reference/tools/quantum_gates_and_linear_algebra.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"../../images/QISKit.gif\" alt=\"Note: In order for images to show up in this jupyter notebook you need to select File => Trusted Notebook\" width=\"250 px\" align=\"left\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## _*Basic Quantum Operations*_ \n",
    "\n",
    "The latest version of this notebook is available on https://github.com/QISKit/qiskit-tutorial.\n",
    "\n",
    "***\n",
    "### Contributors\n",
    "Jay Gambetta, Rudy Raymond and Ali Javadi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the first notebook we did not describe the operations just showed you how to make a quantum circuit and run it. Now its time to learn what each of them do. In this notebook we will go into the different operations that are available  in QISKit-core. These are:\n",
    "* Single-qubit quantum gates\n",
    "* Multi-qubit quantum gates\n",
    "* Measurements\n",
    "* Reset\n",
    "* Conditionals\n",
    "* State initialization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "try:\n",
    "    sys.path.append(\"../../\") # go to parent dir\n",
    "    import Qconfig\n",
    "    qx_config = {\n",
    "        \"APItoken\": Qconfig.APItoken,\n",
    "        \"url\": Qconfig.config['url']}\n",
    "except:\n",
    "    qx_config = {\n",
    "        \"APItoken\":\"YOUR_TOKEN_HERE\",\n",
    "        \"url\":\"https://quantumexperience.ng.bluemix.net/api\"}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "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": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister\n",
    "from qiskit import QuantumProgram\n",
    "from qiskit.backends import discover_local_backends, discover_remote_backends\n",
    "from qiskit.tools.visualization import circuit_drawer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Single Qubit Quantum states\n",
    "\n",
    "A single qubit quantum state can be written as\n",
    "\n",
    "$$|\\psi\\rangle = \\alpha|0\\rangle + \\beta |1\\rangle$$\n",
    "\n",
    "\n",
    "where $\\alpha$ and $\\beta$ are complex numbers. In a measurement the probability of the bit being in $|0\\rangle$ is $|\\alpha|^2$ and $|1\\rangle$ is $|\\beta|^2$. As a vector this is\n",
    "\n",
    "$$\n",
    "|\\psi\\rangle =  \n",
    "\\begin{pmatrix}\n",
    "\\alpha \\\\\n",
    "\\beta\n",
    "\\end{pmatrix}.\n",
    "$$\n",
    "\n",
    "Note due to conservation probability $|\\alpha|^2+ |\\beta|^2 = 1$ and since global phase is undetectable $|\\psi\\rangle := e^{i\\delta} |\\psi\\rangle$ we only requires two real numbers to describe a single qubit quantum state.\n",
    "\n",
    "A convenient representation is\n",
    "\n",
    "$$|\\psi\\rangle = \\cos(\\theta/2)|0\\rangle + \\sin(\\theta/2)e^{i\\phi}|1\\rangle$$\n",
    "\n",
    "where $0\\leq \\phi < 2\\pi$, and $0\\leq \\theta \\leq \\pi$.  From this it is clear that there is a one-to-one correspondence between qubit states ($\\mathbb{C}^2$) and the points on the surface of a unit sphere ($\\mathbb{R}^3$). This is called the Bloch sphere representation of a qubit state.\n",
    "\n",
    "Quantum gates/operations are usually represented as matrices. A gate which acts on a qubit is represented by a $2\\times 2$ unitary matrix $U$. The action of the quantum gate is found by multiplying the matrix representing the gate with the vector which represents the quantum state.\n",
    "\n",
    "$$|\\psi'\\rangle = U|\\psi\\rangle$$\n",
    "\n",
    "A general unitary must be able to take the $|0\\rangle$ to the above state. That is \n",
    "\n",
    "$$\n",
    "U = \\begin{pmatrix}\n",
    "\\cos(\\theta/2) & a \\\\\n",
    "e^{i\\phi}\\sin(\\theta/2) & b \n",
    "\\end{pmatrix}\n",
    "$$ \n",
    "\n",
    "where $a$ and $b$ are complex numbers constrained such that $U^\\dagger U = I$ for all $0\\leq\\theta\\leq\\pi$ and $0\\leq \\phi<2\\pi$. This gives 3 constraints and as such $a\\rightarrow -e^{i\\lambda}\\sin(\\theta/2)$ and $b\\rightarrow e^{i\\lambda+i\\phi}\\cos(\\theta/2)$ where $0\\leq \\lambda<2\\pi$ giving \n",
    "\n",
    "$$\n",
    "U = \\begin{pmatrix}\n",
    "\\cos(\\theta/2) & -e^{i\\lambda}\\sin(\\theta/2) \\\\\n",
    "e^{i\\phi}\\sin(\\theta/2) & e^{i\\lambda+i\\phi}\\cos(\\theta/2) \n",
    "\\end{pmatrix}.\n",
    "$$\n",
    "\n",
    "This is the most general form of a single qubit unitary."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Single-Qubit Gates\n",
    "\n",
    "The single-qubit gates available are:\n",
    "* u gates\n",
    "* Identity gate\n",
    "* Pauli gates\n",
    "* Cliffords gates\n",
    "* $C3$ gates\n",
    "* Standard rotation gates \n",
    "\n",
    "We have provided a backend: `local_unitary_simulator` to allow you to calculate the unitary matrices. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "q = QuantumRegister(\"q\", 1)\n",
    "c = ClassicalRegister(\"c\", 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### u gates\n",
    "\n",
    "In QISKit we give you access to the general unitary using the $u3$ gate\n",
    "\n",
    "$$\n",
    "u3(\\theta, \\phi, \\lambda) = U(\\theta, \\phi, \\lambda) \n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=367x97 at 0x151041B6A0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.u3(pi/2,pi/2,pi/2,q)\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.707+0.j   , -0.   -0.707j],\n",
       "       [ 0.   +0.707j, -0.707+0.j   ]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'], 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The $u2(\\phi, \\lambda) =u3(\\pi/2, \\phi, \\lambda)$ has the martix form\n",
    "\n",
    "$$\n",
    "u2(\\phi, \\lambda) = \n",
    "\\frac{1}{\\sqrt{2}} \\begin{pmatrix}\n",
    "1 & -e^{i\\lambda} \\\\\n",
    "e^{i\\phi} & e^{i(\\phi + \\lambda)}\n",
    "\\end{pmatrix}.\n",
    "$$\n",
    "\n",
    "This is a useful gate as it allows us to create superpositions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=313x97 at 0x1510CEB9B0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.u2(pi/2,pi/2,q)\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.707+0.j   , -0.   -0.707j],\n",
       "       [ 0.   +0.707j, -0.707+0.j   ]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'], 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The $u1(\\lambda)= u3(0, 0, \\lambda)$ gate has the matrix form\n",
    "\n",
    "$$\n",
    "u1(\\lambda) = \n",
    "\\begin{pmatrix}\n",
    "1 & 0 \\\\\n",
    "0 & e^{i \\lambda}\n",
    "\\end{pmatrix},\n",
    "$$\n",
    "\n",
    "which is a useful as it allows us to apply a quantum phase."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=247x97 at 0x1510D726A0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.u1(pi/2,q)\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.+0.j, 0.+0.j],\n",
       "       [0.+0.j, 0.+1.j]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'], 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The $u0(\\delta)= u3(0, 0, 0)$ gate is the identity matrix. It has the matrix form\n",
    "\n",
    "$$\n",
    "u0(\\delta) = \n",
    "\\begin{pmatrix}\n",
    "1 & 0 \\\\\n",
