Qiskit_Reference_Guides/Playing_with_Quantum_Circuits_in_Qiskit.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Playing with Quantum Circuits in Qiskit \n",
    "\n",
    "**Quick reference guide to guide to creating circuits and simulating measurements in Qiskit**\n",
    "\n",
    "This notebook demonstrates some of the ways you can play with circuits using Qiskit, and multiple ways of achieving the same thing where applicable. This is meant to be an easy lookup tool for when you code with Qiskit.\n",
    "\n",
    "I'll assume you have prior knowledge of quantum states, quantum gates, OpenQASM, and basic Qiskit, especially the QuantumCircuit class.\n",
    "\n",
    "If not, check these out:\n",
    "- [Qiskit documentation: QuantumCircuit](https://qiskit.org/documentation/stubs/qiskit.circuit.QuantumCircuit.html#qiskit.circuit.QuantumCircuit)\n",
    "- [Qiskit tutorial: Summary of Quantum Operations](https://qiskit.org/documentation/tutorials/circuits/3_summary_of_quantum_operations.html)\n",
    "- [OpenQASM](https://qiskit.github.io/openqasm/language/gates.html)\n",
    "\n",
    "\n",
    "*Click [here](https://nbviewer.jupyter.org/github/quantum-kittens/quantum-computing-basics/blob/master/Qiskit_Reference_Guides/Playing_with_Quantum_Circuits_in_Qiskit.ipynb) to view this notebook in nbviewer.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# run this cell if you're executing this notebook in your browser\n",
    "!pip install qiskit\n",
    "\n",
    "from IPython.display import clear_output\n",
    "clear_output()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import *\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating a Quantum Circuit\n",
    "\n",
    "Creating a circuit with 2 qubits and 2 classical bits."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Without Registers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 116.552x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2,2)\n",
    "\n",
    "qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### With Registers\n",
    "\n",
    "- [Qiskit documentation: QuantumRegister](https://qiskit.org/documentation/stubs/qiskit.circuit.QuantumRegister.html)\n",
    "- [Qiskit documentation: ClassicalRegister](https://qiskit.org/documentation/stubs/qiskit.circuit.ClassicalRegister.html?highlight=classicalregister#qiskit.circuit.ClassicalRegister)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 151.167x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qreg = QuantumRegister(2, name = 'qreg')\n",
    "creg = ClassicalRegister(2, name = 'creg')\n",
    "\n",
    "qc = QuantumCircuit(qreg, creg)\n",
    "\n",
    "qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Gate Zoo\n",
    "\n",
    "All the gates your heart could ever want. Well, most of them."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Single-Qubit Gates\n",
    "\n",
    "Bonus: check out the difference between **.draw()** with and without **'mpl'**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 855.926x84.28 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐┌───┐┌───┐┌───┐┌─────┐┌───┐┌─────┐┌─────────┐┌─────────┐┌─────────┐»\n",
       "q_0: ┤ X ├┤ Y ├┤ Z ├┤ S ├┤ SDG ├┤ T ├┤ TDG ├┤ RX(π/2) ├┤ RY(π/2) ├┤ RZ(π/2) ├»\n",
