OpenQASM3-Exercise IPE (Solution).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "approximate-charger",
   "metadata": {},
   "source": [
    "# Exercise - Iterative Phase Estimation\n",
    "#### @Quantom  & @Micheal Healy & @Hoss Ajallooiean - Qiskit Slack\n",
    "#### @taalexander & @mbhealy & @katetsu - Github\n",
    "\n",
    "Join us on the Qiskit Slack channel [#ieee-tutorial-openqasm3](https://qiskit.slack.com/archives/C02HQLDS3D3)\n",
    "\n",
    "\n",
    "Before trying to complete this notebook make sure you've completed the installation process as described in [Hello OpenQASM3](./Hello-OpenQASM3.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c4285aa",
   "metadata": {},
   "source": [
    "The goal of this exercise is to understand how the Iterative Phase Estimation (IPE) algorithm works, why would we use the IPE algorithm instead of the QPE (Quantum Phase Estimation) algorithm and how to build it with Qiskit using the same circuit exploiting reset gate and the `c_if` method that allows to apply gates conditioned by the values stored in a classical register, resulting from previous measurements.\n",
    "\n",
    "If you want a further background on iterative phase estimation have a look at the references below.\n",
    "\n",
    "**References**\n",
    "\n",
    "- [Section 2 of Lab 4: Iterative Phase Estimation (IPE) Algorithm](https://qiskit.org/textbook/ch-labs/Lab04_IterativePhaseEstimation.html#2-iterative-phase-estimation-ipe-algorithm) \n",
    "\n",
    "- [Ch.3.6 Quantum Phase Estimation](https://qiskit.org/textbook/ch-algorithms/quantum-phase-estimation.html)\n",
    "- [Arbitrary accuracy iterative phase estimation algorithm as a two qubit benchmark - arXiv:quant-ph/0610214\n",
    "](https://arxiv.org/abs/quant-ph/0610214)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e96a571b",
   "metadata": {},
   "source": [
    "### Preamble"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "bc01809c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "from typing import Any, List, Dict, Union\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from qiskit import IBMQ, Aer, QuantumCircuit, QuantumRegister, ClassicalRegister, transpile, execute\n",
    "from qiskit.tools.visualization import plot_histogram\n",
    "from qiskit.result import marginal_counts\n",
    "import qiskit.tools.jupyter\n",