    "0 & 1\n",
    "\\end{pmatrix}.\n",
    "$$\n",
    "\n",
    "The identity gate does nothing (but can add noise in the real device for a period of time equal to fractions of the single qubit gate time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=247x97 at 0x1510E12DD8>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.u0(pi/2,q)\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.+0.j, 0.+0.j],\n",
       "       [0.+0.j, 1.+0.j]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'], 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Identity gate\n",
    "\n",
    "The identity gate is $Id = u0(1)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=120x36 at 0x1510ED0B38>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.iden(q)\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.+0.j, 0.+0.j],\n",
       "       [0.+0.j, 1.+0.j]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'], 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pauli gates\n",
    "\n",
    "#### $X$: bit-flip gate\n",
    "\n",
    "The bit-flip gate $X$ is defined as:\n",
    "\n",
    "$$\n",
    "X   =  \n",
    "\\begin{pmatrix}\n",
    "0 & 1\\\\\n",
    "1 & 0\n",
    "\\end{pmatrix}= u3(\\pi,0,\\pi)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKcAAABQCAIAAADz4/IaAAANhUlEQVR4nO2de0xT1x/Av20ptDxseQ18xXbDAXOsFIaMZEQwykQQgpPxCsxW9nCMERnZopmwLWwJm3MPndNla9FljMEEcR0o2YRESHjOosAQpgPl6ZRnLQVK+/vjZDf9ldLHbenF9H7+Or33PL6333vu+Z5zvvd7QW3DODs7wyrj0KFDVrhwO6Ivk0hYLFZ4eLhAICBaEAAApVKZmpq6fv16K7Rl01q3t7f38fFJTEwkWhAAgPn5eQBwcHCwQltUK7RBstqgKpVKdJdZk7m5OSu3SKIJ9eDBgy+//LKVW+VwOKdOnbJyoyQY1NHR0dHRUSu3GhQUdOLECSs3SoJBzLguEAh6enqampoIaZ2EGK3HxcW5u7uLRCJCWichRuv29vZpaWk///yzXC4nRAAbh7CZm1AonJ6ePn/+PFEC4GNycnJsbGxsbOz+/fvG5FcoFGP/sdKyGQ9hWufxeHw+XywWEyUAPsrKyry9vb29vdeuXfvPP//ozyyXyyMiIlD+s2fPWkdCYyBylUYoFNbX1xv871YVAoGAy+UCgFKp/OSTT/TkXFxcTE5Obm5uBoCcnJx33nnHSiIaAZFaT01Ntbe3Ly4uJlAGU6HT6fn5+SgtFouHh4eXy5mVlfXrr78CQFJS0ueff24l+YyDSK27ubnFx8cXFxerVCoCxTCV9PT0zZs3A8Dc3NyxY8d05iksLDxz5gwAbN++/dy5cxQKxaoiGoLgdXiBQHDnzp0rV64QK4ZJ0Gi0goIClD5z5sxSs+7s2bNHjx4FgMDAwMrKSnt7e2uLaAhjta5Wq2trazMyMrZu3bpjx44jR46MjIwAQF5enr+//5YtW/AtrUdFRW3YsOGRs+lSUlKeeuopAJDL5VpP78uXL2dmZgIAl8utqalZs2YNMSLqJzY2NiIiQv8m/ODgYEREhFZBFotVV1fn6+sLAAEBAbh3+I8cOcJgMCYmJnDXgBsul5udnY2vbFlZGfY/TE5OooPt7e3IU8PT07O3t9ekClG3OXHiBD55TMJwX79161ZISEh9fT0AODo6pqamFhYWZmZmymSyhISE3t5eANi6dSvu204gECgUitLSUtw1EMK+fft4PB4ATE1NnTx5EgD6+/tjYmJkMpmTk9Nvv/2Gxv5Viv6+Pjk5yeFwUM7w8PCRkRHsVElJCVbJt99+a86tFx4eHhISYk4N+DCnr6vV6gsXLqDLd3d3HxgYQI89Ozu7mpoaHLWtor6ek5PT398PAAcOHLhy5Yq3tzd2Kjk5+fHHH0dprb4+Pz8/OTlp/J0nFApbW1s7OzuNL7IaiI+PDw4OBoAHDx4EBgbevHkTAL777rtdu3YRLZoB9Gn9+vXraEVp8+bNX3/9tZ3d/7lbUSgUHx8fAGAymVu2bEEHOzo6oqKimEymq6srl8tFsxeDJCYmOjs7P3I2HQB8+OGHKDExMQEARUVF1ndWwIE+vzlsMnr69Gmd/lzd3d0AEBwcjG6I9vb2yMhIKpWam5vr6upaUVHx+uuvDw0NYX/Ncjg5OSUmJpaUlBw7dgz31FYqlfb19ZlU5OHDh7Ozs/iaQ+zevZvH43V0dABAZmam+Qtw165dKy8vNz7/zZs3N23axGAwjC9CpVKXHdeVSiWLxQKAwMBAnWPD4OAgqiU3N1etVqtUKh6Px2QypVIpVsPOnTtpNFpnZ6fBkSYtLW3jxo1mDFXqsLAwk/5fRFhYmDmNXrhwgUajoapiY2PNqUqhUOCQHx/L9vW2trapqSkAiIyM1JkB84lAg7pUKu3o6MjOzkaWLQDQaLSioqKgoKCioqJz587pEWJqaqqioiI3NxffNSD++OMPtIRgPBEREWhgxkdjY2NKSsri4iL6KZFImpubQ0ND8dWGHnIFBQUZGRnGl5qbmzPVrdbe3n5ZrQ8MDKDEunXrdGbAtI6u89KlSwDwwgsvaObh8/menp5Xr17VL0dpaens7Oz+/fuNFVwXTCYTsy6NxM7ODveA0t3dvWfPntnZWT8/v1deeeXtt98GgPz8/MuXL+OrEOHh4WHqVeBgWWvuwYMHKIHslKUgrXt6eqKp3e+//w4AAQEBWtl8fX37+/v1u+aJRKJt27Yh2/CRYHBwcNeuXRMTE4899lh1dXV2dvaGDRsAoLa2tqGhgWjpDLOs1j09PVECmSpaDA4OtrS0gMacDT1dl766gfYl9dhZXV1dLS0tQqHQNMGJY3JyMjo6+u7du0wm8+LFi1wul06nHzp0CJ1FK/CrnGW1ji0tVVdXS6VSzVNyuVwgECAvekzrU1NTVCoVM20wmEwmADx8+HC5hkQikYuLy759+/CIb3UUCkVcXFxnZyeVSv3xxx+xUfzVV191dXUFgPr6+rq6OkJlNMyyWufxeM888wwAqNXq6Ojo6urqubm58fHxysrK0NBQ9DwHDa1PT09rTegR6KBMJtPZysLCwg8//JCcnOzo6GjmlVgBlUqVmpqKzJTjx48nJCRgp5ydnbOyslB69Xd3fas077//PpVKBYDR0dGYmBgXFxcPD4+9e/c6OztjyzIhISEowWAwlErl0koWFhbgvx6/FIlE8u+//z4qj/c333yzsrISALKzs3NycrTOvvXWW+gyGxsbzbTpVhp9Wk9ISBCLxVgvVCqVfD5fJBI1NjaiTWUfHx93d3d0ls1mq1QqpGNN0PIym83W2YRIJPLz83vuuefMuwprUFhY+M033wBAXFzcF198sTSDp6cn9nrsKu/uBtbhMzIyhoeH6+vr29raZmZm2tvbBQLB0NAQ8vjUXH5Her17965WDWgxBy34aDEyMlJTU3PgwAHzLsEafP/990iRzz777E8//YQegUvJy8tDlk1raytyn1qdGN5pZbFY27ZtCw4OdnJyQkeQ9Q7/r/Unn3wSdNnqnZ2dDAYDWfJaINei9PR0fKJbDYlE8tprrwEAh8ORSCR6TBAul/vSSy+hdH5+vlqttpKIJoLHg6q1tRUlNLUeHx8PGks3iL6+vnv37m3fvh27YzQRiUQxMTFeXl44ZLAaTU1NSUlJi4uLbDa7urraoLTvvvsuSkil0oqKipUXEA94tI76up2dHZ/Pxw5GR0c7ODiIxWLN/YyvvvoKAOLi4pZW0tjY2Nvbu8rtuJ6entjYWLlcTqfTKyoq/P39DRbh8XjYTmtBQcEqdQQ1xoNKE5VKhXzBgoKCtE6hkS82NvbWrVtyufyzzz6jUCi+vr6zs7NL6xEKhV5eXgsLC2ZsWJiLmV4VlsWaXhUmRyjp6emZnp6G/5bfNSkoKBgfHz916pREIkFHAgICqqqqlu4DymSysrKygwcP6pzik6w0Jv/pOgd1BI1GO3nyZFZWVm1trUwmCwwMjI6O1mnulpeXy2SyVRIGyAYxWespKSkvvvgiACy3k+/v729w/BOLxWFhYcYMkyQrgR2Xy11uuVQndDqdTqeb2erw8HBhYaGZlZDgxg6Z2Vbm77//tn6jJBhk5DFbhNS6LUJq3Rax6enyzMxMXV0dWmMnHLSKZ2TgEzOxaa27ubndu3cP8xAhHEdHRw8PDys0RFGv1n0hkpWDHNdtEVLrtgipdVuE1LotQmrdFiG1bouQWrdFSK3bIqTWbRFS67bICmp9YGDggw8+CAsLW7t2LZvNDggIiI+Pr6mpWbkWSYxlJRxvFQrFe++9t5z/q0mO2CQrgeX33GZmZnbv3o1CNoSEhCQmJnI4nPHx8f7+/tLS0v7+fixsIQlhWPYmWlhYeP755wGAwWAUFxdrnZ2bmzt+/Hhzc7PmEUIiyNo4Ftb64cOH0c30yy+/6M8plUp37tyJvOU5HM7p06ctKwmJHiyp9du3b6OxfM+ePfpztrW1ubi4sFisvLy8jz76CIX/Onr0qAWFIdGDJbWOuSI1NTXpyWZmPEIS87GY1hcXF5H3D5/P15/zzz//BACt1wrRwfT0dEvJQ6IHi9nwN27cQJ5+Tz/9tP6c5sQj1ENycnJtbS3u4uYgk8kcHBzMfyUIBzMzM0wm06SXROl0usW0jsUmQWHS9aAnHmFDQ8Po6KhmPHLjSUhIIGpOeOPGjfXr17u5uVm/6WvXrj3xxBMmfWeERqNZTOvYu6sGv+auJx5hQ0NDX18fPq0nJSUlJSXhKGiDWGxFFntBtaurS39O3PEISSyFxfr6pk2b1q1bNzw8XFVV1d3djT6BpMn169evXr2alZWFLx6hQQ4fPtzW1oavrJn09PR4eXmh2JJWpqura+PGjSY94SkUiiWf8B9//PH+/fuVSuWOHTu+/PLLyMhIJyenoaGhlpaW8vLyixcvvvHGGwDAYDB0fopZfzxCg7i6uhLyvwPAmjVr2Gw2Ia27uLi4urqapHUqlWrJ+bpKpdLzyRMWi3X+/Hm1Wo1iQ8/Pz2sVR3HRGxoaLCgSiU4sudNKoVCqqqoKCgq07no/P79PP/30zp07e/fuBVzxCEksy4q88bSwsICm7ywWi8PhaMVoS0tLKykpuXTpktaU3cvLa3p6+v79+zqD05FYkBXxqqDT6UFBQVFRUaGhoUvD8uGIR0hiWQjwoDI1HiGJ5SHEmjApHiGJxSFG60qlMisrS/NLOwEBAbdv3yZEGBuEyPfX//rrL4PxCElWgv8BIQujGsMBFLYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=167x80 at 0x1510FB5E80>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.x(q)\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.+0.j,  1.-0.j],\n",
       "       [ 1.+0.j, -0.+0.j]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'],3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### $Y$: bit- and phase-flip gate\n",
    "\n",
    "The $Y$ gate is defined as:\n",
    "\n",
    "$$\n",
    "Y  = \n",
    "\\begin{pmatrix}\n",
    "0 & -i\\\\\n",
    "i & 0\n",
    "\\end{pmatrix}=u3(\\pi,\\pi/2,\\pi/2)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=169x80 at 0x1510FFD2E8>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.y(q)\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.+0.j, -0.-1.j],\n",
       "       [ 0.+1.j, -0.+0.j]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'],3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### $Z$: phase-flip gate\n",
    "\n",
    "The phase flip gate $Z$ is defined as:\n",
    "\n",
    "$$\n",
    "Z = \n",
    "\\begin{pmatrix}\n",
    "1 & 0\\\\\n",
    "0 & -1\n",
    "\\end{pmatrix}=u1(\\pi)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=165x80 at 0x15110F0828>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.z(q)\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.+0.j,  0.+0.j],\n",
