Day 2.1 Quantum Circuits Continued.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "urE3_KHdCEpD"
   },
   "source": [
    "# Quantum circuits continued: Rotation operators, decompositions, controlled operations and more!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ewxZplcrCEpE"
   },
   "outputs": [],
   "source": [
    "from qiskit import *\n",
    "from qiskit.compiler import transpile, assemble\n",
    "from qiskit.tools.jupyter import *\n",
    "from qiskit.visualization import *\n",
    "import matplotlib.pyplot as plotter\n",
    "import numpy as np\n",
    "from IPython.display import display, Math, Latex\n",
    "%matplotlib inline\n",
    "# Loading your IBM Q account(s)\n",
    "provider = IBMQ.load_account()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "pOADMNPSCEpH"
   },
   "source": [
    "Congrats on completing Day 1! Let's start Day 2 by getting familiarised with a quantum gate, which you unknowingly utilised while solving yesterday's last question.\n",
    "\n",
    "## The Fredkin gate\n",
    "\n",
    "The Fredkin gate is the controlled swap gate, where the first qubit acts as the control qubit, meaning, it remains unchanged itself but swaps the other two \"target\" qubits if and only if the control qubit is set to $\\vert 1 \\rangle$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "vv6UF-8HCEpI"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 418.992x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc1 = QuantumCircuit(3,3)\n",
    "# All initialized to '0' by default.\n",
    "qc1.x(0) #This is for the purpose of setting the control qubit to '1'\n",
    "qc1.x(2) #As a result, the second target qubit becomes '1' while the first remains '0'. Now, lets's try swapping them.\n",
    "#Fredkin gate:\n",
    "def fredkin(qc):\n",
    "    qc.toffoli(0,1,2)\n",
    "    qc.toffoli(0,2,1)\n",
    "    qc.toffoli(0,1,2)\n",
    "fredkin(qc1)\n",
    "qc1.draw('mpl')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "3JvJj814CEpK"
   },
   "source": [
    "Now, let's observe the result obtained on measuring all three qubits by using a histogram."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "5k0qT9P_CEpK"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'011': 2000}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#First let's measure all three qubits.\n",
    "#We're using the classical bits to store the result obtained on measuring each corresponding qubit. \n",
    "qc1.measure(0,0)\n",
    "qc1.measure(1,1)\n",
    "qc1.measure(2,2)\n",
    "#Now we use the same function we defined yesterday to run a quantum circuit\n",
    "def run_circuit(qc2):\n",
    "    backend = Aer.get_backend('qasm_simulator') # we choose the simulator as our backend\n",
    "    result = execute(qc2, backend, shots = 2000).result() # we run the simulation\n",
    "    counts = result.get_counts() # we get the counts\n",
    "    return counts\n",
    "counts1=run_circuit(qc1)\n",
    "print(counts1)\n",
    "plot_histogram(counts1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "V0tqWk6_CEpN"
   },
   "source": [
