2.b-Two-qubit-circuit.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Two Qubit Circuits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "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": [
    "#### 2.  Double qubit circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Basis states: $|00 \\rangle, |01 \\rangle, |10 \\rangle,|11 \\rangle $\n",
    "\n",
    "$ \\psi _{2q} = \\alpha |00 \\rangle + \\beta |01 \\rangle + \\gamma |10 \\rangle + \\delta |11 \\rangle $ where $\\alpha,\\beta,\\gamma, \\delta \\in \\mathcal{C}^{4}$\n",
    "\n",
    "$\\alpha^{2} + \\beta^{2} + \\gamma^{2} +  \\delta^{2} = 1$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### 2.1. $I \\otimes U$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMIAAAB7CAYAAAAmJF+MAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAABoBJREFUeJzt3V9I1f0dwPG3ptNTPj6k7lHm87Qe8WR28AieZ61oIF3UJNiN1IVNB8qSmYMt6eYhjF1piBfrKgYbFFQ3GkKQN12UBC5QiEK60PAhMZwzt5Y2a6a/XYw1DvKsczT7tfZ+wbn5+Od8BN9+f7+yTkYQBAHS/7nMsBeQPgSGIGEIEmAIEmAIEmAIEmAIEmAIEmAIEmAIEmAIEmAIEmAIEmAIEmAIEmAIEmAIEmAIEmAIEmAIEmAIEmAIEmAIEmAIEmAIEmAIEmAIEgBZYS+g9+PXV8J53t/+NJznTZcngoQhSIAhSIAhSIAhSIAhSIAhSIAhSIAhSIAhpG11dZXe3l6i0Si5ublUV1czNDRERUUFra2tYa/3zvz+l99j7PYfkmZBEHDh5/k8GhkIaavN469YpKmlpYWBgQE6OztJJBIMDw/T0NDA3NwcHR0dYa/3Tiz+5Qkvns3w3R3VSfO//XmSf7xcoLjsq5A22zyeCGm4evUqly5d4vr165w+fZqDBw9y5swZ9u/fz+vXr0kkEgDMzs5y+PBhtm7dSnV1Nffu3Qt58/TMTo6QkbmFws9jSfOnU/fZ+mkxnxR+EdJmm8cQ0tDd3U1dXR21tbVJ8/LycrKzs6mqqgKgra2N3bt3Mz8/T3t7O0ePHmVlZSWMlddldnKE7SW7yPpOJGk+N3Wfz778+E4D8NIoZdPT04yNjXHq1Kk1b5uamiIWi5GTk8PCwgI3btzgyZMnRCIRWltb6erq4u7duxw4cGBTdsvIyHjr+/zqcpDy55udHOHZ7CN+94uipPnyq0W++snX73y3zRQEqX3dhpCi6elpAEpKSpLmS0tLDA0NceTIEQAmJiYoLCykqOg/30RVVVU8fPhw00J412a/GeWH9b+h8kc/S5pf+bqK4o/0RPDSKEX//sYeHx9Pmvf09DAzM0NNTQ0AL168ID8/P+l98vPzWVxc3LTdgiB46yNVz/70iFcv/sr34z/mk8LP3zxWll/y6u/P+CzNG+VUdtvMR6o8EVJUVlZGPB6nq6uLgoICSktL6e/vZ3BwEODNjfK2bdtYWFhI+tjnz5+Tl5f33ndej9nJEbJytq75E6OZiWHyCr9g26fFIW22uTwRUpSZmUlfXx+xWIy2tjaam5spKiqivb2drKws4vE4ANFolKdPnzI/P//mY8fGxtizZ09Yq6dldnKE4i9/QOaW5J+RM4/++NFeFgFkBOmcH1qjqamJ+/fv8+DBgzez+vp6duzYwblz57h8+TJdXV1MTEywZcuW0Pb0n2r+d14abdDo6Cj79u1Lml24cIHGxka2b99ONBrl2rVroUagtzOEDVhcXGR8fJyTJ08mzYuLi7l582ZIW2k9DGED8vLy/qf+okzfzptlCUOQAEOQAEOQAEOQAEOQAEOQAH/FQgI8ESTAECTAECTAECTAECTAECTAECTAECTAECTAECTAECTAECTAECTAECTAECTAECTAECTAECTAECTAECTAECTAECTAECTAECTAENK2urpKb28v0WiU3NxcqqurGRoaoqKigtbW1rDX0zr5ijlpamlpYWBggM7OThKJBMPDwzQ0NDA3N0dHR0fY62m9AqXsypUrARDcvn07aV5fXx8AwcjISBAEQXD27NmgsrIyyMjICPr6+sJYVWny0igN3d3d1NXVUVtbmzQvLy8nOzubqqoq4F+vtXz+/Hn27t0bxppaB0NI0fT0NGNjYxw7dmzN26ampojFYuTk5ADQ2NjIoUOHyM3Nfd9rap28R0jR9PQ0ACUlJUnzpaUlhoaGOHLkSBhrAZCRkRHac3/oghT/s3dPhBQVFRUBMD4+njTv6elhZmaGmpqaMNbSO+KJkKKysjLi8ThdXV0UFBRQWlpKf38/g4ODACQSidB2S/Wnnr6dJ0KKMjMz6evrIxaL0dbWRnNzM0VFRbS3t5OVlUU8Hg97RW2AJ0Iadu3axa1bt5JmTU1NVFZWEolE3syWl5dZWVlhdXWV5eVlXr58SU5OjtfyHzBPhA0aHR1dc1l04sQJIpEId+7c4fjx40QiER4/fhzShkqFIWzA4uIi4+Pja26UL168SBAESY+dO3eGs6RS4osJSngiSIAhSIAhSIAhSIAhSIAhSIAhSIAhSIAhSIAhSIAhSIAhSIAhSIAhSIAhSIAhSIAhSIAhSIAhSIAhSIAhSIAhSIAhSIAhSIAhSIAhSIAhSAD8EzPiAQ1gEzXwAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 238.392x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2)\n",