       "     └───┘└───┘└───┘└───┘└─────┘└───┘└─────┘└─────────┘└─────────┘└─────────┘»\n",
       "«     ┌──────────────┐┌───────────┐┌──────┐\n",
       "«q_0: ┤ U(π/2,π/4,π) ├┤ U2(π/4,π) ├┤ P(π) ├\n",
       "«     └──────────────┘└───────────┘└──────┘</pre>"
      ],
      "text/plain": [
       "     ┌───┐┌───┐┌───┐┌───┐┌─────┐┌───┐┌─────┐┌─────────┐┌─────────┐┌─────────┐»\n",
       "q_0: ┤ X ├┤ Y ├┤ Z ├┤ S ├┤ SDG ├┤ T ├┤ TDG ├┤ RX(π/2) ├┤ RY(π/2) ├┤ RZ(π/2) ├»\n",
       "     └───┘└───┘└───┘└───┘└─────┘└───┘└─────┘└─────────┘└─────────┘└─────────┘»\n",
       "«     ┌──────────────┐┌───────────┐┌──────┐\n",
       "«q_0: ┤ U(π/2,π/4,π) ├┤ U2(π/4,π) ├┤ P(π) ├\n",
       "«     └──────────────┘└───────────┘└──────┘"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qc = QuantumCircuit(1)\n",
    "\n",
    "# set the angles to whatever you want\n",
    "theta = np.pi/2\n",
    "phi = np.pi/4\n",
    "lambdaa = np.pi\n",
    "\n",
    "# comment/uncomment the gates to play with them\n",
    "\n",
    "qc.x(0) # x on qubit 0\n",
    "qc.y(0) # y on qubit 0\n",
    "qc.z(0) # z on qubit 0\n",
    "qc.s(0) # s gate on qubit 0, sqrt of z\n",
    "qc.sdg(0) # s† on qubit 0\n",
    "qc.t(0) # t gate on qubit 0, sqrt of s\n",
    "qc.tdg(0) # t† on qubit 0\n",
    "\n",
    "### rotations\n",
    "qc.rx(theta,0) # rx rotation on qubit 0\n",
    "qc.ry(theta,0) # ry rotation on qubit 0\n",
    "qc.rz(theta,0) # rz rotation on qubit 0\n",
    "\n",
    "### generic\n",
    "qc.u(theta, phi, lambdaa, 0) #u3 gate\n",
    "qc.u2(phi, lambdaa, 0) #u2 = u3(pi/2, phi, lambdaa)\n",
    "qc.p(lambdaa, 0) #p = u1 = u3(0, 0, lambdaa)\n",
    "\n",
    "#\n",
    "\n",
    "display(qc.draw('mpl'))\n",
    "display(qc.draw())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2-Qubit Gates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 447.652x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2)\n",
    "\n",
    "# set the angles to whatever you want\n",
    "theta = np.pi/2\n",
    "phi = np.pi/4\n",
    "lambdaa = np.pi\n",
    "\n",
    "\n",
    "# comment/uncomment any of the following to your heart's content\n",
    "\n",
    "qc.cx(0,1) # CNOT with qubit 0 as control and qubit 1 as target\n",
    "qc.cy(0,1) # controlled-Y with qubit 0 as control and qubit 1 as target\n",
    "qc.cz(0,1) # controlled-Z with qubit 0 as control and qubit 1 as target\n",
    "qc.ch(0, 1) # controlled-H with qubit 0 as control and qubit 1 as target\n",
    "qc.cu3(theta, phi, lambdaa, 0, 1) # controlled-u3 with qubit 0 as control and qubit 1 as target\n",
    "qc.swap(0,1) # swap qubits 0 and 1\n",
    "\n",
    "#\n",
    "\n",
    "qc.draw('mpl')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3-Qubit Gates\n",
    "\n",
    "This shows three ways of creating the **Toffoli gate** with qubits 0 & 1 as controls and qubit 2 as the target. Take particular note of the **circuit library**, **append**, and **.control()**.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 267.197x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit.library import CXGate\n",
    "\n",
    "qc = QuantumCircuit(3)\n",
    "\n",
    "# Method 1:\n",
    "qc.ccx(0,1,2) \n",
    "\n",
    "\n",
    "# Method 2:\n",
    "qc.mct([0,1],2)\n",
    "\n",
    "#Method 3\n",