    "Surprised to see the result to be $\\vert 011 \\rangle $ when it should be $\\vert 110 \\rangle $? Don't be. While representing the state of a multi-qubit system, the tensor order used in Qiskit is different than that used in most physics textbooks. Suppose there are $n$ qubits, and qubit $j$ is labelled as $Q_j$. Qiskit uses an ordering in which the $n$th qubit is on the left side of the tensor product, so that the basis vectors are labelled as $Q_{n-1}\\otimes \\cdots \\otimes Q_1\\otimes Q_0$.\n",
    "\n",
    "For example, if qubit zero is in state 1, qubit 1 is in state 1, and qubit 2 is in state 0, Qiskit would represent this state as $\\vert 011 \\rangle $, whereas many physics textbooks would represent it as $\\vert 110 \\rangle $.\n",
    "\n",
    "To observe the effect of the Fredkin gate, let's again make a similar circuit, this time initialising the control qubit to $\\vert 0 \\rangle$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "2a3h7krmCEpO"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 599.592x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc2 = QuantumCircuit(3,3)\n",
    "# All initialized to '0' by default.\n",
    "qc2.x(2) #The second target qubit is initialised to '1'\n",
    "fredkin(qc2)\n",
    "qc2.measure(0,0)\n",
    "qc2.measure(1,1)\n",
    "qc2.measure(2,2)\n",
    "qc2.draw('mpl')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "kTXAhz_0CEpQ"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'100': 2000}\n"
     ]
    },
    {
     "data": {
      "image/png": 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7P9vsPgr9AdVjyN4PfDcizsnM++sxx/Qz5zF9TRgRs6kXYpgwYQJLliwBYNKkSYwZM4bVq1cDMHbsWKZMmcLSpUsBGDVqFN3d3axatYrt27cD0Gg02Lx5M3DCoDsvSdq/Nm7cyJo1awCYOHEiXV1dLF++HIDRo0fTaDRYtmwZO3fuBKC7u5u1a9eyZcsWAKZOnbqnrz9Rrb2+/0XEBKpHiZ2TmUub2q8G3peZJxXOswh4LjMvrD/vAj6QmQubxswAFmTmSweaq9FoZE9Pz0BDisy6fp+nkCTtowVXDs08EbEyMxt99e3t4gZvA15Hddr2kcxcUrDZVqono4zr1T4O2NTC1y8H3tv0edMQzClJ0qBauhAoIiZGxArgXqrHgX2M6nTp8vpIsl+ZuQtYCUzv1TWd6iraUqdQnbbdbdkQzClJ0qBaPdL8G6qjxcmZ+RhAREwCbq/73j3I9tcBt9XB+wAwh+qRYjfVcy0EyMwZ9ecrgZ8Bj1D9pnkZ8E7g4qY5bwCWRsTHgG8A7wLeCnS3uG+SJA2o1dCcDkzbHZgAmfloRMwDvjvYxpl5R70U3yeo7rd8GDg/M9fXQ3rfr3kI8DmgC9hBFZ4XZOaipjkfjIj3AtdQ3fbyU+CSzFze4r5JkjSgvflNs68rh4qvJsrMG4Eb++mb1uvzZ4HPFsx5J0N3la8kSX1qdXGD7wJfiIhjdzfUq/lcT8GRpiRJL2athuY84OXAoxGxPiLWU50OfXndJ0nSAavV07O/AN4MTAN2L5r+k8z8zlAWJUlSOyoOzYg4GPgV8IbMvJfqthNJkjpG8enZepH09VRXtEqS1HFa/U3zvwF/FRFH7Y9iJElqZ63+pvlRqqecbIiIx+n1bM3MPHmoCpMkqd20Gpp3Ut2TGfuhFkmS2lpRaEbEYVQr87wTeAnVPZlXZObW/VeaJEntpfQ3zfnATODbwFeonn/59/upJkmS2lLp6dmLgD/JzP8FEBFfBh6IiIPrq2olSTrglR5pHgvcv/tDZq4AnqN6QokkSR2hNDQPBnb1anuOvXyItSRJL0aloRfA7RGxs6ntUGBBRDy9uyEzLxzK4iRJaieloXlrH223D2UhkiS1u6LQzMw/3t+FSJLU7lpdRk+SpI5laEqSVMjQlCSpkKEpSVIhQ1OSpEKGpiRJhQxNSZIKGZqSJBUyNCVJKmRoSpJUyNCUJKmQoSlJUiFDU5KkQoamJEmFDE1JkgoZmpIkFTI0JUkqZGhKklTI0JQkqZChKUlSIUNTkqRChqYkSYUMTUmSChmakiQVMjQlSSpkaEqSVMjQlCSpkKEpSVIhQ1OSpEKGpiRJhYY9NCPigxHxWEQ8ExErI+KsAcZeFBGLI+LJiPh1RCyPiAt7jZkZEdnH69D9vzeSpE4yrKEZEZcANwDXAqcCDwJ3RcRx/WxyDvA94IJ6/CLg630E7dPA+OZXZj4z9HsgSepko4b5+64CbsnMBfXnKyLiD4G5wMd7D87MD/dqmh8RFwDvBO7//4fmpv1QryRJewzbkWZEHAK8CVjcq2sxcGYLU40BtvVqe1lErI+IxyPinyPi1H0oVZKkPg3nkeZRwMHA5l7tm4G3l0wQEf8F6AJua2peA1wOrKYK1A8DD0TEGzJzXR9zzAZmA0yYMIElS5YAMGnSJMaMGcPq1asBGDt2LFOmTGHp0qUAjBo1iu7ublatWsX27dsBaDQabN68GTihpHxJ0n60ceNG1qxZA8DEiRPp6upi+fLlAIwePZpGo8GyZcvYuXMnAN3d3axdu5YtW7YAMHXq1D19/YnM3I+70PRFEROADcA5mbm0qf1q4H2ZedIg219MFZaXZOa3Bhh3MPCvwH2ZOW+gORuNRvb09JTvRD9mXb/PU0iS9tGCK4dmnohYmZmNvvqG80KgrcDzwLhe7eOAAX+PjIh3UwXmjIECEyAznwd6gBP3vlRJkl5o2EIzM3cBK4HpvbqmU11