1,1],[1,-1]])\n",
    "CNOT = np.array([[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]])\n",
    "IKH = np.kron(I,H)\n",
    "U = np.dot(CNOT,IKH)\n",
    "print(U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.707+0.j  0.707-0.j  0.   +0.j  0.   +0.j]\n",
      " [ 0.   +0.j  0.   +0.j  0.707+0.j -0.707+0.j]\n",
      " [ 0.   +0.j  0.   +0.j  0.707+0.j  0.707-0.j]\n",
      " [ 0.707+0.j -0.707+0.j  0.   +0.j  0.   +0.j]]\n"
     ]
    }
   ],
   "source": [
    "backend = Aer.get_backend('unitary_simulator')\n",
    "job = execute(qc, backend)\n",
    "result = job.result()\n",
    "print(result.get_unitary(qc, decimals=3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also observe final ket vector by multiplying it with ```U``` matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.70710678, 0.        , 0.        , 0.70710678])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ket_00 = np.array([1,0,0,0])\n",
    "np.dot(U,ket_00)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Bell State Circuit ($\\beta_{01}$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 479.192x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2)\n",
    "qc.x(1)\n",
    "qc.barrier()\n",
    "qc.h(0)\n",
    "qc.cx(0, 1)\n",
    "qc.barrier()\n",
    "qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.        +0.j 0.70710678+0.j 0.70710678+0.j 0.        +0.j]\n"
     ]
    }
   ],
   "source": [
    "# Let's see the result\n",
    "backend = Aer.get_backend('statevector_simulator')\n",
    "out = execute(qc,backend).result().get_statevector()\n",
    "print(out)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Bell State Circuit ($\\beta_{10}$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 479.192x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2)\n",
    "qc.x(0)\n",
    "qc.barrier()\n",
    "qc.h(0)\n",
    "qc.cx(0, 1)\n",
    "qc.barrier()\n",
    "qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.70710678-8.65956056e-17j  0.        +0.00000000e+00j\n",
      "  0.        +0.00000000e+00j -0.70710678+8.65956056e-17j]\n"
     ]
    }
   ],
   "source": [
    "# Let's see the result\n",
    "backend = Aer.get_backend('statevector_simulator')\n",
    "out = execute(qc,backend).result().get_statevector()\n",
    "print(out)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. Bell State Circuit ($\\beta_{11}$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 479.192x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2)\n",
    "qc.x(0)\n",
    "qc.x(1)\n",
    "qc.barrier()\n",
    "qc.h(0)\n",
    "qc.cx(0, 1)\n",
    "qc.barrier()\n",
    "qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.        +0.00000000e+00j -0.70710678+8.65956056e-17j\n",
      "  0.70710678-8.65956056e-17j  0.        +0.00000000e+00j]\n"
     ]
    }
   ],
   "source": [
    "# Let's see the result\n",
    "backend = Aer.get_backend('statevector_simulator')\n",
    "out = execute(qc,backend).result().get_statevector()\n",
    "print(out)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Measurement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}