    "our_ccx = CXGate().control()\n",
    "qc.append(our_ccx, [0,1,2])\n",
    "\n",
    "\n",
    "qc.draw('mpl')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Brief Digression: Creating a Bell Circuit\n",
    "\n",
    "Let's whip up a circuit that generates a Bell state, and then use it as an example for most of this notebook.\n",
    "\n",
    "$\\left|\\phi^+\\right\\rangle = \\frac{1}{\\sqrt{2}}(\\left|00\\right\\rangle + \\left|11\\right\\rangle)$\n",
    "\n",
    "$\\left|\\phi^-\\right\\rangle = \\frac{1}{\\sqrt{2}}(\\left|00\\right\\rangle - \\left|11\\right\\rangle)$\n",
    "\n",
    "$\\left|\\psi^+\\right\\rangle = \\frac{1}{\\sqrt{2}}(\\left|01\\right\\rangle + \\left|10\\right\\rangle)$\n",
    "\n",
    "$\\left|\\psi^-\\right\\rangle = \\frac{1}{\\sqrt{2}}(\\left|01\\right\\rangle - \\left|10\\right\\rangle)$\n",
    "\n",
    "To make things as unnecessarily complicated as possible, I'm going with $\\left|\\psi^-\\right\\rangle$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQUAAAB7CAYAAAB9yZWUAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy86wFpkAAAACXBIWXMAAAsTAAALEwEAmpwYAAALQ0lEQVR4nO3cfXAU5QHH8e/uJRA0jIAZQRCQAKEScxGiyOCMgfEtTKuggsK0GY1MoYRSEdv6Gp3xJaOIFW2d4tQR2lGiJQaKlWHUlhzQ+NKIBqKtR2kgnCIkiC2xMSF32z9OIo+8JBcut3vk95nZGW439+wP5vLj2ef2znIcx0FE5Bu22wFExFtUCiJiUCmIiEGlICIGlYKIGFQKImJQKYiIQaUgIgaVgogYVAoiYlApiIhBpSAiBpWCiBhUCiJiUCmIiEGlICIGlYKIGFQKImJQKYiIQaUgIgaVgogYVAoiYlApiIhBpSAiBpWCiBhUCiJiSHE7gNdVVMOnB90595D+cMPF7pxbei6VQgc+PQg797udQiRxdPkgIgaVgogYVAoiYlApiIhBpSAiBpWCiBhUCiJiUCmIiEGlIIaWNjjUDG1ht5OIWzxdCpFIhKVLlzJ69GjS0tLIzc0lEAgwZswY5s6d63a84yp/ZDLvrX2k0/u9Yud++F0l3P0KlFTAPavhj+/BgSa3k0miefo25zlz5lBRUUFJSQl5eXlUVVUxe/ZsGhoaWLx4sdvxThvVdfBSVfTPzjf7Dofh7R3w4W746ZUwuL9r8STBPFsKZWVlrFy5ksrKSvLz8wGYMmUKW7dupaKigvHjx7uc8PRw8CtY9fa3ZXA0B2g+DC9shnuvBdtKdDpxg2cvH0pLSykoKGgvhCNGjRpFamoqfr8fgF27dpGfn09WVhY5OTls3rzZjbhJq2oHRI7XCN9wHGg8BDs+T1wmcZcnSyEUClFbW8vMmTOPOVZfX092dja9e/cGYN68edx8880Eg0Gee+45Zs2aRWtra4fnsCyrU1sgUBlz/vf+9Ci/ndvP2D4Lbol5nECgstM5u7r9Ye3bOM5JWgFwHIei2x/t9izaunfrLE9ePoRCIQAGDRpk7G9ubiYQCDB16lQAGhsb2bJlC+vWrQNg0qRJDB48mI0bN3LNNdckNvRRJky7jwnT7zf2lT8y2Z0wHbBsXydeMA627UtIHnGfJ2cKGRkZAASDQWP/kiVL2Lt3L3l5eUB01jBw4MD2WQPAiBEj2L17d4fncBynU1t+/uT4/cVilJ8/udM5u7rNKJjQYQ7LsvnN43d3exZt3bt1lidnCpmZmfj9fkpLSxkwYABDhgyhvLyc9evXA7SXgpy6y7Jgy44TH7eAM3tDztCERRKXeXKmYNs2q1evJjs7m/nz51NUVERGRgYLFizA5/O1LzIOGzaMffv20dLS0v7curo6hg8f7lb0pHNuPyjIif75uxcRFmBZ8KPLwOfJV4p0B8uJZV7hssLCQmpqati2bVv7vquvvprp06dTXFxMVVUVM2bMYNeuXfTq1Ssu5/z1m+59HdvIc2DhVYk517s74c1aaDzqZqWR58D3cyHznMRkEG/w5OXDiVRXVzNx4kRj3/Lly7n11ltZtmwZvXr1oqysLG6F0JNcOhImZMIdq6KP778OMvq6m0nckTSl0NTURDAYpLi42NifmZnJpk2bXEp1ejn6TQgVQs+VNKWQnp5OOKxP6Yh0Ny0fiYhBpSAiBpWCiBhUCiJiUCmIiEGlICIGlYKIGJLmPgW3DHHxa8jcPLf0XCqFDtxwsdsJRBJLlw8iYlApiIhBpSAiBpWCiBhUCiJiUCmIiEGlICIGlYKIGFQKImJQKYiIQaUgIgaVgogYVAoiYtCnJMUz7vzkY2oOHXLl3Ll9+/LkmLFdeq5buU8l88moFMQzag4dYtPBL9yOEbNkzX0iunwQEYNKQUQMunwQDn4F2/ZA6KgZ8DNvwOD+MOxs8A+FtFT38kliqRR6sL1fwus18FEInO8c+3dDdAN49e9wyQiYmgtn9k50Skk0lUIPFHHgLx/Bhu0QjnT88y1tsGUH1OyBWZdC9nndn1HcozWFHibiwCvvRmcInSmEox36Gp4PwLs7uyebeINKoYfZsO3Ufqkd4OV34B+fxS2SeIxKoQfZ1Qhv1p78Z5b9MLqdjEN0ttHcGrdo4iGeLoVIJMLSpUsZPXo0aWlp5ObmEggEGDNmDHPnznU7XtJZ8/6xC4pd9eX/4K2P4jSYeIqnFxrnzJlDRUUFJSUl5OXlUVVVxezZs2loaGDx4sVux0sqew7A7sb4