    "qc.h(0)\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.707+0.j  0.707-0.j  0.   +0.j  0.   +0.j]\n",
      " [ 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"
     ]
    }
   ],
   "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": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.707+0.j,  0.707+0.j,  0.   +0.j,  0.   +0.j],\n",
       "       [ 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]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H = np.array([[ 0.707+0.j,  0.707-0.j],[ 0.707+0.j, -0.707+0.j]])\n",
    "I = np.eye(2)\n",
    "np.kron(I,H)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### 2.2. $U \\otimes I$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 238.392x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2)\n",
    "qc.h(1)\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.707+0.j  0.   +0.j  0.707-0.j  0.   +0.j]\n",
      " [ 0.   +0.j  0.707+0.j  0.   +0.j  0.707-0.j]\n",
      " [ 0.707+0.j  0.   +0.j -0.707+0.j  0.   +0.j]\n",
      " [ 0.   +0.j  0.707+0.j  0.   +0.j -0.707+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": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.707+0.j,  0.   +0.j,  0.707+0.j,  0.   +0.j],\n",
       "       [ 0.   +0.j,  0.707+0.j,  0.   +0.j,  0.707+0.j],\n",
       "       [ 0.707+0.j,  0.   +0.j, -0.707+0.j, -0.   +0.j],\n",
       "       [ 0.   +0.j,  0.707+0.j, -0.   +0.j, -0.707+0.j]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H = np.array([[ 0.707+0.j,  0.707-0.j],[ 0.707+0.j, -0.707+0.j]])\n",
    "I = np.eye(2)\n",
    "np.kron(H,I)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### 2.3 $U \\otimes U$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 249.228x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = QuantumRegister(2)\n",
    "qc = QuantumCircuit(q)\n",
    "qc.h(0)\n",
    "qc.h(1)\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 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]]\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": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.499849+0.j,  0.499849+0.j,  0.499849+0.j,  0.499849+0.j],\n",
       "       [ 0.499849+0.j, -0.499849+0.j,  0.499849+0.j, -0.499849+0.j],\n",
       "       [ 0.499849+0.j,  0.499849+0.j, -0.499849+0.j, -0.499849+0.j],\n",
       "       [ 0.499849+0.j, -0.499849+0.j, -0.499849+0.j,  0.499849-0.j]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H = np.array([[ 0.707+0.j,  0.707-0.j],[ 0.707+0.j, -0.707+0.j]])\n",
    "np.kron(H,H)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.4.  $(U \\otimes U) \\times (U\\otimes U)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 479.192x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2)\n",
    "qc.barrier()\n",
    "qc0 = qc.copy()\n",
    "qc.h(0)\n",
    "qc.x(1)\n",
    "qc.barrier()\n",
    "qc1 = qc.copy()\n",
    "qc.y(0)\n",
    "qc.h(1)\n",
    "qc.barrier()\n",
    "qc2 = qc.copy()\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.-0.5j  0.+0.5j  0.-0.5j  0.+0.5j]\n",