       "       [ 0.+0.j, -1.+0.j]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'],3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Clifford gates\n",
    "\n",
    "#### Hadamard gate\n",
    "\n",
    "$$\n",
    "H = \n",
    "\\frac{1}{\\sqrt{2}}\n",
    "\\begin{pmatrix}\n",
    "1 & 1\\\\\n",
    "1 & -1\n",
    "\\end{pmatrix}= u2(0,\\pi)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=167x80 at 0x1511131B70>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.h(q)\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.707+0.j,  0.707-0.j],\n",
       "       [ 0.707+0.j, -0.707+0.j]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'], 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### $S$ (or, $\\sqrt{Z}$ phase) gate\n",
    "\n",
    "$$\n",
    "S = \n",
    "\\begin{pmatrix}\n",
    "1 & 0\\\\\n",
    "0 & i\n",
    "\\end{pmatrix}= u1(\\pi/2)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=163x80 at 0x15111CDE80>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.s(q)\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.+0.j, 0.+0.j],\n",
       "       [0.+0.j, 0.+1.j]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'], 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### $S^{\\dagger}$ (or, conjugate of $\\sqrt{Z}$ phase) gate\n",
    "\n",
    "$$\n",
    "S^{\\dagger} = \n",
    "\\begin{pmatrix}\n",
    "1 & 0\\\\\n",
    "0 & -i\n",
    "\\end{pmatrix}= u1(-\\pi/2)\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=175x89 at 0x10DD7A320>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.sdg(q)\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.+0.j, 0.+0.j],\n",
       "       [0.+0.j, 0.-1.j]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'], 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $C3$ gates\n",
    "#### $T$ (or, $\\sqrt{S}$ phase) gate\n",
    "\n",
    "$$\n",
    "T = \n",
    "\\begin{pmatrix}\n",
    "1 & 0\\\\\n",
    "0 & e^{i \\pi/4}\n",
    "\\end{pmatrix}= u1(\\pi/4) \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=168x80 at 0x1510FEB898>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.t(q)\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.   +0.j   , 0.   +0.j   ],\n",
       "       [0.   +0.j   , 0.707+0.707j]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'], 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### $T^{\\dagger}$ (or, conjugate of $\\sqrt{S}$ phase) gate\n",
    "\n",
    "$$\n",
    "T^{\\dagger} =  \n",
    "\\begin{pmatrix}\n",
    "1 & 0\\\\\n",
    "0 & e^{-i \\pi/4}\n",
    "\\end{pmatrix}= u1(-pi/4)\n",
    "$$\n",
    "\n",
    "They can be added as below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAALUAAABZCAIAAAD3t/IHAAANS0lEQVR4nO2dfUyTRxzHr6XFVloKKJQ6jMXACltqKQQ7F5likIk6CUyMg+EoW6LMkCVMl2zRuBlmZqYm29S4ZWlRF8JgsrCAGueQZNUoL9puoMRO1kodDBBtqS30dX9c0nR9eejz9OUp8T5/kCfXu+f3e47vc8/dPffcj+J0OsHzSmdnZ0VFRWpqKpVKJdsXHMzMzHA4HLVaHQFbtAjYiFoMBsPs7GxxcXFiYiLZvuDgypUrY2NjkbH1XOuDxWIBAPbv35+RkUG2LzgwGAxXr16NjK2F1K4iIg/SBwILpA8EFkgfCCyoNpvNYrFE2Orc3FyELSKIQa2rq3vnnXcibJXP558+fTrCRhEEoI6Pj4+Pj0fYam5u7jfffBNhowgCkNP/kEqlw8PDN2/eJMU6InDI0ce2bduWLFkik8lIsR5VPH78uKCgIGpvFXL0ERsbW1VV9eOPP5pMJlIciB60Wq1CoRgYGCDbEd+QNr6tra01GAwXLlwgy4Eogcfjuf5GIaTpQyQSicViuVxOlgNRApfLpdFoSB8+qK2t7enp+fvvv0n0gXSoVGpqauqyZcvIdsQ3ZOqjsrIyNja2qamJRB+igWXLlqH2wwdJSUmlpaVNTU0Oh4NEN/Dy4Ycf0oNAp9MBAK5du1ZeXn7gwIH29vbU1NTu7u7Gxsbt27d/9913ZF/f/yB5/YdUKm1tbe3u7i4qKiLXk8C5ceOGzWYjVpbH46WlpQEAtFptX1/fzMyMxWKZnJzs7e29c+eOUqlcvnx5SJ0NlkD14XQ6f/311x9++GF4eDg+Pn716tX19fU8Hm/fvn1dXV1UKvX27duLFi3Ca764uDgtLU0uly8gfTQ0NLi/saLT6TExMQAAtVr98ccfAwBWrFhx/PhxAIDT6bTb7e5iSklJgQc1NTU1NTXwWCQS7d+/n8lkRuoK8LB169b169c7MdHpdOvXr/coyOFwrl27JhAIAABCoRD7DBh88sknDAbjyZMnhM9AmI6ODgCAWq0Oydm+//57WDNvv/02roJMJvPu3buB56+rq8vMzMTpHUHm7388ePAgPz+/p6cHALB48eLKysrGxsb33nvPaDSWlZXdv38fALB69WrCApVKpbOzsy0tLYTPECXcunULHuCqDb1ebzabI7aeFC/zPF/0en1RURH0vqCgoLW1NTU1Ff60YcOGyspKeCyRSAh7kJGRUVBQIJPJ9uzZQ/gk0UBvby88wKWPiYkJAEDU6mOe9uODDz7QaDQAgHfffbe7u9slDgDAzp07V65cCY+9a8RisTx9+jRAJ2pra/v6+gYHBwPMH4WYTCboP51Oz8nJCbzg48ePAQBTU1NhcixIsPTxxx9/nD17FgCQmZl56tQpGu1/jQ2FQoHLvplM5ssvv+xKV6lUxcXFTCYzMTExPT3922+/ndeJiooKFou1oOdSBwYG7HY7ACAnJwdXPx3WKp1OD5dnwYH1fDl27Bg8OHPmjM9rvnv3LgAgLy/PJZ2BgYHCwkIqldrQ0JCYmNje3r5nz55Hjx4dPnwYw1BcXFxFRUVzc/OxY8coFAqxK7FarV1dXVarNfAi/f39xGx5Q+zhAgCAFctgMAIvYjKZjEZjW1tb4EWePn2q1+tXrFiByzeBQOB3/GKz2TgcDgAgJyfHZ88WzvMAABoaGmCKw+EQiURMJlOpVLpOsnHjxpiYmMHBQex+clVV1fLly4PoaDtd3UO89Pf3B2MXsmPHDni2s2fP4ioIO/jNzc2BF8nPzyd2pXgpKCjw23709/fr9XoAQGFhoc8MriULrjtGqVSqVKr6+nqRSARTYmJijh49mpube/To0XPnzvmzpdfr29vbGxoaiF2Gy42xsTFcCwauXr26e/dueBsECbHBCyDUfuTl5U1OTv7222+BF3E4HDabLTY2FpdvPB7Prz60Wi088PfqyKUP1+Dl8uXLAIDXX3/dPZtYLE5OTv79998x/GhpaTGbza75IsK4d5/Dkd8fExMTsLri4+PhhFDgQGXgmhyjUCh0Ot01OAgrfvunsF8NAHjy5InPDFAfycnJfD4fpsCP/oRCoUdOgUCg0WgwVrnKZLJ169YtrI8c3XF1PvLz8/H2n6AycLUfkcSvPpKTk+GBSqXy/lWn08FKcW9O4SD+hRde8Micnp4OAPD3vfnQ0FBvb29tbS0+x6MJ18OFwDwQm82m0WjwS+AoxK8+MjMz4cHFixeVSqX7TyaTSSqVwncQ7vrQ6/VUKhW+jHAH3iLPnj3zaUgmk7HZ7O3btxNxPzogPHiBJCUlLVmyJKQehQy/+hCJRKtWrQIAOJ3OkpKSixcvzs3NTU9P//zzzxKJxPX9uHuNGAwGjzkSCEw0Go3eP1mt1vPnz+/cuXPx4sVBXglZOJ3Ovr4+eExsZJGUlJSUlBRSp0IG1vzYp59+CjdOGR8f37JlC5vNXrp0aXl5OYvFck2IudcIg8Hw+eIbzkn47IJ1dnZOTk4u6IeLWq2GXbS0tDRiy8C4XG58fHyo/QoNWPooKyuTy+WuO9tms4nFYplMdv36dTgfnJGR4d4wJiQkOBwO7xkq+DVlQkKCtwmZTJaVlfXKK68EdxVkEuTDBQBw+PBhwrOC4Wae93O7du0qLS1VKpUsFisrKysuLg4AMDo6+u+//wKvGoEKGB0d9Rh6wZk072mGsbGxS5cuffHFF8FeBKkEr4/XXnstdO6EmPnf73M4nHXr1uXl5UFxAP818uKLLwJf45TBwUEGgwFHMe6cO3eOQqFUV1cTcz1KCGbwEv0QWX/q6o556KO0tBS4zZtB1Gr1xMTEhg0bXPJyIZPJtmzZwuVyCfgQJVgsFji4o1KpeXl5ZLsTeojoA7YfNBpNLBa7p5eUlCxatEgul5vNZlfi119/DQDYtm2bx0muX79+//79Bd0zBQCoVCo4zs/Ozmaz2WS7E3pw68PpdMKPAVetWuUx68dmsz/66COtVrtjx46RkRGz2XzixIlTp04JBALvLSRkMhmXy928eXMw3pMO4dcuCwXc69eHh4cNBgPw87g9dOjQ9PT06dOnOzs7YYpQKOzo6PBQktFobG1traur8zlfsoAIvnMa5eD+9/jrfEBiYmJOnjy5d+/eK1euGI3GnJyckpIS791n29rajEajVCol4HFUgfThyVtvvfXmm28CzFdK2dnZ2dnZGCeRy+Vr1qzBzrMgGB4eJtuF8EJLT0/3OfPtD/gRWJBW//nnn8bGxiBPgogANDi+iDB//fVX5I0iCID2t0RggfSBwALpA4EF0gcCC6QPBBZIHwgsFvb0dpDAVSxlZWUEdi4hkYcPHxLeoAYvz7U+JBJJdna2QCBYWPHnWCyW6+uCcENxPsfxCRHzspDuG0TkQfpAYIH0gcAC6QOBBdIHAgukDwQWSB8ILJA+EFggfSCwQPpAYIH0gcAC6QOBBdIHAovw6kOr1X722Wdr1qzh8XgJCQlCobC0tPTSpUthNYoIJbg2+w2c2dnZAwcO+Pu8dt6IM4goISzrg2ZmZjZv3qxQKAAA+fn5FRUVfD5/enpao9G0tLRoNBrXlqmIaCfkirNarWvXrgUAMBiMpqYmj1/n5uZOnDhx69Yt9xRSgkchAiH0+oAx2AAAP/30E3ZOpVK5ceNGuLaPz+efOXMm5M4ggiTE+hgZGYF9jjfeeAM7Z39/P5vN5nA4+/bt+/zzz+HmTAcPHgytP4ggCbE+du/eDRuPmzdvYmQLJhIIIpKEcn2yw+HgcrlTU1Nisfj27dsYOe/cuZObm1tfX+++ewBMrK6uxogEgoHdbu/q6oJ7rUYDGo0mJSUlSvaFNhgMBoMBht4NnJdeeimU7Ydrm/bq6mrsnEeOHAEAdHZ2eqTDaBDErHvsm4gInrVr14ZyfDs6OgoP5o2BghEJRKFQjI+PE4jMIpFIdDpd9LQfz549YzKZUfJljd1ut1gseEMwp6SkhFIfrrpwDy/tE4xIIAqFQq1WE4vc431CRJCEUh+u/cSGhoawcxKLBDIv9+7dwxVfLKzo9XoWi+V9jaRgsVjm5ubw7tCanp4eyv6H3W6HAQxoNNrQ0JB3BpVKdfLkSafTyWKxYmNjvTO8//77AIC2tjYC1m/cuBGWqn2OefXVV0P8fDly5EhNTY3NZisqKvrqq68KCwvj4uIePXrU29vb1tb2yy+/QAUwGAyfNzpGJJB5kUgkPT09uOKbhhWdTrd06dIoCRxmNBpnZmZ4PB6uUitXrgzx/IfD4di0aZM/exwO58KFC06nE4aas1gsHsV37doFAFAoFKH1CkGYEPeuKRRKR0fHoUOHEhMT3dOzsrK+/PLLhw8flpeXA7dIIB7F/UUCQZBFuL7ft1qtf/7559TUFIfD4fP5HkEaqqqqmpubL1++7BEMlcvlGgyGqakp72APCFII1+icTqfn5uYWFxdLJBLvCB54I4EgyIKc2RtckUAQZEJWx+fgwYMAgK1btz548MBkMh0/fpxCoQgEArPZTJZLCG9I04fNZtu7d697XD6hUDgyMkKWPwifkLy/1L1797AjgSDI5T/4Pu7mxefSUAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=181x89 at 0x1510E2FD68>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.tdg(q)\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.   +0.j   , 0.   +0.j   ],\n",