F26eIeA9VYM7MzDsH+56ICOBkYOPeVytJ0gsN99Wz1wG3RcQK4AFgDjABuAkgIhYCZOaM+vN7qQLzo8DSiDimnmdXZj5Vj/kL4CFgHXA4MI8qNOcO0z5JkjrEsIZmZt4REWOBT1DdT/kwcH5mrq+H9L5fcw5VjdfXr92+D0yr378SuBk4BvgV8C/A2Zm5Ysh3QJLU0Yb7SJPMvBG4sZ++aQN97mebjwAfGYraJEkaiGvPSpJUyNCUJKmQoSlJUiFDU5KkQoamJEmFDE1JkgoZmpIkFTI0JUkqZGhKklTI0JQkqZChKUlSIUNTkqRChqYkSYUMTUmSChmakiQVMjQlSSpkaEqSVMjQlCSpkKEpSVIhQ1OSpEKGpiRJhQxNSZIKGZqSJBUyNCVJKmRoSpJUyNCUJKmQoSlJUiFDU5KkQoamJEmFDE1JkgoZmpIkFTI0JUkqZGhKklTI0JQkqZChKUlSIUNTkqRChqYkSYUMTUmSChmakiQVMjQlSSpkaEqSVMjQlCSpkKEpSVIhQ1OSpEKGpiRJhYY9NCPigxHxWEQ8ExErI+KsQcafU497JiIejYg5+zqnJEl7Y1hDMyIuAW4ArgVOBR4E7oqI4/oZ/xpgUT3uVOAzwBci4uK9nVOSpL013EeaVwG3ZOaCzPxJZl4BbATm9jN+DvBEZl5Rj18A3Ap8dB/mlCRprwxbaEbEIcCbgMW9uhYDZ/az2Rl9jL8HaETES/ZyTkmS9sqoYfyuo4CDgc292jcDb+9nm2OA7/QxflQ9X7Q6Z0TMBmbXH38TEWtKipc6wFHA1pEuQtpb//iRIZvq1f11DGdotoXMvBm4eaTrkNpNRPRkZmOk65Da2XCG5lbgeWBcr/ZxwKZ+ttnUz/jn6vliL+aUJGmvDNtvmpm5C1gJTO/VNZ3qite+LOtnfE9mPruXc0qStFeG+/TsdcBtEbECeIDq6tgJwE0AEbEQIDNn1ONvAj4UEdcD/wC8BZgJXFo6p6Ri/mwhDWJYQzMz74iIscAngPHAw8D5mbm+HnJcr/GPRcT5wP+guoXkCWBeZn6thTklFah/75c0gMjMka5BkqQXBdeelSSpkKEpSVIhQ1OSpEKGpiRJhQxNSUSE/xZIBbx6VpKkQh239qyk34uIY4HLgdOAnwJrgEeAH2bmtoiI9H/W0h4eaUodqn7I+9eAlwE/AKZSrdv8C+B+4LrM/OnIVSi1H0NT6lARcRMwEZiVmZvqtuOolqn8IHAY8IHM/ObIVSm1F0NT6lARcT/wzcz8fES8BMjMfK6p/yvAK4EL6j7/sVDH84o5qXN9F7gsIsbUTw16LiJeEhEvq/v/Dvh3wJsNTKliaEqd61vA0cD3I+JCgDo8d9T9W6lO3/5whOqT2o6nZ6UOtPuq2IiYDHwWOJ3fXwB0F/A64N3AY5n5npGrVGovhqbU4SLiUODtVA9vfzMwBXgKWADc7mP2pN8zNKUOU6/+8w7gVVS3m/wUuD8zf1UHaAJjMnPrCJYptSVDU+ogETEG+CLwVuB3wAYggKeB71AdWa6rxx6Umb8bqVqlduSKQFJnmQecBJyfmT+IiNcCDeAtwH8E3hgRl2fmkwam9EIeaUodpL438+uZeV2v9oOpgvOLwE8z8w9Hoj6p3XnLidQhImIU8DBwcUS8qm47uD4N+3xmLgXmAF0R8YaRrFVqV4am1CHq1X5uBY4BPhoR4+qwbD4NuxY4nuoeTUm9eHpW6hD1VbMHAX8MXEt1TcPXgDuAfwNOpvpd83WZedpI1Sm1M0NT6kAR8UpgJvCfgFOAXwPPUD3t5DOZuXykapPamaEpdYCIOBz4dfMasvWR56HAaKrHgv3WsJQGZmhKHSAi/gFYUb/WZ+b2PsYc4YOnpYEZmtIBLiIuBb4MbKdaHu9e4B6qhdg3ZOaOiBgN3A58MjN/NGLFSm3O0JQOcBGxAHieamH2i4A/Ak4A1gCLqB4RdhJwQ2YeMlJ1Si8GhqZ0AKvvzfwz4PDM/FhT+xRgFtWTTA6letj0rZn5JyNRp/RiYWhKB7iIOAIYl5n/NyIOAZ7tdUHQJcBXgDdm5r+OUJnSi4Jrz0oHuMzcBmyr3++CPVfORmY+DxwOPGNgSoMzNKUO1GsVoDHAX4xULdKLiadnpQ4XES8Bei+nJ6kPhqYkSYVcsF2SpEKGpiRJhQxNSZIKGZqSJBUyNCVJKvT/AO0unVT/wBGfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counts2=run_circuit(qc2)\n",
    "print(counts2)\n",
    "plot_histogram(counts2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "T4xySn3BCEpS"
   },
   "source": [
    "This time the control qubit remains the same like last time, but so do the target qubits, because the control qubit was set to $\\vert 0 \\rangle$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Ul6GSapECEpS"
   },
   "source": [
    "## The Rotation Operators\n",
    "\n",
    "To bring about rotations in the Bloch sphere, we have the rotation operators where we can specify the angle of rotation about each axis. These operators are defined for each Pauli matrix $P=\\{ X, Y, Z \\}$ as follows $$R_P(\\theta)\\equiv e^\\frac{-i\\theta P}{2}=\\cos\\frac{\\theta}{2}I-i\\sin\\frac{\\theta}{2}P$$\n",
    "\n",
    "Hence, the following are the Rotation operators about the $\\hat{x}, \\hat{y}$ and $\\hat{z}$ axes:\n",
    "\n",
    "$$R_x(\\theta)=\\begin{bmatrix}\n",
    "\\cos\\frac{\\theta}{2} & -i\\sin\\frac{\\theta}{2}\\\\\n",
    "-i\\sin\\frac{\\theta}{2} & \\cos\\frac{\\theta}{2}\n",