    "\n",
    "from run_openqasm3 import run_openqasm3\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "pi = np.pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "78eb7de1",
   "metadata": {},
   "outputs": [],
   "source": [
    "backend_sim = Aer.get_backend('aer_simulator')\n",
    "\n",
    "hub = 'ibm-q-community'\n",
    "group = 'ieee-session'\n",
    "project = 'event-2021'\n",
    "backend_name = 'ibm_perth'\n",
    "\n",
    "IBMQ.load_account()\n",
    "provider = IBMQ.get_provider(hub=hub, group=group, project=project)\n",
    "backend_real = provider.get_backend(backend_name)\n",
    "\n",
    "basis_gates = backend_real.configuration().basis_gates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "9f75dd93",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3d15ef072aff45338bc606e15be4f7bd",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "VBox(children=(HTML(value=\"<h1 style='color:#ffffff;background-color:#000000;padding-top: 1%;padding-bottom: 1…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<IBMQBackend('ibm_perth') from IBMQ(hub='ibm-q-community', group='ieee-session', project='event-2021')>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import qiskit.tools.jupyter\n",
    "backend_real"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6843f80a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import qasm3\n",
    "\n",
    "def dump_qasm3(circuit, backend=backend_real):\n",
    "    return qasm3.Exporter(includes=[], basis_gates=basis_gates+[\"reset\"], disable_constants=True).dumps(circuit)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "prescribed-skill",
   "metadata": {},
   "source": [
    "## Conditined gates: the c_if method"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "protective-tender",
   "metadata": {},
   "source": [
    "Before starting the IPE algorithm, we will give a brief tutorial about the Qiskit conditional method, c_if, as it goes into building the IPE circuit.\n",
    "\n",
    "`c_if` is a function (actually a method of the gate class) to perform conditioned operations based on the value stored previously in a classical register. With this feature you can apply gates after a measurement in the same circuit conditioned by the measurement outcome.\n",
    "\n",