      " [ 0.+0.5j  0.+0.5j  0.+0.5j  0.+0.5j]\n",
      " [ 0.+0.5j -0.-0.5j  0.-0.5j  0.+0.5j]\n",
      " [-0.-0.5j -0.-0.5j  0.+0.5j  0.+0.5j]]\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": [
    "#### Operator : $(H \\otimes Y) \\times (X\\otimes H)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.-0.499849j, 0.+0.499849j, 0.-0.499849j, 0.+0.499849j],\n",
       "       [0.+0.499849j, 0.+0.499849j, 0.+0.499849j, 0.+0.499849j],\n",
       "       [0.+0.499849j, 0.-0.499849j, 0.-0.499849j, 0.+0.499849j],\n",
       "       [0.-0.499849j, 0.-0.499849j, 0.+0.499849j, 0.+0.499849j]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H = np.array([[ 0.707+0.j,  0.707-0.j],[ 0.707+0.j, -0.707+0.j]])\n",
    "X = sigmax()\n",
    "Y = sigmay()\n",
    "XKH = np.kron(X,H)\n",
    "HKY = np.kron(H,Y)\n",
    "np.dot(HKY,XKH)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
      "[0.        +0.j 0.        +0.j 0.70710678+0.j 0.70710678+0.j]\n",
      "[-6.123234e-17-0.5j  6.123234e-17+0.5j  6.123234e-17+0.5j\n",
      " -6.123234e-17-0.5j]\n"
     ]
    }
   ],
   "source": [
    "backend = Aer.get_backend('statevector_simulator')\n",
    "qc_vec = []\n",
    "for qc in [qc0,qc1,qc2]:\n",
    "    out = execute(qc,backend).result().get_statevector()\n",
    "    qc_vec.append(out)\n",
    "    print(out)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### State Vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 414.176x84.28 with 1 Axes>"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qca = QuantumCircuit(1)\n",
    "\n",
    "qca.barrier()\n",
    "qca0 = qca.copy()\n",
    "qca.h(0)\n",
    "\n",
    "qca.barrier()\n",
    "qca1 = qca.copy()\n",
    "qca.y(0)\n",
    "\n",
    "qca.barrier()\n",
    "qca2 = qca.copy()\n",
    "qca.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.+0.j 0.+0.j]\n",
      "[0.70710678+0.j 0.70710678+0.j]\n",
      "[0.-0.70710678j 0.+0.70710678j]\n"
     ]
    }
   ],
   "source": [
    "backend = Aer.get_backend('statevector_simulator')\n",
    "qca_vec = []\n",
    "for qc in [qca0,qca1,qca2]:\n",
    "    out = execute(qc,backend).result().get_statevector()\n",
    "    qca_vec.append(out)\n",
    "    print(out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUcAAABOCAYAAACzMdQXAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAABqJJREFUeJzt3W9oVXUcx/HPvdv8U/ZHXFPSikLTeVFRC6HCPw9Kk/JB2krCQCt1TUiRIqmcZiHYagVOKeqBkUbb1eiJQlrsppm0IUw0bciMi7GWUpNWc+m9pweSdevndq/bOb9z93u/wCe/HTlfPhuf/e7uOedGPM/zBADIELU9AACEEeUIAAaUIwAYUI4AYEA5AoAB5QgABpQjABhQjgBgQDkCgAHlCAAGlCMAGFCOAGBAOQKAAeUIAAaUIwAYUI4AYEA5AoAB5QgABpQjABhQjgBgUGh7gHx24sSJHo/ZvHmzVqxY0e0x48aN66uR+i2yDg5ZX8LO0Wc1NTW2R3AGWQfHhawpRwAwoBwBwIBy9Fk8Hrc9gjPIOjguZE05AoAB5eizBQsW2B7BGWQdHBeyphwBwIDrHPuxAXv3BH7OP+9/MPBzhsHK7cGf8+0ngj+nS9g5+qyiosL2CM4g6+C4kDXl6LOe7iJA3yHr4LiQNeXos+nTp9sewRlkHRwXsqYcfXbmzBnbIziDrIPjQtaUIwAYUI4+Gz9+vO0RnEHWwXEha8rRZzt37rQ9gjPIOjguZE05+mzt2rW2R3AGWQfHhaxDU47pdFpVVVUaM2aMBg0apEmTJimRSGjs2LFaunSp7fGuWl1dne0RsuJ1durCo48rvf/AP2tdXbq4crUuvvq6vHTa4nTZyZesJen9FTfraP0HGWue52nr09frZMOnlqbKXj5lfbVCU45LlizRhg0btGzZMu3Zs0dlZWVauHChWlpaNHXqVNvj9XuRwYMVXTBfqe0fy/M8eamUUq9tlIqKVPDiC4pEQ/Ojkvc6fvlRv7e36qZbJ2Wsn/u5RX+e/03D77jL0mT4t1DcPrhjxw5t27ZN9fX1mjFjhiRp1qxZOnz4sHbt2kU5BiQ672Gl47vkHfha6W8b5Z09q8KqTYoMKLI9Wr/S1tKgSLRAw0bFMtbPJpt0zQ3Ddd2wWyxNhn8LRTlu3LhRc+bMuVyMfxs9erSKioo0YcIES5P1XiKRsD1C1iKDByn66Hyl3nhLGnqjCt9+U5Frr7E9VtbyJeu2lgYNHXGnCgcMzlg/k2xSye35sWvMl6x7w3o5nj59WkePHtWqVav+97VkMqlYLKaBAwdamKxvHDt2TCUlJbbHyM358yp4rEyRoUNtT5KTfMm6raVB7W0n9e7y4oz1C10duuvhNZamyk2+ZN0boShHSRoxYkTGemdnpxKJhObOnevr+SORyFX/X1Oh/1d1dXWPx1VXV1/1DN0p+nx3Tsen932p9Ce1isx+QKlPP1Pkwdk559ObPLsT9qyf+8jL+ti2U42a9sg6ld73ZMb69jUTNDyHnaOrWfeG52X/fbL+V/bi4ku/PZubmzPWN23apNbWVk2ZMsXGWM5Jf9ug1OYaFVS+ooJnl0vt7fK+2m97rH6n/aeT6vr9V902cbauGzbq8r/UhfPq+qNdJbwZExoRL5cq9UE6ndbkyZPV2tqqqqoqjRw5UvF4XLt371YymdShQ4c0bdo0myNeUTaf71taWqrjx493e4xfn++b7fMc08e+U+qlV1Tw/GpF771HkpSqjSu99wsVvluT0zvVfj3PMexZZ/s8x+8Pfqx9Hzyt8vfOKVrwzwu34/s/1MH4y3rqnWTW5/TreY5hzzoo1neO0WhUdXV1isViKi8v1+LFi1VcXKyKigoVFhZq4sSJtkfslfXr19seoVveqR+UWrtOBcueuVyMkhSd95B07lxe7R7DnrV06e+Nw2+/O6MYJan15Dc5vaS2LR+y7i3rO8crWbRokZqamnTkyBHbo1xRNr9hs2F759iXbO4cs2F759iXbO4cs8HO0SeNjY394vrG0tJS2yM4g6yD40LWoSzHjo4ONTc382YMAGusX8pjMmTIEKVSKdtjAHBYKHeO/cnMmTNtj+AMsg6OC1lTjj7bunWr7RGcQdbBcSFrytFn5eXltkdwBlkHx4WsKUef1dfX2x7BGWQdHBeyphwBwIByBAADytFnPd1/ir5D1sFxIetQXufYn9TW1qqsrMzKuf26lS+sbGbt1618YWUz66Cwc/RZZWWl7RGcQdbBcSFryhEADChHADCgHH22ZcsW2yM4g6yD40LWlKPPYrFYzwehT5B1cFzImnL02X8/bhb+IevguJA15QgABlzn2AvZPAa+srIy7x8XHwZkHRyyviS0nyEDADbxshoADChHADCgHAHAgHIEAAPKEQAMKEcAMKAcAcCAcgQAA8oRAAwoRwAw+AsI3PyTDc34OgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 414.176x84.28 with 1 Axes>"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qcb = QuantumCircuit(1)\n",
    "\n",
    "qcb.barrier()\n",
    "qcb0 = qcb.copy()\n",
    "qcb.x(0)\n",
    "\n",
    "qcb.barrier()\n",
    "qcb1 = qcb.copy()\n",
    "qcb.h(0)\n",
    "\n",
    "qcb.barrier()\n",
    "qcb2 = qcb.copy()\n",
    "qcb.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.+0.j 0.+0.j]\n",
      "[0.+0.j 1.+0.j]\n",
      "[ 0.70710678-8.65956056e-17j -0.70710678+8.65956056e-17j]\n"
     ]
    }
   ],
   "source": [
    "backend = Aer.get_backend('statevector_simulator')\n",
    "qcb_vec = []\n",
    "for qc in [qcb0,qcb1,qcb2]:\n",
    "    out = execute(qc,backend).result().get_statevector()\n",
    "    qcb_vec.append(out)\n",
    "    print(out)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\psi_{2q} = \\psi_{q} \\otimes \\psi_{q}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.+0.j 0.+0.j 0.+0.j 0.+0.j] | [1.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
      "[0.        +0.j 0.        +0.j 0.70710678+0.j 0.70710678+0.j] | [0.        +0.j 0.        +0.j 0.70710678+0.j 0.70710678+0.j]\n",
      "[-6.123234e-17-0.5j  6.123234e-17+0.5j  6.123234e-17+0.5j\n",
      " -6.123234e-17-0.5j] | [-6.123234e-17-0.5j  6.123234e-17+0.5j  6.123234e-17+0.5j\n",
      " -6.123234e-17-0.5j]\n"
     ]
    }
   ],
   "source": [
    "for qcv,qcav,qcbv in zip(qc_vec,qca_vec,qcb_vec):\n",
    "    print(qcv,\"|\", np.kron(qcbv,qcav))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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
}