    "\\end{bmatrix} , \n",
    "R_y(\\theta)=\\begin{bmatrix}\n",
    "\\cos\\frac{\\theta}{2} & -\\sin\\frac{\\theta}{2}\\\\\n",
    "\\sin\\frac{\\theta}{2} & \\cos\\frac{\\theta}{2}\n",
    "\\end{bmatrix} , \n",
    "R_z(\\theta)=\\begin{bmatrix}\n",
    "e^\\frac{-i\\theta}{2} & 0\\\\\n",
    "0 & e^\\frac{i\\theta}{2}\n",
    "\\end{bmatrix}$$ \n",
    "\n",
    "If we want to bring about a rotation around an arbitrary axis, say, $\\hat{n} =(n_x,n_y,n_z)$ which is a real unit vector, then we define a rotation by an angle $\\theta$ about the $\\hat{n}$ axis by the operator\n",
    "$$R_{\\hat{n}}(\\theta)\\equiv \\exp(-i\\theta \\hat{n}\\cdot \\vec{\\sigma}/2)=\\cos\\left(\\frac{\\theta}{2}\\right)I-i\\sin\\left(\\frac{\\theta}{2}\\right)(n_x X+n_y Y+n_z Z)$$\n",
    "where $\\vec{\\sigma}$ denotes the three component vector $(X,Y,Z)$ of Pauli matrices.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "cDu6MGTUCEpU"
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJEAAABOCAYAAAAgsPTZAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy86wFpkAAAACXBIWXMAAAsTAAALEwEAmpwYAAAFRklEQVR4nO3df0zUdRzH8df3TuSHiHbe5KeiFz+Km0dy2aYryZJlrqX9EKfJH8gGoc4gWrVcWxt1NaMfS0OnudlysoKZZf7YdMlNt2pHbCCWHInEnWLIEOyUMO6uP5q3Mdus3t8fA16PjQ2+x/i+jz33uS/f75edEg6HwyASMBk9AI19jIjEGBGJMSISY0QkxohIjBGRGCMiMUZEYoyIxBgRiTEiEmNEJMaISIwRkRgjIjFGRGKMiMQYEYkxIhJjRCTGiEiMEZEYIyIxRkRijIjEGBGJMSISm2T0AGPBiRpj9rv0JWP2+19xJSIxRkRijIjEeEykotXVKQjcuAqTyQyTyYyc2QtRuWo3Zk6fZfRomuJKpJK+wYvov9aD2opmHHorgM9e7cTA9V58cvgVo0fTHCNSSbvPg7iYBMyeeQ8AIGHKDGSk5mEg0GvwZNpjRCpp93mQnbYAiqIgGByB59wxuFs+xyPz1xo9muZ4TKSSdp8HbV2nsfL16Ri6GUBMVByqVu1Bfm6h0aNpTpeVKBQKoaamBpmZmYiJiUFubi7cbjeys7NRWlqqxwia6/A34bW1dThYPYD9W3ywTktDd+85o8fShS4RlZSUoLq6GmVlZTh69CgKCwuxZs0adHZ2wul06jGCpi72/YLfh64iMy0PADAjIRnP5lfhm+93IhQKAQDC4TA2b1uIS33n0Td4CZW1D+Fyf5eBU6tH85ezuro67N27F42NjcjPzwcALFmyBM3NzThw4ADy8vK0HkFz7T4PpsZZkHhXemTbIvsKfNhQirau03DYFkNRFKx/3IWdh17EjeFrqHhmF5Isc4wbWkWar0QulwvLli2LBHRLRkYGoqKi4HA4tB5Bc16fBxkp80dtmzbFipw5i3CqtSGyzZbsQNuFU3hswXqkJ96r95ia0XQl8vv9aGtrQ2Vl5W2PdXd3w263Izo6WssRdPH8k+//4/YPNpyKfD40HMCb+1Zjw4qPcMyzBwXOIr3G05ymK5Hf7wcAJCUljdo+NDQEt9ut+kuZoiiafEjdHBlG9b5CrH10C5Y61yHZYsPpM18a9nzUft6arkRWqxUA4PV6sXz58sj2rVu3oqenZ1wcVP8bkydFw1VyJPJ1VeEeA6dRn6YR2Ww2OBwOuFwuWCwWpKamoqGhAUeO/P0LVTsird7rxqj7icbKe/do+nJmMplQX18Pu92O8vJyFBcXw2q1YuPGjTCbzePioJp0+BM/KysLJ0+eHLWtqKgIOTk5iI2N1Xr3pANDrp01NTVNmOOhiUD3iAKBALxe77g4yXgnfYMXUftVBX7u/gEvbF+Eio8fxI6vbz/dMdbpfgE2Pj4ewWBQ790a4kfvcTizCpA4PR3vln2LyVExeHv/c7jQcwZzk+cZPZ5qeBVfJS3nG/HGp0/BlpyLy/0XcHfKfZgaZ8GmldsQGx0f+T6zKQomk9nASdXH+4lUMm/uYmTPegDvlTfCYcvH5qdr8cfN66MC6rzUisHrV5CemGPgpOpjRCrp6e9EssUGALgy6MNA4ApsKbmRx6/d6Mf2g5tQtWp8nWgEGJFqfr18FulJdgRDQSiKCc0dx+HMLAAABIMjeKduHUqfqIElIekOP2nsYUQq6frtLOYk2vHnyDAGAr1o7jiBrLT7AQDu1np4fR7sPvwyqnY8jJ+6vjN4WnUp4bFybt1A/+eyh7vlC/Gtsfw36gluItxbfQtXIhLjSkRijIjEGBGJMSISY0QkxohIjBGRGCMiMUZEYoyIxBgRiTEiEmNEJMaISIwRkRgjIjFGRGKMiMQYEYn9BZiBZJRBgIdPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 173.376x84.28 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(1)\n",
    "#This is how we apply the rotation operators in Qiskit, mentioning the angle of rotation and qubit no. as parameters\n",
    "qc.rx(np.pi/2,0) \n",
    "qc.draw('mpl')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "9H5OY1SNCEpX"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.707+0.j    0.   -0.707j]\n"