jvnOTpjqhxRffMftLOfwYdoW3oE9LhffvB+37w+vWUvk1TWkLH8WKz3dnXAnENleS/i+B449EA7D4cP4nlyCnXNh4oMdxbOlUFZWxsqVK6msrCQ/Px+AKVOmsHXrVioqKhg/frzLCZPL1t3xH/OrFvhkr3vvRlipqaTc/QvaFi7CmnAJ9riLcOrqiLzwe3yPPuS5QgCwcy7EXldh7HNaWwnf+Uvo1w8rO/6fZYiVZy8fSktLKSgoaC+EI0aNGkVqaip+vx+ABx54gKysLGzbpry83I2oSaH+QDeN6/It/9b5w7Fvu4Xw0qdwvviCtseewJ52LbY/x91gMQg/+RROayu+e+/Cst3/lXQ/wXGEQiFqa2uZOXPmMcfq6+vJzs6md+/oXTQFBQVs2LCByy+/PNExk8rn/+mmcb/snnFjYU+fhjVsKG3zFoDPh31LoduROi384iqcD2pIeehBrD593I4DePTyIRQKATBo0CBjf3NzM4FAgKlTp7bvmzRpUpfOYVlW1wMmoeLnm0hNO7P9cUfvMJzo+KKXzMdrX3ud2/J/cIrponxPPIad64/5eZZlYflzcN7fij3rJqzU2O/JrqysxLpkYszPg67njmzaTOSV1fgeL8UaODDm58ea2XE6t8zsyZlCRkYGAMFg0Ni/ZMkS9u7dS15enhuxklrb4a+7Zdxwa/eMGwunro7Iqpexb55J5MVVOPv3ux2pQ5FgkPATv8K36GfYYy9wO47BkzOFzMxM/H4/paWlDBgwgCFDhlBeXs769esB4lIKnW3N08XTb0Bdw7ePv/s//hFHZggnOv5dxbfdyJ+fjs+/5ZXV78b8vQRO6+HoOsIN0/EV3YJz8GD0l+3x0piuzydPnsxbXXxNxJrbaWwk/ODD2Ddej33FlC6dE04t88l4cqZg2zarV68mOzub+fPnU1RUREZGBgsWLMDn87UvMkrnDR2QXON2VuSFFVgpKdiF0TbzFf8E5/N9RF5d426wE3C+/prwgw9hjb3As2sfnpwpAGRlZbFx40ZjX2FhIWPHjqWPRxZkksm44bDpk/iO2ScVxpwb3zFjEfngQyLrN5Dy7DNYKdGXsnXGGfju+jnhe+7Hvng81ogR7gU8DmfL33B2/Avq99A27cZjjvtuX3hKs4d48GwpHE91dTUTJ5oLKyUlJaxYsYKGhga2b9/OokWLCAQCjBw50qWU3nR+BpzXH0IH4zfmhJHQy8VXkD3uomPe8wewL8zGfs2bMwX7yiuwr7zC7Rgn5cnLh+NpamoiGAwec9PSww8/TCgUoqWlhQMHDhAKhVQIx2FZMD2O67PpaXBVdvzGE+9ImplCeno64XDY7RhJbdRAyP8eBP554p/p7ALjTROixSCnn6SZKUh8XDcOLhp2amNcnxf9ijY5PSXNTEHiw2dD4WVwdjr89ePYPjXZJxVmTIC887srnXiBSqEH8tlw7TjIGQqvfQA7O7jXx2fDuGHR55x1RmIyintUCj3Y+Rmw8Kro5yK21cOeL2D/f6EtAr1TYXC/6Lc5jxsOfbV+0GOoFIRBZ8Gg5PlQoXQzLTSKiEGlICIGXT6IZ+T27ZuU53Yrd3ed13J62scFReSkdPkgIgaVgogYVAoiYlApiIhBpSAiBpWCiBhUCiJiUCmIiEGlICIGlYKIGFQKImJQKYiIQaUgIgaVgogYVAoiYlApiIhBpSAiBpWCiBj+D3XYqSPx+wuPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 327.252x144.48 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qc_bell = QuantumCircuit(2)\n",
    "\n",
    "qc_bell.h(0)\n",
    "qc_bell.cx(0,1)\n",
    "qc_bell.x(1)\n",
    "qc_bell.z(1)\n",
    "\n",
    "display(qc_bell.draw('mpl'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want to quickly double check that the above circuit indeed generates $\\left|\\psi^-\\right\\rangle$, you can retrieve the state of the circuit using Statevector. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\n",
       "\\left|\\psi^-\\right\\rangle = \n",
       "\\begin{bmatrix}\n",
       "0 & \\tfrac{1}{\\sqrt{2}} & -\\tfrac{1}{\\sqrt{2}} & 0  \\\\\n",
       " \\end{bmatrix}\n",
       "$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.quantum_info import Statevector \n",
    "\n",
    "state = Statevector(qc_bell)\n",
    "\n",
    "state.draw('latex', prefix = '\\\\left|\\\\psi^-\\\\right\\\\rangle = ' )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This isn't the only way to look at states. For more on quantum states, I point you to the reference guide: [Playing with Quantum States in Qiskit](https://nbviewer.jupyter.org/github/quantum-kittens/quantum-computing-basics/blob/master/Qiskit_Reference_Guides/Playing_with_Quantum_States_in_Qiskit.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## OpenQASM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using OpenQASM to Create a Circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 447.652x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bell_qasm_string = \"\"\"\n",