    "For example, the following code will execute the $X$ gate if the value of the classical register is $0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "spoken-willow",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 253.926x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = QuantumRegister(1,'q')\n",
    "c = ClassicalRegister(1,'c')\n",
    "qc = QuantumCircuit(q, c)\n",
    "qc.h(0)\n",
    "qc.measure(0,0)\n",
    "qc.x(0).c_if(c, 0)\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "worth-speech",
   "metadata": {},
   "source": [
    "We highlight that the method c_if expects as the first argument a whole classical register, not a single classical bit (or a list of classical bits), and as the second argument a value in decimal representation (a non-negative integer), not the value of a single bit, 0, or 1 (or a list/string of binary digits).\n",
    "\n",
    "Let's make another example. Consider that we want to perform a bit flip on the third qubit after the measurements in the following circuit, when the results of the measurement of $q_0$ and $q_1$ are both $1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "excellent-count",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 387.597x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = QuantumRegister(3,'q')\n",
    "c = ClassicalRegister(3,'c')\n",
    "qc = QuantumCircuit(q, c)\n",
    "qc.h(q[0])\n",
    "qc.h(q[1])\n",
    "qc.h(q[2])\n",
    "qc.barrier()\n",
    "qc.measure(q,c)\n",
    "qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "entertaining-adams",
   "metadata": {},
   "source": [
    "We want to apply the $X$ gate, only if both the results of the measurement of $q_1$ and $q_2$ are $1$. We can do this using the c_if method, conditioning the application of $X$ depending on the value passed as argument to c_if.\n",
    "\n",
    "We will have to encode the value to pass to the c_if method such that it will check the values 011 and 111 (in binary representation), since it does not matter what is in the rightmost position.\n",
    "\n",
    "The 2 integer values in decimal representation:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "finished-failure",
   "metadata": {},
   "source": [
    "\n",
    "<img src=\"figs/binary.png\" width=\"50%\" >\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "brutal-slope",
   "metadata": {},
   "source": [