     ]
    }
   ],
   "source": [
    "def final_vector(qc):\n",
    "    backend = Aer.get_backend('statevector_simulator')\n",
    "    job = execute(qc, backend)\n",
    "    result = job.result()\n",
    "    outputstate = result.get_statevector(qc, decimals=3)\n",
    "    return outputstate\n",
    "print(final_vector(qc))\n",
    "# This prints the vector obtained on applying the above gate to the qubit state '0'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "-y1XNzfOCEpZ"
   },
   "source": [
    "## **Your Task:**\n",
    "1) Find a gate, say '$Q$', such that for any angle $\\theta$, $$QR_y(\\theta)Q=R_y(-\\theta).$$ (**2 points**)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "0J9VyxXXCEpa"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.154+0.j 0.988+0.j]\n",
      "[0.154+0.j 0.988+0.j]\n"
     ]
    }
   ],
   "source": [
    "qc3=QuantumCircuit(1)\n",
    "#your code here\n",
    "theta = 60\n",
    "qc3.x(0)        # Both X gate and Z gate works\n",
    "qc3.ry(theta,0) # Enter an angle of your choice\n",
    "qc3.x(0)\n",
    "print(final_vector(qc3))\n",
    "\n",
    "qc3=QuantumCircuit(1)\n",
    "qc3.ry(-theta,0)\n",
    "print(final_vector(qc3))\n",
    "#Run this code for different values of theta and see if the two vectors printed are equal in each case"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "hyon_FBiCEpc"
   },
   "source": [
    "The significance of the Rotation operators is further highlighted when we understand that any unitary operation for a single qubit can be decomposed into rotations about two of the coordinate axes by some angle each, along with a global phase factor, which is what's stated in the following theorem.\n",
    "\n",
    "### **Theorem:** $Z-Y$ decomposition for a single qubit\n",
    "**Suppose $U$ is a unitary operation on a single qubit. Then there exist real numbers $\\alpha, \\beta, \\gamma$ and $\\delta$ such that\n",
    "$$U=e^{i\\alpha}R_z(\\beta)R_y(\\gamma)R_z(\\delta).$$**\n",
    " **Proof:**\n",
    " Since $U$ is unitary, its rows and columns are orthonormal, so it can be expressed as follows\n",
    " $$U=\\begin{bmatrix}\n",
    "e^{i(\\alpha-\\beta/2-\\delta/2)}\\cos\\frac{\\gamma}{2} & -e^{i(\\alpha-\\beta/2+\\delta/2)}\\sin\\frac{\\gamma}{2}\\\\\n",
    "e^{i(\\alpha+\\beta/2-\\delta/2)}\\sin\\frac{\\gamma}{2} & e^{i(\\alpha+\\beta/2+\\delta/2)}\\cos\\frac{\\gamma}{2}\n",
    "\\end{bmatrix}$$\n",
    "By multiplying the matrices mentioned in the theorem, we obtain the exact form for $U$ as above.\n",
    "\n",
    "\n",
    "\n",
    "### **Corollary:**\n",
    "**Suppose $U$ is a unitary gate on a single qubit. Then there exist unitary operators $A,B,C$ on a single qubit such that $ABC = I$ and $U = e^{i\\alpha}AXBXC$, where $\\alpha$ is some overall phase factor.**\n",
    "\n",
    "**Proof:**\n",
    "Set $$A=R_z(\\beta)R_y(\\gamma/2) ,  B=R_y(-\\gamma/2)R_z(-(\\delta+\\beta)/2) ,  C=R_z((\\delta-\\beta)/2).$$\n",
    "This assignment satisfies all the identities mentioned in the corollary.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "uolK2oUJCEpc"
   },
   "source": [
    "## Your Task\n",
    "2) Find out $A, B, C$, and $\\alpha$ for the Hadamard gate and show that both representations are identical, by printing the final vectors on applying both transformations on the same initial state. (**2 points**)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 3/2*pi\n",