       "       [0.   +0.j   , 0.707-0.707j]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'], 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standard Rotations\n",
    "\n",
    "The standard rotation gates are those that define rotations around the Paulis $P=\\{X,Y,Z\\}$. They are defined as \n",
    "\n",
    "$$ R_P(\\theta) = \\exp(-i \\theta P/2) = \\cos(\\theta/2)I -i \\sin(\\theta/2)P$$\n",
    "\n",
    "#### Rotation around X-axis\n",
    "\n",
    "$$\n",
    "R_x(\\theta) = \n",
    "\\begin{pmatrix}\n",
    "\\cos(\\theta/2) & -i\\sin(\\theta/2)\\\\\n",
    "-i\\sin(\\theta/2) & \\cos(\\theta/2)\n",
    "\\end{pmatrix} = u3(\\theta, -\\pi/2,\\pi/2)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=247x97 at 0x15111557B8>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.rx(pi/2,q)\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.707+0.j   , -0.   -0.707j],\n",
       "       [ 0.   -0.707j,  0.707+0.j   ]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'], 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Rotation round Y-axis\n",
    "\n",
    "$$\n",
    "R_y(\\theta) =\n",
    "\\begin{pmatrix}\n",
    "\\cos(\\theta/2) & - \\sin(\\theta/2)\\\\\n",
    "\\sin(\\theta/2) & \\cos(\\theta/2).\n",
    "\\end{pmatrix} =u3(\\theta,0,0)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=247x99 at 0x151109A2B0>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.ry(pi/2,q)\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.707+0.j, -0.707+0.j],\n",
       "       [ 0.707+0.j,  0.707+0.j]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'], 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Rotation around Z-axis\n",
    "\n",
    "$$\n",
    "R_z(\\phi) = \n",
    "\\begin{pmatrix}\n",
    "e^{-i \\phi/2} & 0 \\\\\n",
    "0 & e^{i \\phi/2}\n",
    "\\end{pmatrix}\\equiv u1(\\phi)\n",
    "$$\n",
    "\n",
    "Note here we have used an equivalent as is different to u1 by global phase $e^{-i \\phi/2}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=247x97 at 0x1511128F60>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.rz(pi/2,q)\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.707-0.707j, 0.   +0.j   ],\n",
       "       [0.   +0.j   , 0.707+0.707j]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(np.exp(-1j*pi/4)*result.get_data('test')['unitary'], 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note this is different due only to a global phase"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multi-Qubit Gates\n",
    "\n",
    "The space of quantum computer grows expodential with the number of qubits. For $n$ qubits the complex vector space has dimensions $d=2^n$. \n",
    "\n",
    "Notice that in the QISKit, the order of qubits are represented from the most significant bit (MSB) on the left to the least significant bit (LSB) on the right (big-endian). This is similar to bitstring representation on classical computers, and enables easy conversion from bitstrings to integers after measurements are performed.  That is the first four states of two qubits are $|00\\rangle$, $|01\\rangle$, $|10\\rangle$, and $|11\\rangle$.\n",
    "\n",
    "The joint space is a tensor product space:\n",
    "\\begin{equation}\n",
    "\tX\\otimes Y = \n",
    "\t\\begin{pmatrix} \n",
    "\t\tx_{00} \\begin{pmatrix} \n",
    "\t\t\ty_{00} & y_{01} \\\\\n",
    "\t\t\ty_{10} & y_{11}\n",
    "\t\t\\end{pmatrix} & x_{01} \t\\begin{pmatrix} \n",
    "\t\t\t\ty_{00} & y_{01} \\\\\n",
    "\t\t\t\ty_{10} & y_{11}\n",
    "\t\t\t\\end{pmatrix} \\\\\n",
    "\t\tx_{10} \t\\begin{pmatrix} \n",
    "\t\t\t\t\ty_{00} & y_{01} \\\\\n",
    "\t\t\t\t\ty_{10} & y_{11}\n",
    "\t\t\t\t\\end{pmatrix} & x_{11} \t\\begin{pmatrix} \n",
    "\t\t\t\t\t\t\ty_{00} & y_{01} \\\\\n",
    "\t\t\t\t\t\t\ty_{10} & y_{11}\n",
    "\t\t\t\t\t\t\\end{pmatrix}\n",
    "\t\\end{pmatrix}\t\t\t\t\t\t\n",
    "\\end{equation} which means for the states we have \n",
    "\\begin{equation}\\begin{split}\n",
    "\t|{00}\\rangle &= \\begin{pmatrix} \n",
    "\t\t\\begin{pmatrix} \n",
    "\t\t\t1  \\\\\n",
    "\t\t\t0\n",
    "\t\t\\end{pmatrix} \\\\\n",
    "\t\t\\begin{pmatrix} \n",
    "\t\t\t0  \\\\\n",
    "\t\t\t0 \n",
    "\t\t\\end{pmatrix}\n",
    "\t\\end{pmatrix} ~  \t|{01}\\rangle = \\begin{pmatrix} \n",
    "\t\\begin{pmatrix} \n",
    "\t0 \\\\\n",
    "\t1\n",
    "\t\\end{pmatrix} \\\\\n",
    "\t\\begin{pmatrix} \n",
    "\t0  \\\\\n",
    "\t0 \n",
    "\t\\end{pmatrix}\n",
    "\t\\end{pmatrix} ~ \t|{10}\\rangle = \\begin{pmatrix} \n",
    "\t\\begin{pmatrix} \n",
    "\t0  \\\\\n",
    "\t0\n",
    "\t\\end{pmatrix} \\\\\n",
    "\t\\begin{pmatrix} \n",
    "\t1 \\\\\n",
    "\t0 \n",
    "\t\\end{pmatrix}\n",
    "\t\\end{pmatrix} ~ \t|{11}\\rangle = \\begin{pmatrix} \n",
    "\t\\begin{pmatrix} \n",
    "\t0  \\\\\n",
    "\t0\n",
    "\t\\end{pmatrix} \\\\\n",
    "\t\\begin{pmatrix} \n",
    "\t0  \\\\\n",
    "\t1 \n",
    "\t\\end{pmatrix}\n",
    "\t\\end{pmatrix}\\end{split}\n",
    "\\end{equation}\n",
    "\n",
    "Thus, we write the tensor product of qubits $q_0$, $q_1$, and $q_2$ as $q_2 \\otimes q_1 \\otimes q_0$. The physics community often writes this in the opposite way, and care must be taken when working with these scenarios, as demonstrated in multi-qubit gates below.\n",
    "\n",
    "A common two-qubit gate is $C_U$. The $C_U$ when qubit 0 is the control and qubit 1 is the target (eg `cU(q[0],q[1])`) is\n",
    "\n",
    "\\begin{equation}\n",
    "\tC_U = \\begin{pmatrix}\n",
    "\t1 & 0 & 0 & 0 \\\\\n",
    "\t0 & u_{00} & 0 & u_{01} \\\\\n",
    "\t0 & 0 & 1 & 0 \\\\\n",
    "\t0 & u_{10} &0 & u_{11}\n",
    "\t\t\\end{pmatrix},\n",
    "\\end{equation} \n",
    "\n",
    "\n",
    "The $C_U$ when qubit 1 is the control and qubit 0 is the taget (eg `cU(q[1],q[0])`)\n",
    "\\begin{equation}\n",
    "\tC_U = \\begin{pmatrix}\n",
    "\t1 & 0 & 0  & 0 \\\\\n",
    "\t0 & 1 & 0 & 0 \\\\\n",
    "\t0 & 0 & u_{00} & u_{01} \\\\\n",
    "\t0 & 0 & u_{10} & u_{11}\n",
    "\t\t\\end{pmatrix}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The standard multi-qubit gates consist of two-qubit gates and three-qubit gates. The two-qubit gates are:\n",
    "* controlled Pauli gates\n",
    "* controlled Hadamard gate\n",
    "* controlled rotation gates\n",
    "* controlled phase gate\n",
    "* controlled u3 gate\n",
    "* swap gate\n",
    "\n",
    "The three-qubit gates are: \n",
    "* Toffoli gate \n",
    "* Fredkin gate\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "q = QuantumRegister(\"q\", 2)\n",
    "c = ClassicalRegister(\"c\", 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Controlled Pauli Gates\n",
    "\n",
    "#### Controlled-X (or, controlled-NOT) gate\n",