    "We can check the solutions using the bin() method in python (the prefix `0b` indicates the binary format)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "boxed-electronics",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0b11\n",
      "0b111\n"
     ]
    }
   ],
   "source": [
    "print(bin(3))\n",
    "print(bin(7))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d47e359e-ad29-4fb7-a428-cfcb69904257",
   "metadata": {},
   "source": [
    "So we have to apply $X$ to $q_2$ using c_if  two times, one for each value corresponding to 011 and 111.\n",
    "\n",
    "*Note*: Conditioning on multiple bits is not supported just yet through IBM backends but it will be very soon."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "following-surfing",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAADWCAYAAAAtmd5RAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAhEElEQVR4nO3de1iUdcI+8HsGOagE6suLxkEKFAQURgHXQ8JgVFgeEdn0F790MY1w10MHafN8QEVT3g7qapZttpQgnvbFNlSYLDyAihFKLGohLCUqipiAMfP+wTIrDsw8EPB9wPtzXV7X+BzmuUcuuef5PieFTqfTgYiISAKl6ABERNRxsDSIiEgylgYREUnG0iAiIslYGkREJBlLg4iIJGNpEBGRZCwNIiKSjKVBRESSsTSIiEgylgYREUnG0iAiIslYGkREJBlLg4iIJGNpEBGRZCwNIiKSjKVBRESSsTSIiEgylgYREUnWRXQAan/5+flG57/33nuYM2eO0WUGDBjQmpGIqIPgngYZeP/990VHICKZYmkQEZFkLA0iIpKMpUEGkpOTRUcgIpliaRARkWQsDTIQHh4uOgIRyRRPuTUhJRsoKRezbceeQJi/mG2LMG/ePOTk5AjZtkqlQkJCgpBtE3UkLA0TSsqBi1dFp3g45OTkQKPRiI5BREZweIoMxMTEiI5ARDLF0iADpq4GJ6KHF0uDDAQGBoqOQEQyxdIgA2VlZaIjEJFMsTSIiEgylgYZ8PLyEh2BiGSKpUEG9uzZIzpCmzI3NxcdgajD4nUaZGDJkiVYsWKF6BgmDR48GIGBgfDz84O9vT10Oh1KSkpw+vRpHDlyBAUFBQbrTJ8+HQsWLEBISAiuXuUFOETNxdIgA0lJSbIujYiICLz22msICAhodH5UVBQA4OjRo4iLi8ORI0cA1BXGjh07oFQqMW7cOOzYsaPdMhN1FrIentJqtdiwYQP69+8PKysr+Pr6QqPRwMPDA7NmzRIdr1HJq9Q4tW+V5Okknb29Pfbv34/PP/8cAQEBuH79Oj744APMnj0bY8aMwbPPPos//elP+PTTT1FZWYnRo0fj8OHD2L59O15++WV9YSxcuJCFQdRCst7TiIqKQkpKChYvXgw/Pz9kZmZi6tSpKCsrw4IFC0THo3bk7OyM9PR0uLm54datW4iNjcXOnTtRVVVlsOy7774LGxsbzJkzB0uWLMHMmTMRFRUFhUKBhQsXIj4+XsAnIOocZFsaiYmJ2LlzJzIyMhAUFAQACA4OxpkzZ5CSkoIhQ4YITth5ye3+T927d0daWhrc3NyQnZ2NiRMnoqSkxOg6FRUViIuLAwCsWrUKCoUCly5dwoYNG9ojMlGnJdvhqbi4OISGhuoLo16/fv1gbm4OHx8fAMAPP/yAoKAguLu7Y9CgQTh27JiIuJ1KXl6e6AgNxMfHw8PDA7m5uQgJCTFZGPWmT5+OlStXQqFQoKKiAq6urpg/f34bpyXq3BQ6nU4nOsSDiouL4ezsjB07duAPf/hDg3lTp05Ffn4+zp49CwB45plnMGHCBLzyyivIzMzElClTcPnyZVhYWBjdhkKhkJRl8lvpcPJUS86evEqNny6ehJm5ZYPp96oqMSxsGYZOXCT5vYovZGDP6mDJy0tl6hfnpk2bJC3THnx9fZGTk4Oamhr4+/sjNzdX0nr3H/ReuHAhcnNzkZqaiqqqKri4uPDMKaIHSK