    "OPENQASM 2.0; \n",
    "include \"qelib1.inc\"; \n",
    "\n",
    "gate bell a, b {\n",
    "    u(pi/2, 0, pi) a;\n",
    "    cx a, b;\n",
    "}\n",
    "\n",
    "qreg q[2];\n",
    "creg c[2];\n",
    "\n",
    "bell q[0], q[1];\n",
    "x q[1];\n",
    "z q[1];\n",
    "\n",
    "barrier q[0],q[1];\n",
    "measure q[0] -> c[0];\n",
    "measure q[1] -> c[1];\n",
    "\"\"\"\n",
    "\n",
    "qc_bell_qasm = QuantumCircuit.from_qasm_str(bell_qasm_string)\n",
    "qc_bell_qasm.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This one has measurements. What I'm calling the 'bell' gate is the basic requirement for a Bell state to be generated. The bell gate alone generates the state $\\left|\\phi^+\\right\\rangle$. I've made it a little more complicated than it needs to be, just to demonstrate how to define a gate.\n",
    "\n",
    "And $u(pi/2, 0, pi)$ is the Hadamard gate.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Return the OpenQASM String for a Circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OPENQASM 2.0;\n",
      "include \"qelib1.inc\";\n",
      "qreg q[2];\n",
      "h q[0];\n",
      "cx q[0],q[1];\n",
      "x q[1];\n",
      "z q[1];\n",
      "\n"
     ]
    }
   ],
   "source": [
    "qc_bell_string = qc_bell.qasm()\n",
    "print(qc_bell_string)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bonus: Wrap a Circuit to a Gate\n",
    "\n",
    "We can also create the bell gate without OpenQASM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 206.852x144.48 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 206.852x144.48 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qc_bell_init = QuantumCircuit(2)\n",
    "qc_bell_init.h(0)\n",
    "qc_bell_init.cx(0,1)\n",
    "\n",
    "display(qc_bell_init.draw('mpl'))\n",
    "\n",
    "bell_gate = qc_bell_init.to_gate()\n",
    "bell_gate.name ='Bell Gate'\n",
    "\n",
    "qc_bell_gate = QuantumCircuit(2)\n",
    "qc_bell_gate.append(bell_gate, [0,1])\n",
    "\n",
    "display(qc_bell_gate.draw('mpl'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unitary Representation of a Circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Method 1: Operator from quantum_info"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\n",
       "U = \n",
       "\\begin{bmatrix}\n",
       "0 & 0 & \\tfrac{1}{\\sqrt{2}} & \\tfrac{1}{\\sqrt{2}}  \\\\\n",
       " \\tfrac{1}{\\sqrt{2}} & -\\tfrac{1}{\\sqrt{2}} & 0 & 0  \\\\\n",
       " -\\tfrac{1}{\\sqrt{2}} & -\\tfrac{1}{\\sqrt{2}} & 0 & 0  \\\\\n",
       " 0 & 0 & -\\tfrac{1}{\\sqrt{2}} & \\tfrac{1}{\\sqrt{2}}  \\\\\n",
       " \\end{bmatrix}\n",
       "$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.quantum_info import Operator\n",
    "from qiskit.visualization import array_to_latex\n",
    "\n",
    "U = Operator(qc_bell)\n",
    "\n",
    "array_to_latex(U.data, prefix = 'U = ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Method 2: Using the Unitary Simulator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\n",
       "U = \n",
       "\\begin{bmatrix}\n",
       "0 & 0 & \\tfrac{1}{\\sqrt{2}} & \\tfrac{1}{\\sqrt{2}}  \\\\\n",
       " \\tfrac{1}{\\sqrt{2}} & -\\tfrac{1}{\\sqrt{2}} & 0 & 0  \\\\\n",