    "The controlled-not gate flips the `target` qubit when the control qubit is in the state $|1\\rangle$. If we take the MSB as the control qubit (e.g. `cx(q[1],q[0])`), then the matrix would look like\n",
    "\n",
    "$$\n",
    "C_X = \n",
    "\\begin{pmatrix}\n",
    "1 & 0 & 0 & 0\\\\\n",
    "0 & 1 & 0 & 0\\\\\n",
    "0 & 0 & 0 & 1\\\\\n",
    "0 & 0 & 1 & 0\n",
    "\\end{pmatrix}. \n",
    "$$\n",
    "\n",
    "However, when the LSB is the control qubit, (e.g. `cx(q[0],q[1])`), this gate is equivalent to the following matrix:\n",
    "\n",
    "$$\n",
    "C_X = \n",
    "\\begin{pmatrix}\n",
    "1 & 0 & 0 & 0\\\\\n",
    "0 & 0 & 0 & 1\\\\\n",
    "0 & 0 & 1 & 0\\\\\n",
    "0 & 1 & 0 & 0\n",
    "\\end{pmatrix}. \n",
    "$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=147x86 at 0x15110DAF60>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.cx(q[0],q[1])\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "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, 0.+0.j, 1.+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]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'], 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Controlled $Y$ gate\n",
    "\n",
    "Apply the $Y$ gate to the target qubit if the control qubit is the MSB\n",
    "\n",
    "$$\n",
    "C_Y = \n",
    "\\begin{pmatrix}\n",
    "1 & 0 & 0 & 0\\\\\n",
    "0 & 1 & 0 & 0\\\\\n",
    "0 & 0 & 0 & -i\\\\\n",
    "0 & 0 & i & 0\n",
    "\\end{pmatrix},\n",
    "$$\n",
    "\n",
    "or when the LSB is the control\n",
    "\n",
    "$$\n",
    "C_Y = \n",
    "\\begin{pmatrix}\n",
    "1 & 0 & 0 & 0\\\\\n",
    "0 & 0 & 0 & -i\\\\\n",
    "0 & 0 & 1 & 0\\\\\n",
    "0 & i & 0 & 0\n",
    "\\end{pmatrix}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=169x121 at 0x1510EA2F98>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.cy(q[0],q[1])\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "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, 0.+0.j, 0.-1.j],\n",
       "       [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n",
       "       [0.+0.j, 0.+1.j, 0.+0.j, 0.+0.j]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'], 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Controlled $Z$ (or, controlled Phase) gate\n",
    "\n",
    "Similarly, the controlled Z gate flips the phase of the target qubit if the control qubit is $1$. The matrix looks the same regardless of whether the MSB or LSB is the control qubit:\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": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=165x121 at 0x1510FA8588>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.cz(q[0],q[1])\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.-0.j,  0.+0.j,  0.+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,  1.-0.j,  0.+0.j],\n",
       "       [ 0.+0.j, -0.+0.j,  0.+0.j, -1.+0.j]])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'], 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Controlled Hadamard gate\n",
    "\n",
    "Apply $H$ gate to the target qubit if the control qubit is $|1\\rangle$. Below is the case where the control is the LSB qubit.\n",
    "\n",
    "$$\n",
    "C_H = \n",
    "\\begin{pmatrix}\n",
    "1 & 0 & 0 & 0\\\\\n",
    "0 & \\frac{1}{\\sqrt{2}} & 0 & \\frac{1}{\\sqrt{2}}\\\\\n",
    "0 & 0 & 1 & 0\\\\\n",
    "0 & \\frac{1}{\\sqrt{2}}  & 0& -\\frac{1}{\\sqrt{2}}\n",
    "\\end{pmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=167x121 at 0x1510FA8F60>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.ch(q[0],q[1])\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.   -0.j,  0.   +0.j, -0.   +0.j,  0.   +0.j],\n",
       "       [ 0.   +0.j,  0.707-0.j,  0.   +0.j,  0.707-0.j],\n",
       "       [ 0.   -0.j,  0.   +0.j,  1.   -0.j,  0.   +0.j],\n",
       "       [ 0.   +0.j,  0.707-0.j,  0.   +0.j, -0.707+0.j]])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(np.exp(-1j*pi/4)*result.get_data('test')['unitary'], 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Controlled rotation gates\n",
    "\n",
    "#### Controlled rotation around Z-axis\n",
    "\n",
    "Perform rotation around Z-axis on the target qubit if the control qubit (here LSB) is $|1\\rangle$.\n",
    "\n",
    "$$\n",
    "C_{Rz}(\\lambda) = \n",
    "\\begin{pmatrix}\n",
    "1 & 0 & 0 & 0\\\\\n",
    "0 & e^{-i\\lambda/2} & 0 & 0\\\\\n",
    "0 & 0 & 1 & 0\\\\\n",
    "0 & 0 & 0 & e^{i\\lambda/2}\n",
    "\\end{pmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=247x143 at 0x1510D7A4A8>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.crz(pi/2,q[0],q[1])\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.   +0.j   , 0.   +0.j   , 0.   +0.j   , 0.   +0.j   ],\n",
       "       [0.   +0.j   , 0.707-0.707j, 0.   +0.j   , 0.   +0.j   ],\n",
       "       [0.   +0.j   , 0.   +0.j   , 1.   +0.j   , 0.   +0.j   ],\n",
       "       [0.   +0.j   , 0.   +0.j   , 0.   +0.j   , 0.707+0.707j]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'], 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Controlled phase rotation\n",
    "\n",
    "Perform a phase rotation if both qubits are in the $|11\\rangle$ state. The matrix looks the same regardless of whether the MSB or LSB is the control qubit.\n",
    "\n",
    "$$\n",
    "C_{u1}(\\lambda) = \n",
    "\\begin{pmatrix}\n",
    "1 & 0 & 0 & 0\\\\\n",
    "0 & 1 & 0 & 0\\\\\n",
    "0 & 0 & 1 & 0\\\\\n",
    "0 & 0 & 0 & e^{i\\lambda}\n",
    "\\end{pmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=247x143 at 0x151131C940>"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.cu1(pi/2,q[0], q[1])\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I THINK SHOULD BE CALLED $C_\\mathrm{PHASE}(\\lambda)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.+0.j, 0.+0.j, 0.+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, 1.+0.j, 0.+0.j],\n",
       "       [0.+0.j, 0.+0.j, 0.+0.j, 0.+1.j]])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'], 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Controlled $u3$ rotation\n",
    "\n",
    "Perform controlled-$u3$ rotation on the target qubit if the control qubit (here LSB) is $|1\\rangle$. \n",
    "\n",
    "$$\n",
    "C_{u3}(\\theta, \\phi, \\lambda) \\equiv \n",
    "\\begin{pmatrix}\n",
    "1 & 0 & 0 & 0\\\\\n",
    "0 & e^{-i(\\phi+\\lambda)/2}\\cos(\\theta/2) & 0 & -e^{-i(\\phi-\\lambda)/2}\\sin(\\theta/2)\\\\\n",
    "0 & 0 & 1 & 0\\\\\n",
    "0 & e^{i(\\phi-\\lambda)/2}\\sin(\\theta/2) & 0 & e^{i(\\phi+\\lambda)/2}\\cos(\\theta/2)\n",
    "\\end{pmatrix}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=367x143 at 0x1510DC8390>"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.cu3(pi/2, pi/2, pi/2, q[0], q[1])\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.   +0.j   ,  0.   +0.j   ,  0.   +0.j   ,  0.   +0.j   ],\n",
       "       [ 0.   +0.j   ,  0.   -0.707j,  0.   +0.j   , -0.707+0.j   ],\n",
       "       [ 0.   +0.j   ,  0.   +0.j   ,  1.   +0.j   ,  0.   +0.j   ],\n",
       "       [ 0.   +0.j   ,  0.707+0.j   ,  0.   +0.j   ,  0.   +0.707j]])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'], 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "NOTE I NEED TO FIX THIS AND DECIDE ON CONVENTION - I ACTUALLY THINK WE WANT A FOUR PARAMETER GATE AND JUST CALL IT CU AND TO REMOVE THIS GATE."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Swap gate\n",