0CWe5pFBcXAwD69OnTYPrdu3eh0Wj0Q1PXrl3D119/rT9bZsSIEXBwcEB6enr7Bn7A0AlvIXrbzQZ/HNyfEJqpo3rllVcAAFu3bm1xYcTHx+PQoUM4ePAgrKysDL6IEJF0sjymYWdnBwAoKCjAs88+q58eHx+P0tJS+Pn5AQCKiorQu3dvWFr+51v9448/jh9//NHkNqS26rtp4p6nERSkRvKq1t8RzM/PNzp/06ZNJs9O27hxY2tGAgCo1eoGx1PMzMwwbdo0AMD7778v6T0aK4x677//PsaNG4fIyEisXbu2wXpBQUHIyMj47R+CqJOTZWm4urrCx8cHcXFx6NWrFxwdHZGcnIzU1FQA0JcGtY3ly5eLjgAA8PT0hLW1NS5dutTohXoPMlYYAJCeno7q6moMGDAA1tbWqKysbKvoRJ2WLIenlEolkpKS4O3tjejoaMyYMQN2dnaIiYmBmZmZ/iB437598fPPP6O6ulq/7uXLl+Hi4iIqeqcQEREhOgIAYNCgQQCgP35ljKnCAICamhrk5eVBqVRi4MCBrZ6X6GEgyz0NAHB3dzc4NhEZGQkvLy907doVQN0w1siRI7Fjxw79gfCSkhIEB7f+wWOpwhdlNGu6HHl6euLChQuiY+DHH3/Etm3bcOLECaPLDR8+3GRh1Pvss8+QlZWF8nJBD34n6uBkWxqNyc7OxrBhwxpM27p1K6ZPn46EhARYWFggMTHR5JlT1DFkZmYiMzPT5HLHjx/Hli1bUFRUZPLCvfXr17dWPKKHUocpjcrKShQUFOjPpqnn6uqKr776SlAqkgs+opaofXSY0rC2tkZtba3oGA8FtVotOgIRyZQsD4STWFu2bBEdgYhkiqVBBqKjo0VHICKZYmmQAV7kRkRNYWkQEZFkLA0iIpKMpUEG5HBhHxHJE0uDDOzevVt0BCKSqQ5znYYojj0fvm0vXbpUyP2nVCpVs9e5VFQKAHDt+2iD1+2xbaKHEUvDhDB/0QkeHgkJCc1eJ3bdNgDA2oWzGrwmorbB4SkiIpKMpUEGNm/eLDoCEckUS4MMeHt7i45ARDLF0iADQUFBoiMQkUyxNIiISDKWBhERScbSIAMBAQGiIxCRTLE0yEBWVpboCEQkUywNIiKSjKVBRESSsTTIQHJysugIRCRTLA0iIpKMpUEGwsPDRUcgIpniXW5NSMkGSsrFbNuxJ++y2xHMmzcPOTk57b5dlUrVojsDE/0WLA0TSsqBi1dFpyA5y8nJgUajER2DqF1weIoMxMTEiI5ARDLF0iADc+bMER2BiGSKpUEGAgMDRUcgIpliaZCBsrIy0RGISKZYGkREJBlLgwx4eXmJjkBEMsVTbsnAnj17REfo9Pr06QMPDw9YWFigsrISeXl5qKioaHL5mTNn4sCBA7h6led/k1jc0yADS5YsER2hU/L09MQ777yDkpISlJaWIiMjA19++SUyMzNx69YtXLhwAX/+859hb2/fYL3Y2Fhs374dhw8fhrm5uaD0RHVkXRparRYbNmxA//79YWVlBV9fX2g0Gnh4eGDWrFmi43VaSUlJoiN0KjY2Nti+fTvOnz+PP/7xj3BwcMCtW7fwzTffIC0tDadPn0Z1dTUGDBiA1atX48cff8Rrr70GpVKJ2NhYrFmzRv9/4d69e6I/Dj3kZD08FRUVhZSUFCxevBh+fn7IzMzE1KlTUVZWhgULFoiO16jkVWr0HRiCoRMXSZpOnZunpycOHToEFxcXVFdX46OPPsK2bduQk5MDnU6nX87c3BzBwcGIiYnB+PHjsX79ekRHR8PV1RVarRYzZszAX//6V4GfhKiObEsjMTERO3fuREZGBoKCggAAwcHBOHPmDFJSUjBkyBDBCYmMc3d3R0ZGBuzt7ZGVlYUXX3wRFy5caHTZe/fu4csvv8SXX36J0NBQfPbZZ3B1dYVOp0N0dDQLg2RDtsNTcXFxCA0N1RdGvX79+sHc3Bw+Pj4A6sbf3d3doVQq+RyIVsL7KP125ubm+Pzzz2Fvb49//OMfCAwMbLIwHqRSqWBrawudTgeFQgF/f961kuRDlqVRXFyM7777DlOmTDGYV1RUBG9vb1haWgIAQkND8cUXX/Aq5laUl5cnOkKHt3DhQqhUKly8eBGTJ09GVVWVpPXuP4bx1ltvobq6Gi+99BKefPLJNk5MJI0sh6eKi4sB1J2WeL+7d+9Co9FgzJgx+mkjRoxo0TYUCoWk5Sa/lQ4nT3Wz3vvU/tU4nbqhwbR7VZXoOzCkWe+j0WTgT08HN2sdKebPn290/qZNmyQtIwcL1/4FQN3P8/7XInXt2lX/7/fSSy/hzp07kta7vzDqj2EolUqsWrUKsbGxOHLkSIPlNRqN8M9Kncf9x9iMkeWehp2dHQCgoKCgwfT4+HiUlpbCz89PRCzJhk54C9Hbbjb44+D+hOhY1E4iIiLQq1cvnDx5Eunp6ZLWaawwAOC9997DnTt3EBISAnd397aMTSSJLPc0XF1d4ePjg7i4OPTq1QuOjo5ITk5GamoqALRKaUht1XfTxD1PIyhIjeRV0nI2R35+vtH5mzZtMnlK88aNG1szUovFrtsGoO7nef/r9qRWqxscB6ofSvrkk08krd9UYQDArVu3sH//fkybNg3BwcENvkgFBQUhIyOjdT4EkUSy3NNQKpVISkqCt7c3oqOjMWPGDNjZ2SEmJgZmZmb6g+DUNpYvXy46QodWf2bfyZMnTS5rrDDqnTp1CkDrfFki+q1kuacB1J2u+OCufWRkJLy8vNC1a1dBqR4OERERoiN0aI6OjgCAixcvGl1OSmEAQGFhIQDAwcGhdYMStYBsS6Mx2dnZGDZsWINpixcvxkcffYSysjLk5uZi3rx50Gg0cHNzE5IxfFFGs6bLkaenp+TTQ8mQo6MjrKyscPPmTaPLOTk5SbpwLy0tDT179sTdu3dbOSlR88lyeKoxlZWVKCgoMLiob+XKlSguLkZ1dTWuX7+O4uJiYYVBBAC//PILbty4YfLYypw5czBy5EiTF+7V1NTg5s2bqK6ubs2YRC3SYfY0rK2tUVtbKzoGUas6ceKE6AhEzdJh9jSo/ajVatERiEimWBpkYMuWLaIjEJFMsTTIQHR0tOgIRCRTLA0ywAvGiKgpLA0iIpKMpUFERJKxNMgAL+wjoqZ0mOs0RHHs+fBte/fu3byVSDOoVKpmr3OpqBQA4Nr30Qav23q7RL8VS8OEsIfwoWlLly5laTRDQkJCs9epvyPv2oWzGrwmkjsOTxERkWQsDSIikoylQQY2b94sOgIRyRRLgwx4e3uLjkBEMsXSIANBQUGiIxCRTLE0iIhIMpYGGQgICBAdgYhkiqVBBrKyskRHICKZYmkQEZFkLA0iIpKMpUEGkpOTRUcgIpliaRARkWQsDTIQHh4uOgIRyRTvcmtCSjZQUi5m2449H8677FLbmzdvHnJycoRsW6VStejOwADw6vfnce727dYNJIHvI4/gbQ+vFq0rKjPw23I3haVhQkk5cPGq6BRErSsnJwcajUZ0jGY7d/s2viq/ITpGs3TEzMZweIoMxMTEiI5ARDLF0iADc+bMER2BiGSKpUEGAgMDRUcgIpliaZCBsrIy0RGISKZYGkREJBlLgwx4ebXuKXpE1HmwNMjAnj17REegTsLGxkZ0BGplLA0ysGTJEtERSEYsLCwQFhaGt99+G+np6Th37hzOnj2Lffv2YfHixU0+fyUhIQHHjx9H79692zkxtSVZl4ZWq8WGDRvQv39/WFlZwdfXFxqNBh4eHpg1a5boeJ1WUlKS6AgkAxYWFli0aBGKioqwZ88eLFiwAGq1Gj4+PlCpVJgwYQJWrFiBU6dOISsrC2PHjtWvm5CQgLlz58LNzQ0DBw4U+Cmotcn6ivCoqCikpKRg8eLF8PPzQ2ZmJqZOnYqysjIsWLBAdLxGJa9So+/AEAyduEjSdCI58vX1xaeffgpvb28AwLfffoukpCRkZ2fjX//6F7p06QIPDw8MHz4c06ZNg7+/Pw4ePIhdu3bh9u3biI6ORnV1NcLCwnDkyBEhn0F37x5+/eN8KAf7wmz2S/rptXv3QbtnL7psfR8Ka2sh2YyRe27ZlkZiYiJ27tyJjIwMBAUFAQCCg4Nx5swZpKSkYMiQIYITEnVOI0aMwKFDh2BjY4Pvv/8e0dHRSE9PN1juzJkzSExMxBtvvIGXX34Zq1evxgsvvAAA+sJITU1t7/h6CnNzdIl9Hb/+cR4UQwOgHKyC7vJlaD/8GGarV8iyMAD555bt8FRcXBxCQ0P1hVGvX79+MDc3h4+PD8rLyzF27Fi4u7vD19cXTz/9NAoLCwUl7jw64j2JqHU89thjSE1NhY2NDRITE6FSqRotjPtVVVUhISGhwbDm+fPncejQobaOa5LiMRco//Aiajdsgu7GDfy6dj2UE8ZB6TNIdDSj5JxblqVRXFyM7777DlOmTDGYV1RUBG9vb1haWkKhUGDevHkoKCjAuXPnMHbsWMyYMUNA4s4lLy9PdAQSQKFQ4MMPP4StrS3279+PF154AVVVVZLWTUhIwIsvvojq6mqUl5dj8ODBiI6ObuPE0ignToCirzN+nR0DmJlB+WKk6EiSyDW3LIeniouLAQB9+vRpMP3u3bvQaDQYM2YMAKBHjx4ICQnRzx8xYgTi4+MlbUOhUEhabvJb6XDyVEtatt6p/atxOnVDg2n3qirRd2BIE2s0TqPJwJ+eDm7WOlLMnz/f6PxNmzZJWkYOFq79C4C