       " -\\tfrac{1}{\\sqrt{2}} & -\\tfrac{1}{\\sqrt{2}} & 0 & 0  \\\\\n",
       " 0 & 0 & -\\tfrac{1}{\\sqrt{2}} & \\tfrac{1}{\\sqrt{2}}  \\\\\n",
       " \\end{bmatrix}\n",
       "$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from qiskit.providers.aer import UnitarySimulator\n",
    "\n",
    "backend = UnitarySimulator() # alternative: backend = Aer.get_backend('unitary_simulator')\n",
    "\n",
    "job = execute(qc_bell, backend)\n",
    "U = job.result().get_unitary()\n",
    "\n",
    "display(array_to_latex(U.data, prefix = 'U = '))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulating Measurements Using the Qasm Simulator\n",
    "\n",
    "Includes an example of how to use **.compose()**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 507.852x204.68 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Counts: {'01': 502, '10': 522}\n"
     ]
    }
   ],
   "source": [
    "from qiskit.providers.aer import QasmSimulator\n",
    "\n",
    "qc_measure = QuantumCircuit(2,2)\n",
    "\n",
    "qc_measure.barrier()\n",
    "qc_measure.measure([0,1], [0,1]) # alternative: qc_measure = QuantumCircuit(2) | qc_measure.measure_all() = .barrier() + measure every qubit + creates a classical register\n",
    "\n",
    "qc_bell_measure = qc_measure.compose(qc_bell, range(2), front = True) # combines two circuits, placing qc_bell in front of qc_measure\n",
    "\n",
    "display(qc_bell_measure.draw('mpl'))\n",
    "\n",
    "backend = QasmSimulator() # alternative: backend = Aer.get_backend('qasm_simulator')\n",
    "\n",
    "job = execute(qc_bell_measure, backend, shots = 1024) # alternative: qc_transpiled = transpile(qc_bell_measure, backend), job = backend.run(qc_transpiled, shots = 1024)\n",
    "\n",
    "counts = job.result().get_counts()\n",
    "\n",
    "print('Counts: ' + str(counts))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing Measurements Using plot_histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.visualization import plot_histogram\n",
    "\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can do a lot more with histograms. For instance, you can compare the results of two experiments side by side!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Counts, second experiment: {'10': 525, '01': 499}\n"
     ]
    }
   ],
   "source": [
    "job = execute(qc_bell_measure, backend, shots = 1024) \n",
    "\n",
    "counts_2 = job.result().get_counts()\n",
    "\n",
    "print('Counts, second experiment: ' + str(counts_2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "legend = ['First Experiment', 'Second Experiment']\n",
    "plot_histogram([counts, counts_2], legend = legend, color = ['teal', 'black'], figsize = (10, 7), bar_labels = False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Decomposing Circuits\n",
    "\n",
    "To demonstrate decomposition, it'd be better to look at a more complicated circuit. \n",
    "\n",
    "So let's extend the Bell state $\\left|\\phi^+\\right\\rangle = \\frac{1}{\\sqrt{2}}(\\left|00\\right\\rangle + \\left|11\\right\\rangle)$ to the GHZ state: $\\left|GHZ\\right\\rangle = \\frac{1}{\\sqrt{2}}(\\left|000\\right\\rangle + \\left|111\\right\\rangle)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 267.197x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc_ghz = QuantumCircuit(3)\n",