    "beta = 2*pi\n",
    "gamma = pi/2\n",
    "delta = pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "pe34KpZ8CEpd"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.707+0.j 0.707-0.j]\n",
      "[0.707+0.j 0.707+0.j]\n"
     ]
    }
   ],
   "source": [
    "qc4 = QuantumCircuit(1)\n",
    "qc4.rz((delta-beta)/2,0) # C\n",
    "qc4.x(0)                 # X\n",
    "qc4.rz(-(delta+beta)/2,0)# B\n",
    "qc4.ry(-gamma/2,0)\n",
    "qc4.x(0)                 # X\n",
    "qc4.ry(gamma/2,0)        # A\n",
    "qc4.rz(beta,0)\n",
    "qc4.u1(alpha, 0)         # To shift phase by alpha\n",
    "qc4.x(0)\n",
    "qc4.u1(alpha, 0)\n",
    "qc4.x(0)   \n",
    "print(final_vector(qc4))\n",
    "\n",
    "# Apply the Hadamard gate and see if both operations are identical\n",
    "qc4 = QuantumCircuit(1)\n",
    "qc4.h(0)\n",
    "print(final_vector(qc4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Mi9xauFDCEpf"
   },
   "source": [
    "## Controlled operations\n",
    "We will now see how to implement the controlled-$U$ operation for an arbitrary single qubit operation $U$, using only single qubit operations and the CNOT gate. \n",
    "\n",
    "A controlled $U$ operation is a two qubit operation, again with a control and a target qubit. If the control qubit is set to $\\vert 1 \\rangle$, then $U$ is applied to the target qubit, otherwise the target qubit is left alone.\n",
    "\n",
    "To achieve our goal, we first decompose it as done in the above corollary. The following is the circuit for implementing the controlled-$U$ operation.\n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/mnp-club/Quantum_Computing_Workshop_2020/master/images/contabc.jpg\" width = \"600\" height = \"400\"></img>\n",
    "\n",
    "We now explain how the above circuit works. Suppose that the control qubit is set. Then the operation $U = e^{i\\alpha}AXBXC$ is applied to the second qubit. If, on the other hand, the control qubit is not set, then the operation $ABC = I$ is applied to the second qubit; that is, no change is made. Hence, this circuit implements the controlled-$U$ operation. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "gkNFupmaCEpf"
   },
   "source": [
    "## Your Task\n",
    "3) Using the decomposition from the second task, your work here is to simply type out the code for implementing the controlled Hadamard gate using only single qubit and CNOT gates. Plot a histogram for the result obtained after applying your gate to two qubits initialised to $\\vert 1\\rangle$ and $\\vert 0\\rangle$ respectively. (You should also change the control qubit to '0' and observe the result obtained in that case.) (**2 points**) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "pzg74J2aCEpf"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 960.792x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc5 = QuantumCircuit(3,3)\n",
    "qc5.x(0)                 # 0 is control qubit, initialised to |1⟩\n",
    "qc5.x(2)                 # 1 is initialised to |0⟩ and 2 is initialised to |1⟩\n",
    "# Controlled Hadamard to |0⟩\n",
    "qc5.rz((delta-beta)/2,1) # C\n",
    "qc5.cx(0,1)\n",
    "qc5.rz(-(delta+beta)/2,1)# B\n",
    "qc5.ry(-gamma/2,1)\n",
    "qc5.cx(0,1)\n",