    "\n",
    "The swap gate exchange the first and second qubits. \n",
    "\n",
    "$$\n",
    "{SWAP} = \n",
    "\\begin{pmatrix}\n",
    "1 & 0 & 0 & 0\\\\\n",
    "0 & 0 & 1 & 0\\\\\n",
    "0 & 1 & 0 & 0\\\\\n",
    "0 & 0 & 0 & 1\n",
    "\\end{pmatrix}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=120x36 at 0x1510F8BDD8>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.swap(q[0], q[1])\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "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": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'], 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Toffoli gate ($ccx$ gate)\n",
    "\n",
    "The Toffoli gate flips the third qubit if the first two qubits (LSB) are both $|1\\rangle$.\n",
    "\n",
    "$$\n",
    "C_{CX} = \n",
    "\\begin{pmatrix}\n",
    "1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
    "0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
    "0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n",
    "0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n",
    "0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n",
    "0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n",
    "0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\\n",
    "0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\n",
    "\\end{pmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "q = QuantumRegister(\"q\", 3)\n",
    "c = ClassicalRegister(\"c\", 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJMAAAByCAIAAADYn3RlAAAUnklEQVR4nO2daVQTVxvH7yRhCSESBBRECyKbCrJYBLS+iAqIbIrVQ12ogJxWqHhU2oqWqtVaOWrrXk4PgmgVqIIFFTlu4L6hDQIW2WWvVbYECGR7P9zTNA3JJJkMGZD8PsHMM3OfyTNz5y7P/w6ybt06NpudkZEB1IiZmVliYmJMTIw6C33PILW1tbW1tam5VFdX16NHj6q50PcMEiGlRkREVFRUPHr0iJDS3w+IiVxwcLCRkVFqaiohpb8fEBM5bW3tVatWZWVl9fb2EuLAewAxkQMAREZGdnd3Z2dnE+XASIewyDk5Obm4uKSlpRHlwEiHsMgBACIjI4uKiurq6gj0YeRCZORWrlypra196tQpAn0YuRAZubFjx4aEhJw6dUogEBDoxgiFyMgBACIiIhoaGm7dukWsG3IRCATD7fZSNHJCofDatWvh4eGzZs1auHDhtm3bWltbAQDx8fFTp06dPn16f38/huJ9fX0nTpw4bNspbW1tX3/9tb29vY6Ojra2tq2t7ZYtW5qbm4n2CwAAQGBg4Lx584SoNDU1zZs3T+JAAwODwsJCOzs7AICjoyP6GVDYtm2brq5uR0cH5jMMEVlZWTQabfAvRqVST58+TbR3QvmRq66uNjMzg07r6emtXLlyz54969atI5PJDAYDQRAAQFRUFGYPqqqqAAA///wz5jMMBVlZWfDSZJGenk6sh3Ii19nZaWlpCX2dO3dua2uraNe5c+dEl/HLL7+o4sTcuXPd3NxUOQO+tLW16evro9dVVCq1qamJQCflRO7TTz+FjkZFRXG5XPFdAoHAysoK7mUymeK7+vv7lar94HuutLRUSeeHiq1bt6KHDbJ582YCnUSLXElJCXTRxsaGw+EMNvD19YV3nyioTCbTx8eHRCIBACwtLZOTkxVxgs1m6+vrE/tDiDN9+nRFImdtbU2gkxQUzw4cOAD/SE5O1tHRGWzw8uVLAMDMmTMpFAoA4NmzZ97e3iQSafPmzYaGhjk5OZ9//nlzc/N3332H/hPQaLTly5efO3fuwIED6G8XFP7444/q6mpsx0pQWVmpiFltbW1WVha8TVUsbtKkSVQqVfFDSCSSzGeOx+MZGBgAAJydnaXGvKmpCZ4FPisCgcDJyYlKpYpqTh6P5+PjQyaTy8rK5N5Bq1atmjRpkgq3oNDNzU3FX3BkIfOZKy4u7urqAgB4e3tLNRDNi86aNQsAwGQyS0pKNmzY4OTkBLeTyeSkpCRXV9ekpKTTp0+jONHV1ZWTk7N582Zs1wApKirCa3J/8eLFr169kmtmZWV1/fp11Yvr7++XWqWhoKWlJTNyr1+/hn9MmDBBqoEocu7u7gCAgoICAICfn5+4jYuLi4mJyd27d9H9yMzM7OvrW7t2raKOS0NPT0/UYlKRFStW7N69WxEzvErEgMw6+t27d/CPjo4OqQYwciYmJrDbcOPGDQCAo6OjhJmdnV19fT3605Camurl5WVtba2E40NJXFwcfFOgQKfTN23apB5/pCIzciYmJvAPUQtTnKampidPnoB/qkoAABwMMzc3l7CcPHkyAAB2t6VSXl7+5MmTyMhI5RwfSoyNjc+cOYPS9CCRSOnp6ePGjVOnV5I+yNphY2MD/8jPz2cymeK7ent7IyIiBgYGgFjkurq6SCQSmUyWOA9sMvX09MgqKDU1lU6nf/zxx1jcHzKCgoLy8vLGjh07eJehoeHvv/++dOlS9XsljszIOTk5zZgxAwAgFAr9/f3z8/P7+/vb29svXrzo7u4O60YgFrnu7m7YN5AAbmSz2VJL4XK5Z86cCQsL09PTU/FKcCcgIKCmpmbv3r0eHh4Igujp6bm7u+/evbumpiYoKIho71BHnHNycsRrDC0tLdjZ8vDwEPVV3759C42NjY1JJNLgk0RHRwMALl++LKsIAMDDhw9V6Q+oATqdvnPnTqK9+A9ovcilS5empaWJngYej+fi4pKamnr//v23b98CAKytrY2MjOBeBoMhEAi4XK7ESeDsD4PBkFpEamqqvb29h4eHsjecBopQKESZMwwPDw8JCWEymfr6+vb29nDWo7Gx8a+//gJiVSX4JzaNjY0SDWXYYZdoqsEeTGtr69WrV/ft24fnBY0aKKWlpRwOB8XCwMDAy8tLfAtsVYL/Rs7W1ra4uLiqqkoicmVlZbq6urCFKcLS0jIxMZHFYiEIsmbNGlUvYlRC6u/vh61ExXn69Cn8QzxyISEhQKx7Dqmqqnrz5s38+fMlpiihriA1NTUgIGD8+PEYfR/dYBkthc8chUJxcXERbfT399fR0UlLS+vr6xNtPHLkCAAgODhY4gxQV1BZWTmsunEjjPHjxzMYDMWbNAKBYMyYMQAAV1dXiV2JiYkAgMDAwJqamt7e3oMHDyIIYmdn19fXJ2EJ33Pi00PDnGHYtkSb5ZFKRUVFd3c3+Ge4UpwdO3a0t7efOHHi8uXLcIujo2Nubq6urq6E5cDAgEAgEAqFAwMDUnuBGuSi9K8m9SUHIZPJx44di42NvXbtGpvNdnZ29vf3lzqGdP78edh/yM7O1rRQsIGMHz8eJh8oeACXy4UtGl1d3cFjXQryv//9j8fjcTgcBoMx/JMtAQBjxozZsmXLjh07iHbkXyhUKlWpaWgtLS0tLS0VS21padmzZ8/bt2/j4uLq6uok+gwaFIHk4OBgb2+v5lKrq6vDwsI0ugJV0OgKRioaXYGiCIVCol34DxpdARoiXQGLxdq9e7dGV/AfNLoCbGh0BdLR6AoUQqMrwMCQ6AqEQiGPx2OxWAo6odEVYABnXQGkrq5u7ty5hw4dUtAJja4AA3jqCrKysu7du1deXn779m2BQLBs2TJFrh/gpCvIz88vLS3FdqwEiiQ4AwBqa2t/+OEH1XUFpaWllpaWdDpd8UPIZDJuugKhUOjl5WVubu7n5/fRRx8BABR/5oR46AoWLFig4i9IFBhuVgqFIvN+UVZXAAAoLCxsamoqKCiAkVMcqCsIDw9X6igJbty4oUrgxRmcqS0VOzs7XIqDE15KweVyZUZOWV0BwHTvQHDRFeDIkiVLFDEjNlkWN12BKmh0BRjATVeAGY2uABu46Qowo9EVYAM3XQE2NLoC7OClKxAHjkEo0ivQ6Aowg5uuABsaXQFmcNMVKIVGV6A6uOkKlEKjK1AdCl66AqWAugKBQKDRFWAGN12BUmh0BaqjdI6zUCh89uwZAGDGjBkSaeei0fqHDx8CAG7cuAHrYQ8PD4n6Njg4WEdHh0QiLV68WBXv1QOLxeLz+Z2dnVwuV/VcU9xQVhECZ3YAAOvXr5fYJWvgcevWrRKWLBZLS0tLW1u7p6dHtbbxUPHq1aukpKTZs2eLdzQRBJkwYUJ4eHh2djbhnisdufT0dHgZaWlpmEsVfR1kOKTiSFBRUREaGoogiJaWlo+Pz65du06ePKmrqxsaGnro0KEvvvgCZmSbmJgcOXKkv7+fKD+VjtzAwACbzWaz2TweD3Opc+fO9fT0dHFx8fb2xnwS3OHz+d988w2FQjE1NT127Jh4OppET/z58+crVqxAEMTGxmZwJod6AJaWlqampmoudcqUKRkZGUePHkUQpLa2Vs2lS4XFYi1ZsgRBkPj4+MEZNFLHUB4/fmxvb6+vr5+dna0uN/9FoXzLIeLdu3c6OjrffvstIaWLw+VyFyxYoKOjIysXT9boV3d3d1BQEIlEys3NHWIfJdHoCgAAYOPGjUVFRdnZ2crOy9Pp9JycnAULFqxevbqsrGyI3JOKRlcALl26dOLEiX379gUEBGA4nEKhZGVlmZqafvLJJ3w+H3f3ZDHadQV8Pj8hIWHWrFlbtmzBfBJDQ8OUlJSysjK1KspGua4ALplaVFSEbqbILE9AQIC5ubna1iyQ/8zV1NS4ubkVFRWB/+oK2Gz20qVL4ZLHqsyvRkREcDiczMxMzGdQhYyMDDc3N4khHmzEx8c3NzffuXNH9VMpxGjWFbBYLF1d3b1798q1VOSZ4/F4xsbGcXFxOHknBznP3MaNG+vr6wEAUVFRt27dMjU1Fe0KCwsT6Qoknjk2m63UuzoyMvLp06dqbpsBAB48eMDhcBYtWoTL2chksq+vL6yc1ABa5F68eAHHumxsbI4fPy6xcAmCIDDPjkqlwuQGPp//008/WVlZjRkzhk6nz549++zZs4o4sXz5cn19ffW3UxobGwEAU6ZMweuEVlZWotTvoQZPXcHatWvPnj27bNmy8PDwioqKvLy81atXFxYWpqSkoDuBi64gJSVFNHGoIHfv3iWRSF9++aVcSw6Hc+nSpZaWFnQzJpPZ3t4eFRWl1PI8paWlFhYWcGUnBaGgFMDn8/Py8gAAzs7O8+fPH2zQ3NwM7y9YVWZnZ//6668ZGRlhYWHQ4OXLl35+fidPnvT395erDhkYGBBlKGHjzp079+/fV+qQtrY2oVAoymNDgc/n19bWyl01BhrcvHlTqZVi2tra6uvrlfrSBJoiRJR8vmnTJqlvyAsXLkCDzMxMoVDo5eW1aNEiCZusrCwgW1MiorOzk0qlbt++HcubWgVOnDgBAOjt7ZVrqWDu165du2g0Gh6uyQc3XYGVldXgoaPAwEASiVReXj54rVlxiNIVwEvDUbHf0tIi6+fCHZm1pbK6guPHj/N4PAkbKpVKo9FYLFZHRwdKLjdRuoIPP/wQQZDCwkK8ii4sLFTbR2Zw0xVQqdTB2r1Xr16xWKyxY8eihI1AXYG5ufnMmTNzc3NxOVt5eXllZSVcoVUNDK2uID8/HwCwbt06FBtidQWhoaHXr1+HfVYVSUlJoVKpePUO5YMyhgJ1BQAAU1PTK1eucDicd+/e5eTkODg4iA6/evWqrFdoU1OToaHhlClTUMYkBwYGTExMoqOjVX9jY6Ojo8PIyGjVqlXoZnJbKLW1tTo6OgkJCbh6h8aQ6AqEQmFXV5eTk9O4ceMqKipQih8OuoKDBw+SSKSbN2+i2KBHjs/nBwQEGBkZqXPcXM64ZXp6uij5CUEQV1fX1NRUPp8P01tlLU7Q1dXl6elpYWFRWVmJXnxgYKC9vb1KV6AyHA7H09PTyMiourpalg165LZv344gCOwdqQ35szydnZ1FRUXFxcVsNhtuaWhogLFcuXLlYPuuri4PDw9ra+vXr1+jl93S0kImk/fv34/Ze7xobW2dNGmSjY2NrFsNJXL79+9HEET9nVEseSiiPvhgnVVnZ6e7u/v06dPFZxVksW/fPgqFAgcyCAcOQRkaGhYUFAzeKzVybDYbdmFjY2P5fL5a3PwXLNkMsnQFXV1dvr6+AwMDRUVF4rMKshhW3ytwcHB49uyZk5PTokWLfHx80JdWEQgEp0+ftrW1PXfu3OHDh48dO6b6qihKg+GZg+tsUCgU8eXsOzo63Nzc3N3dFXxL37t3DwCg/pQpdLhcbnJyspmZGYlEmjNnTlJS0oMHDxobG+l0ekJCQnl5