6n+f9r+VOjrknTZqE4OBgXL16FTNnzoRWq5W0Xv1B7/ohKUtLS6SkpGDNmjX45JNPcPuB24JrNJoWf1az9Wuh9PVp1joKhQIKn0HQnT4D5fMRUJibN3u7GRkZUAQMa/Z6QMsyA+2fW6fTSVpOlnsadnZ2AICCgoIG0+Pj41FaWgo/P79G10tISMDEiRPbOp5JQye8hehtNxv8cXB/QnQsIqPq7268atUqXLt2TdI6DxZGamoq9u7di4yMDNjY2OiPcYiku3wZ2r99BuXvp0C762/QXe0YzzqQa25Z7mm4urrCx8cHcXFx6NWrFxwdHZGcnKw/qNZYaSxfvhyFhYU4evSopG1IbdV308Q9TyMoSI3kVdJyNkd+fr7R+Zs2bTJ5SvPGjRtbM1KLxa7bBqDu53n/a7kTnVutVjc4dmVvb4/Ro0fjl19+wccffyzpPRorjHpbt26FWq3G1KlTsWXLlgbrBQUFISMjo0W5Q7JPNuvZFLqae3XHA8ImwmzGi9CVl6N2/UaYrYuDQin9O7NarcbhFv58mpsZkEfupshyT0OpVCIpKQne3t6Ijo7GjBkzYGdnh5iYGJiZmcHHp+Gu3qpVq/D3v/8dX3zxBbp16yYodeexfPly0RGonfn71z0i8uTJk6ioqDC5vLHCAIDDhw8DAIYMGQJlM37JtTbthx9B0aULlJH/DwBg9srL0P30M7R79grLJIWcc8uyNADA3d0d6enpuHPnDoqKirBy5Urk5ubCy8sLXbt21S+3fPlyHDx4EGlpaejRo4e4wJ1IRESE6AjUzuqvxzh37pzJZU0VBgBcv34dV65cQffu3eHi4tLqeaXQns2BNvULmMW+AUWXukEVRbduMFv4GrR/3QXd5ctCcpki99yyHJ5qSnZ2NoYN+89Bnby8PCxbtgxubm5Qq9X66aKefQwA4YsymjVdjjw9PXHhwgXRMagdnThxAitWrMCxY8eMLjd58mSThVFv48aNsLW1NTgQ3l6Ug1VQHkgxnD7QG8qD4r+xN0XuuTtMaVRWVqKgoACvvPKKfpq3t3eHGL8mkrtjx46ZLAyg7maWCQkJSEtLM3nhXkJCQiulIznpMKVhbW2N2tpa0TGIHnqmTsemzk22xzRInPuH+oiI7sfSIAMPniJJRFSPpUEG5HL7ByKSH5YGGWjphVdE1PmxNIiISDKWBhERScbSIAO8sI+ImsLSIAO7d+8WHYGIZKrDXNwnimPPh2/bS5cu5f2nOjmVStXsdS4VlQIAXPs+2uB1e2y7nu8jjzR7nUtF/wIAuPZ1aPC6rbf7W9Ztjcwt3bYpLA0TwvxFJyBqfS25xUf9LdzXLpzV4HV7etvDq9nrxB75d9awSQ1et5eOmNkYDk8REZFkLA0ysHnzZtERiEimWBpkoP7ZCkRED2JpkIGgoCDREYhIplgaREQkGUuDiIgk4ym3D6EBAwYYnb906VKTyxDRw4l7GmRg2bJloiMQkUyxNIiISDKWBhERScbSICIiyVgaREQkGUuDiIgkY2kQEZFkLI0mPP3001CpVBg0aBDCw8NRUVEhOhK1gYyMDHh7e6Nfv36YOXMmamtrRUcyae7cuXByckKXLh3nMqsrV67gySefhKenJ7y9vfHmm2+KjkQtxNJoQlJSEnJycpCbmwsnJyds3LhRdCRqZVqtFjNnzkRSUhIKCwtRUVGBXbt2iY5l0pQpU5CdnS06RrN06dIF69atw4ULF3D27Fl8/fXX2L9/v+hY1AIsjSbY2toCqPvFUlVVBYVCITgRtbasrCw4ODjAy6vuITlRUVHYs2eP4FSmPfHEE+jTp4/oGM3y6KOPwt+/7olmFhYWGDx4MIqKigSnopZgaRgxadIk2Nvb4/vvv8err74qOg61suLiYjg7O+v/3rdvX1y5ckVgoofDjRs3sG/fPjz11FOio1ALdJxBUQH27t2LmpoaREVFITk5GdOnTxcdiQAcPJyJS1dKG0z7n4/2NPpa5dUPQb/zbfR9dDpd2wRsRMlP15B8SGMwvbHclhbm+P+Tn0E3K8t2y9cYnU6Hz/+ejp+vlTeY3tS/9Ui/gfD38TD6njU1NQgPD8fcuXN5f7MOinsaJlhYWOD555/H3r17RUehf3siYBBu3KxA6dXr+mkPvi69eh13q6rxO5Vnk+/j7OzcYM+iqKgITk5ObZLZsY8dHHvb6bMZy+030F14YQCAQqFA4FAfXL1WbjIzAKi8+xl9v9raWkybNg0qlYp77h0YS6MRt2/fRmlp3TdZrVaLAwcO8Gl2MtLT9hGMDxlpdBkFgCnPqWFladHkMv7+/iguLsb58+cBADt27EBYWFhrRm1g7JPD0dP2EaPLePZzMfltvT059LbDU6P8jS5jZqbE78