    "\n",
    "qc_ghz.h(0)\n",
    "qc_ghz.cx(0,1)\n",
    "qc_ghz.ccx(0,1,2)\n",
    "qc_ghz.draw('mpl') #original circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Method 1: .decompose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 808.997x204.68 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 808.997x204.68 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(qc_ghz.decompose().draw('mpl')) #decompose one level down\n",
    "display(qc_ghz.decompose().decompose().draw('mpl')) #decompose two levels down"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Method 2: Unroller + PassManager"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 808.997x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.transpiler import PassManager\n",
    "from qiskit.transpiler.passes import Unroller\n",
    "\n",
    "gates_pass = Unroller(['u1', 'u2', 'u3', 'cx']) #play around with this\n",
    "pm = PassManager(gates_pass)\n",
    "pm.run(qc_ghz).draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Circuit Depth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The circuit depth of the Bell circuit without measurements is: 4\n",
      "The circuit depth of the Bell circuit with measurements is: 5\n"
     ]
    }
   ],
   "source": [
    "print('The circuit depth of the Bell circuit without measurements is: ' + str(qc_bell.depth()))\n",
    "\n",
    "#Qiskit counts the measurements in the depth calculation:\n",
    "print('The circuit depth of the Bell circuit with measurements is: ' + str(qc_bell_measure.depth()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Practice figuring out the depth of a randomly generated circuit:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 387.597x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit.random import random_circuit\n",
    "import random\n",
    "\n",
    "#play around with these parameters:\n",
    "num_qubits = 3 \n",
    "max_depth = 10\n",
    "add_measurements = True #True/False\n",
    "\n",
    "#random circuit:\n",
    "rand_circ = random_circuit(num_qubits, depth = random.randint(1,max_depth), measure=add_measurements) \n",
    "rand_circ.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# run this cell to see if you are correct\n",
    "\n",
    "print('The circuit depth is: ' + str(rand_circ.depth()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More to explore:\n",
    "\n",
    "- [Adder in OpenQASM](https://github.com/Qiskit/openqasm/blob/master/examples/adder.qasm)\n",
    "- [Quantum Fridays: Clifford exercises](https://github.com/qiskit-community/quantum-fridays/blob/main/Exercise5.ipynb)\n",
    "- [Quantum Fridays: Effects of garbage in quantum circuits](https://github.com/qiskit-community/quantum-fridays/blob/main/Exercise6.ipynb)\n",
    "- [Playing with Quantum States in Qiskit](https://nbviewer.jupyter.org/github/quantum-kittens/quantum-computing-basics/blob/master/Qiskit_Reference_Guides/Playing_with_Quantum_States_in_Qiskit.ipynb)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Created by quantum-kittens"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
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