eW5ubnR0NLwvg4KCysvLiXIVCQwMZLPZhYWFCkZaKBQyGIzu7m5XV1coMICEhoZevHjRy8uLTqcLhUKJ+bnU1FTRgn2QqKioK1euNDU1DcNV73t6etLT0y9evHj79u3B43bm5uZBQUFr1qyZPXs2Ie5BcPtewd9//w0AuH37ttSjent7xf9ls9m//fbb+vXrh2HYAAA0Gi0mJiYmJqazs7O8vLy1tfXKlSvTpk1zcHCwsLCYOnWqKnMaeIHb9wrkfgZXnPPnz7PZ7IiICGVLVzMMBmPOnDkAgOG2dAQAQOnaEsfvFTx48ADb4RoAAKTJkycr9bkALS0tGo1Go9Hkhu3169e7du3y9PQ0MzNjMBiOjo4hISFXr14FALS0tMTFxankuIahaPZwOBwoipFaIlEyhvcM/BsILBZr8eLFsNHv5ua2fPlyS0vL9vb2+vr6zMzM+vp61dcJ0wAA3s8cl8uFSyTq6uqeOnVKYm9/f/+PP/74+PFjfAsdneAcuYSEBHhDXLhwQRF7+DEnfH0YJeAZudraWvhuCwoKkmvMZDJ9fHzgoJGlpWVycjKOnowG8IzcZ599Bh+4R48eoVsWFxfT6XQDA4P4+Pjvv/9+5syZAIDExEQcnXnvwS1yfD7f2NgYAODi4oJuKRAInJycqFSqSGHN4/F8fHzIZHJZWRle/rz34Na2LC0thcu4iec6SIXJZJaUlGzYsMHJyQluIZPJSUlJrq6uSUlJUBaFgU2bNik1jqMUDQ0NhoaGSi1vrjj19fUmJiZSvyQjC7QcZ2WBOfoAAKioQ6GgoAAA4OfnJ77RxcXFxMRElZ/ezMxM4lPmOMLhcExNTaUuVKo6PT09H3zwgdz1h8Uhk8m4RU40QSV3FTGYDT54fXI7O7t79+61tbUpMrc3mK+++grDUSMX3OYDp06dCv8oLy9Ht4QyZXNzc4ntcBAOfmBJg1xwe+YsLCwmTJjQ0tKSm5v78uXLadOmSRi8ePHi7t27sbGxXV1dJBJp8LAnlET09PRgc+D48eMvXrzAdqxcSkpKJk6cqOIyrLJ4/vy5lZUVg8FQ/BAEQfCsLffu3bt27Voej7dw4cLDhw97e3vTaLTm5uYnT56cP38+Ly8vJiYGANDd3S31/Qo3stlsbA6UlZWJz/TiS11dXXt7u1JCKcWpqalhsVhyv74lDoIgePbnBAIBSoavgYEBXKvH2NiYRCINPjw6OhoAcPnyZRxdeo/BM+8FQZDc3NwdO3YYGhqKb7e3t9+/f39DQ0NoaCgAgMFgCASCwVkCcF0OpSqN0QzOcwXa2to7d+7cvn077N4ZGBhYWlpKZHfB2DQ2Nko04qGOUqnG8WhmSNJAtLS0XF1dZe21tbUtLi6uqqqSiFxZWZmurq7mq/AKQsDqUVCnJBJOQqqqqt68eTN//nylhhJGMwREzt/fX0dHJy0tra+vT7TxyJEjAIDg4GD1+zNSIaRdlJiYCAAIDAysqanp7e09ePAggiB2dnbiqbca0CEmcjweLzY2Vjxr0dHRcZgsUTpSQIRCIVGP+59//nnt2jU2m+3s7Ozv709Aav5I5v8Soqa4+RQWnQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=147x114 at 0x1510634D68>"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.ccx(q[0], q[1], q[2])\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.-0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,\n",
       "         0.+0.j],\n",
       "       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,\n",
       "         0.+0.j],\n",
       "       [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,\n",
       "         0.+0.j],\n",
       "       [ 0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,\n",
       "         1.-0.j],\n",
       "       [ 0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  1.-0.j,  0.+0.j,  0.+0.j,\n",
       "         0.+0.j],\n",
       "       [ 0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  1.-0.j,  0.+0.j,\n",
       "         0.+0.j],\n",
       "       [ 0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  1.-0.j,\n",
       "         0.+0.j],\n",
       "       [ 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]])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.round(result.get_data('test')['unitary'], 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Controlled swap gate (Fredkin Gate)\n",
    "\n",
    "The controlled swap gate exchange the second and third qubits if the first qubit (LSB) is $|1\\rangle$.\n",
    "\n",
    "$$\n",
    "C_{SWAP} = \n",
    "\\begin{pmatrix}\n",
    "1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
    "0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
    "0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n",
    "0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n",
    "0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\\n",
    "0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n",
    "0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\\n",
    "0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\n",
    "\\end{pmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=237x114 at 0x1510EB7780>"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.cswap(q[0], q[1], q[2])\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  1.,  0., -0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "np.real(np.round(result.get_data('test')['unitary'], 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Non unitary operations\n",
    "\n",
    "Now we have gone through all the unitary operations in quantum circuits we also have access to non-unitary operations. These include measurements, reset of qubits, and classical conditional operations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "q = QuantumRegister(\"q\", 1)\n",
    "c = ClassicalRegister(\"c\", 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Measurements\n",
    "\n",
    "We dont have access to all the information when we make a measurement in a quantum computer. The quantum state is projected onto the standard basis. Below are two examples showing a circuit that is prepared in a basis state and the quantum computer prepared in a superpostion state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=181x83 at 0x1510F5AC88>"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.measure(q, c)\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'0': 1000}"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_qasm_simulator', shots=1000)\n",
    "result.get_counts('test')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " The simulator predicts that 100 percent of the time the classical registor returns 0. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=245x83 at 0x1510D5AC88>"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.h(q)\n",
    "qc.measure(q, c)\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'0': 474, '1': 526}"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_qasm_simulator', shots=1000)\n",
    "result.get_counts('test')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " The simulator predicts that 50 percent of the time the classical registor returns 0 or 1. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reset\n",
    "It is also possible to `reset` qubits to the $|0\\rangle$ state in the middle of computation. Note that `reset` is not a Gate operation, since it is irreversible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit._instructionset.InstructionSet at 0x10b201828>"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.reset(q[0])\n",
    "qc.measure(q, c)\n",
    "# circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'0': 1000}"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_qasm_simulator', shots=1000)\n",
    "result.get_counts('test')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit._instructionset.InstructionSet at 0x1511008be0>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.h(q)\n",
    "qc.reset(q[0])\n",
    "qc.measure(q, c)\n",
    "#circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'0': 1000}"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_qasm_simulator', shots=1000)\n",
    "result.get_counts('test')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we see that for both of these circuits the simulator always predicts that the output is 100 percent in the 0 state."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conditional operations\n",
    "It is also possible to do operations conditioned on the state of the classical registor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit._instructionset.InstructionSet at 0x1510d6af28>"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.x(q[0]).c_if(c, 0)\n",
    "qc.measure(q,c)\n",