    "qc5.ry(gamma/2,1)        # A\n",
    "qc5.rz(beta,1)\n",
    "qc5.u1(alpha, 0)\n",
    "# Controlled Hadamard to |1⟩\n",
    "qc5.rz((delta-beta)/2,2) # C\n",
    "qc5.cx(0,2)\n",
    "qc5.rz(-(delta+beta)/2,2)# B\n",
    "qc5.ry(-gamma/2,2)\n",
    "qc5.cx(0,2)\n",
    "qc5.ry(gamma/2,2)        # A\n",
    "qc5.rz(beta,2)\n",
    "qc5.u1(alpha, 0)\n",
    "qc5.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'011': 1249, '001': 1221, '111': 1246, '101': 1284}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc5.measure(0,0) # Measure first qubit and store it in first classical bit \n",
    "qc5.measure(1,1) # Measure second qubit and store it in second classical bit\n",
    "qc5.measure(2,2) # Measure third qubit and store it in third classical bit\n",
    "# The code below plots a histogram of the measurement result. You can copy it for further use.\n",
    "def run_circuit(qc):\n",
    "    backend = Aer.get_backend('qasm_simulator') # we choose the simulator as our backend\n",
    "    result = execute(qc, backend, shots = 5000).result() # we run the simulation\n",
    "    counts = result.get_counts() # we get the counts\n",
    "    return counts\n",
    "\n",
    "counts = run_circuit(qc5)\n",
    "print(counts)\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "QbzDzB_rCEpi"
   },
   "source": [
    "## U3 gate\n",
    "U3 gate is a single qubit rotation gate, whose function takes the parameters ($\\theta, \\phi, \\lambda$, qubit). The matrix representation of the gate is:\n",
    "$$U3(\\theta, \\phi, \\lambda)=\\begin{bmatrix}\n",
    "\\cos\\frac{\\theta}{2} & -e^{i\\lambda}\\sin\\frac{\\theta}{2}\\\\\n",
    "e^{i\\phi}\\sin\\frac{\\theta}{2} & e^{i(\\phi+\\lambda)}\\cos\\frac{\\theta}{2}\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "For example, we observe that $U3(\\theta, -\\pi/2, \\pi/2)=R_x(\\theta)$.\n",
    "\n",
    "Let us verify this by applying both gates on a state vector for $\\theta=\\pi/6$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "zbP_aIKwCEpi"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.966+0.j    0.   -0.259j]\n",
      "[0.966+0.j    0.   -0.259j]\n"
     ]
    }
   ],
   "source": [
    "qc_u3=QuantumCircuit(1)\n",
    "qc_u3.u3(np.pi/6,-np.pi/2,np.pi/2,0)\n",
    "print(final_vector(qc_u3))\n",
    "\n",
    "qc_rx=QuantumCircuit(1)\n",
    "qc_rx.rx(np.pi/6,0)\n",
    "print(final_vector(qc_rx))\n",
    "#Getting the same results will verify our observation stated above"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "FHFvscfVCEpl"
   },
   "source": [
    "### Conditioning on multiple qubits\n",
    "Suppose we have $n + k$ qubits, and $U$ is a $k$ qubit unitary operator. Then we define the controlled operation $C^n(U)$ by the equation $$C^n(U)\\vert x_1x_2\\dots x_n\\rangle \\vert\\psi\\rangle=\\vert x_1x_2\\dots x_n\\rangle U^{x_1x_2\\cdots x_n}\\vert\\psi\\rangle.$$ This basically means the operation $U$ will be applied to the $k$ target qubits if and only if all the $n$ control qubits are set to '1'.\n",
    "\n",
    "Given below is the circuit for the $C^2(U)$ gate. $V$ is any unitary operator satisfying $V^2 = U$.\n",
    "<img src=\"https://raw.githubusercontent.com/mnp-club/Quantum_Computing_Workshop_2020/master/images/contv.jpg\" width = \"600\" height = \"400\"></img>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "BLXTz6CsCEpl"
   },
   "source": [
    "We encourage you to type out the explanation for the above circuit in this cell, just as we did in the case of controlled-$U$ operation.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "fwsWO6FGCEpl"
   },
   "source": [
    "## Your Task\n",
    "4) Implement the $C^4(H)$ gate using only single qubit and CNOT gates. \n",
    "\n",
    "**Hint:** Finding the gate $V$ satisfying $V^2=X$ **might** just prove to be useful, and you're free to use ancilla qubits (additional qubits used in intermediate stages), there is no restriction on the number of qubits to be used.\n",
    "\n",
    " (**4 points**)"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "jUTlPsvTCEpm"
   },
   "outputs": [],
   "source": [
    "def toffoliGate(qc,a,b,t):\n",
    "    qc.h(t)\n",
    "    qc.cx(b,t)\n",
    "    qc.tdg(t)\n",
    "    qc.cx(a,t)\n",
    "    qc.t(t)\n",
    "    qc.cx(b,t)\n",
    "    qc.tdg(t)\n",
    "    qc.cx(a,t)\n",
    "    qc.t(b)\n",
    "    qc.t(t)\n",
    "    qc.h(t)\n",
    "    qc.cx(a,b)\n",
    "    qc.t(a)\n",
    "    qc.tdg(b)\n",
    "    qc.cx(a,b)"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cHGate(qc,a,t):\n",
    "    qc.sdg(t)\n",
    "    qc.h(t)\n",
    "    qc.tdg(t)\n",
    "    qc.cx(a,t)   \n",
    "    qc.t(t)\n",
    "    qc.h(t)\n",
    "    qc.s(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def c4HGate(qc,a,b,c,d,t,ancilla):\n",
    "    toffoliGate(qc,a,b,ancilla[0])\n",
    "    toffoliGate(qc,c,ancilla[0],ancilla[1])\n",
    "    toffoliGate(qc,d,ancilla[1],ancilla[2])\n",
    "    cHGate(qc,ancilla[2],t)\n",
    "    toffoliGate(qc,d,ancilla[1],ancilla[2])\n",
    "    toffoliGate(qc,c,ancilla[0],ancilla[1])\n",
    "    toffoliGate(qc,a,b,ancilla[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "qc6 = QuantumCircuit(10,5)\n",
    "for i in range(4):\n",
    "    qc6.x(i)\n",
    "ancillaBits = [7,8,9]\n",
    "c4HGate(qc6,0,1,2,3,4,ancillaBits) # 4th bit is target bit\n",
    "#qc6.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'01111': 2458, '11111': 2542}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc6.measure(0,0) # Measure first qubit and store it in first classical bit \n",
    "qc6.measure(1,1) # Measure second qubit and store it in second classical bit\n",
    "qc6.measure(2,2) # Measure third qubit and store it in third classical bit\n",
    "qc6.measure(3,3) # Measure fourth qubit and store it in fourth classical bit\n",
    "qc6.measure(4,4) # Measure target qubit and store it in target classical bit\n",
    "# The code below plots a histogram of the measurement result. You can copy it for further use.\n",
    "def run_circuit(qc):\n",
    "    backend = Aer.get_backend('qasm_simulator') # we choose the simulator as our backend\n",
    "    result = execute(qc, backend, shots = 5000).result() # we run the simulation\n",
    "    counts = result.get_counts() # we get the counts\n",
    "    return counts\n",
    "\n",
    "counts = run_circuit(qc6)\n",
    "print(counts)\n",
    "plot_histogram(counts)"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "Day 2.1 Quantum Circuits Continued.ipynb",
   "provenance": []
  },
  "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": "3.7.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}