    "# circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'1': 1000}"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_qasm_simulator', shots=1000)\n",
    "result.get_counts('test')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here the classical bit always takes the value 0 so the qubit state is always flipped. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=389x83 at 0x1510F7E630>"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c)\n",
    "qc.h(q)\n",
    "qc.measure(q,c)\n",
    "qc.x(q[0]).c_if(c, 0)\n",
    "qc.measure(q,c)\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'1': 1000}"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_qasm_simulator', shots=1000)\n",
    "result.get_counts('test')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here the classical bit by the first measurement is random but the conditional operation results in the qubit being deterministically put into $|1\\rangle$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Arbitrary initialization\n",
    "What if we want to initialize a qubit register to an arbitrary state? An arbitrary state for $n$ qubits may be specified by a vector of $2^n$ amplitudes, where the sum of amplitude-norms-squared equals 1. For example, the following three-qubit state can be prepared:\n",
    "\n",
    "$$|\\psi\\rangle = \\frac{i}{4}|000\\rangle + \\frac{1}{\\sqrt{8}}|001\\rangle + \\frac{1+i}{4}|010\\rangle + \\frac{1+2i}{\\sqrt{8}}|101\\rangle + \\frac{1}{4}|110\\rangle$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=3017x214 at 0x1510EA87B8>"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Initializing a three-qubit quantum state\n",
    "import math\n",
    "desired_vector = [\n",
    "    1 / math.sqrt(16) * complex(0, 1),\n",
    "    1 / math.sqrt(8) * complex(1, 0),\n",
    "    1 / math.sqrt(16) * complex(1, 1),\n",
    "    0,\n",
    "    0,\n",
    "    1 / math.sqrt(8) * complex(1, 2),\n",
    "    1 / math.sqrt(16) * complex(1, 0),\n",
    "    0]\n",
    "\n",
    "\n",
    "q = QuantumRegister(\"q\", 3)\n",
    "c = ClassicalRegister(\"c\", 1)\n",
    "\n",
    "qc = QuantumCircuit(q, c)\n",
    "\n",
    "qc.initialize(desired_vector, [q[0],q[1],q[2]])\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.50000000e-01+0.00000000e+00j,  5.55111512e-17-3.53553391e-01j,\n",
       "        2.50000000e-01-2.50000000e-01j, -2.19980517e-18-3.09536077e-17j,\n",
       "       -2.62603921e-17+5.08377096e-17j,  7.07106781e-01-3.53553391e-01j,\n",
       "        8.67361738e-17-2.50000000e-01j,  0.00000000e+00+0.00000000e+00j])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp = QuantumProgram()\n",
    "qp.add_circuit(\"test\", qc)\n",
    "result = qp.execute(['test'], backend='local_unitary_simulator')\n",
    "ground = np.zeros(2**3)\n",
    "ground[0]=1.0\n",
    "qc_state = np.dot(result.get_data('test')['unitary'], ground)\n",
    "qc_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def norm(state1, state2):\n",
    "    return abs(np.dot(np.array(state1).conj(), state2))**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm(desired_vector,qc_state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Further details:\n",
    "\n",
    "How does the desired state get generated behind the scenes? There are multiple methods for doing this. QISKit uses a [method proposed by Shende et al](https://arxiv.org/abs/quant-ph/0406176). Here, the idea is to assume the quantum register to have started from our desired state, and construct a circuit that takes it to the $|00..0\\rangle$ state. The initialization circuit is then the reverse of such circuit.\n",
    "\n",
    "To take an arbitrary quantum state to the zero state in the computational basis, we perform an iterative procedure that disentangles qubits from the register one-by-one. We know that any arbitrary single-qubit state $|\\rho\\rangle$ can be taken to the $|0\\rangle$ state using a $\\phi$-degree rotation about the Z axis followed by a $\\theta$-degree rotation about the Y axis:\n",
    "\n",
    "$$R_y(-\\theta)R_z(-\\phi)|\\rho\\rangle = re^{it}|0\\rangle$$\n",
    "\n",
    "Since now we are dealing with $n$ qubits instead of just 1, we must factorize the state vector to separate the Least Significant Bit (LSB):\n",
    "\n",
    "$$\\begin{align*}\n",
    "& |\\psi\\rangle = \\alpha_{0_0}|00..00\\rangle + \\alpha_{0_1}|00..01\\rangle + \\alpha_{1_0}|00..10\\rangle + \\alpha_{1_1}|00..11\\rangle + ... + \\alpha_{(2^{n-1}-1)_0}|11..10\\rangle + \\alpha_{(2^{n-1}-1)_1}|11..11\\rangle \\\\\n",
    "&= |00..0\\rangle (\\alpha_{0_0}|0\\rangle + \\alpha_{0_1}|1\\rangle) + |00..1\\rangle (\\alpha_{1_0}|0\\rangle + \\alpha_{1_1}|1\\rangle) + ... + |11..1\\rangle (\\alpha_{(2^{n-1}-1)_0}(|0\\rangle + \\alpha_{(2^{n-1}-1)_1}|1\\rangle) \\\\\n",
    "&= |00..0\\rangle|\\rho_0\\rangle + |00..1\\rangle|\\rho_1\\rangle + ... + |11..1\\rangle|\\rho_{2^{n-1}-1}\\rangle\n",
    "\\end{align*}$$\n",
    "\n",
    "Now each of the single-qubit states $|\\rho_0\\rangle, ..., |\\rho_{2^{n-1}-1}\\rangle$ can be taken to $|0\\rangle$ by finding appropriate $\\phi$ and $\\theta$ angles per the equation above. Doing this simultaneously on all states amounts to the following unitary, which disentangles the LSB:\n",
    "\n",
    "$$U = \\begin{pmatrix} \n",
    "R_{y}(-\\theta_0)R_{z}(-\\phi_0) & & & &\\\\  \n",
    "& R_{y}(-\\theta_1)R_{z}(-\\phi_1) & & &\\\\\n",
    "& . & & &\\\\\n",
    "& & . & &\\\\\n",
    "& & & & R_y(-\\theta_{2^{n-1}-1})R_z(-\\phi_{2^{n-1}-1})\n",
    "\\end{pmatrix} $$\n",
    "\n",
    "Hence,\n",
    "\n",
    "$$U|\\psi\\rangle = \\begin{pmatrix} r_0e^{it_0}\\\\ r_1e^{it_1}\\\\ . \\\\ . \\\\ r_{2^{n-1}-1}e^{it_{2^{n-1}-1}} \\end{pmatrix}\\otimes|0\\rangle$$\n",
    "\n",
    "\n",
    "U can be implemented as a \"quantum multiplexor\" gate, since it is a block diagonal matrix. In the quantum multiplexor formalism, a block diagonal matrix of size $2^n \\times 2^n$, and consisting of $2^s$ blocks, is equivalent to a multiplexor with $s$ select qubits and $n-s$ data qubits. Depending on the state of the select qubits, the corresponding blocks are applied to the data qubits. A multiplexor of this kind can be implemented after recursive decomposition to primitive gates of cx, rz and ry."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<h2>Version information</h2>\n",
       "<p>Please note that this tutorial is targeted to the <b>stable</b> version of the QISKit. The following versions of the packages are recommended:</p>\n",
       "<table>\n",
       "<tr><th>Package</th><th colspan=\"2\">Version</th></tr>\n",
       "<tr><td>QISKit</td><td> 0.4.10</td></tr>\n",
       "<tr><td>IBMQuantumExperience</td><td>&gt;= 1.8.26</td></tr>\n",
       "<tr><td>numpy</td><td>&gt;= 1.13, &lt; 1.14</td></tr>\n",
       "<tr><td>scipy</td><td>&gt;= 0.19, &lt; 0.20</td></tr>\n",
       "<tr><td>matplotlib</td><td>&gt;= 2.0, &lt; 2.1</td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run \"../../version.ipynb\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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    "name": "ipython",
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