cGo4uZmdHlZs2ahUceeQRvv/12a0akdsbSaMTt27cxfvx4+Pj4wMfHB7/++isWLVokOhbdZ8jA/vB2f6zJ+U8E+MCtr4PR9zAzM8MHH3yA8PBwuLm5wdraGpGRka2c9D+sLC0Q8ZwaTZ1S0b2bFSaHBpo86WL27NlwcnJCbW0tnJycEBMT0/ph7xM41Acujr2bnP9M4FD0+e9eRt/jm2++wYcffojs7GwMHjwYKpUK77zzTmtHpXbAYxqNcHBwQFZWVqPzdDodz6SSAYVCgUnPjMKPJT+j8s7dBvN62/XE04HGvx3XGz16tH5Poz087vwoAn/nC83JcwbzwkIDYd29q8n3+Mtf/tIW0ZqkVCoRMTYY//PRHtTU3Gsw73HnR/FEwCCT7zFy5Mh2PYZEbYd7Gs2kOXkOn+5Lw68d4CKwzs66W1eEj2n4PHMzZd1QibmML3x76gl/g2/m/oM84N3/MTGBJPivHjYYO3p4g2mWFuaIeE4NpYy/RGm1Wlz6/jv8Y++niIyMxNeHD6Li5g3RsUyquFWOb478LyIjI/FFyi5czM+VzYWn8v2fJVFubi6WLVsGjUaDyspKODs7IyIiAqtXr271bVVX1+Crk+fg7GBvcvyW2scAt74Y6jsAp87lAwCeGuUPh952glMZ16WLGZ4fNxrvfpyC2lotetk+gnFPDje9omABPh64UPgDLhTWXV8xPmSkyWM0Iv3www947rnncP78eSgUCuRmK1FbW4tvjvwvbHQ3sWbNGtmNGuh0Oixbtgxb166ETqfDcTMzaLVanDt1DF6ZXyI1NRVubm5CM3boPY3Tp09j2LBhyMvLw/r165GamorY2Fj89NNPbbK9zDN5+KWqGiEj/drk/allnhs9HP/VwwYujr0RONRHdBxJ+vx3Lzw9KkB/wN7SyAF7uVAoFAgLDUT3blbwdn8MQwb2Fx2pSbdv38bo0aORn1/3ZUKn0/3nm7pOh3Xr1iEuLk5gwsZt2LABK1as0A/l1dbW6l8XFhYiODgY5eXlxt6izSl0HXigUa1W4/z58/jnP/+pv4Jbqth129ooFRGJduZ4OtL2f2Z0GXNzC8QsWg9LS6t2SmXcvZoavLf6ddRUVxldLvi5cAwd1foXRq5dOEvSch12T+OXX37BsWPHMHXq1GYXBhF1bt9mZ5ocerp3rwb/zMtpn0ASFOZ/a7IwACA3O7Md0jStwx7TKC8vh1arbfHFWFJbFag7lrFuayKcHewxY8qYFm2PiNrPrndXSDpbK8jfE6+/Lv13QVt6991qHPibhAVra5r1+6u1ddjS6NmzJ5RKJUpKSlq0fkuGp76/dIXDWkQdwD2tAnWXeBovjvRT3+G6TP5Pn88xPA27MVqFWZv8Hur0w1PdunVDYGAgEhMT+awLImrAe8gwmCqMLl3M4e49uH0CSeDm6QNzc9MnRAwcIvZMuw59IPz06dMIDAyEi4sL3njjDbi4uKCoqAjHjh3DBx980CrbSD9+Fv/4KgsxkRPh7GDfKu9JRG2rvLwcAwcOxE8//QStVtvoMm+++abszqBavnw5li1b1ug8pVIJOzs75OXlwc5O3GnlHXZPAwD8/Pxw/Phx9O/fH/Pnz8ezzz6L1atXw8HB+O0jpKqursGxU9/Cw9WZhUHUgfTs2RNHjx7V3/rezMwMSqVSf3A8OjoaK1euFBmxUYsXL8bcuXMB1J3irFQqYfbva8IcHBxw9OhRoYUBdPA9jbZWevU6du1Lw/NjR7M0iDqgmpoa7Nu3D3v37sWdO3fg5uaGl156Sf/gLbnKz8/H9u3bUVhYiK5du2LChAkICwuDpaUM7n7M0jBOq9VCqezQO2RERK2GpUFERJLxKzQREUnG0iAiIslYGkTUqcyfPx+jRo3Sn4X0oI8//hiBgYEICAjA5s2b2zld00zlXrt2LdRqNdRqNbp3744bN8Tc4p2lQUSdxpkzZ1BZWYljx46hpqam0YepTZs2DV999RVOnDjR7g+0aoqU3LGxscjIyEBycjICAgLQq5fxpyW2FZYGEXUaJ06cwFNP1d0BNiQkBMePH8frr78OrVaL0NBQFBUVwdzcHEDd6bienp4i4+pJyV3vwIEDGD9+vKioLA0i6jxu3rwJGxsbAICtrS1u3ryJn3/+GbNmzcK4cePQt29fAMCKFSvQv39/+PnJ49k4UnMDwN69ezFp0iRRUVkaRNR52Nra6u9FV1FRgR49emD27NnYvXs3Zs6cqV9uyZIluHjxIpKSknD9+nVRcfWk5r59+zauXbuGxx9/XFRUlgYRdR7Dhw/HkSNHAACHDx/GsGHDsHLlSixduhRr164FAFRXVwMALCws0K1bN1lcZS0lNwAcOnQIY8aIfTwDS4OIOo0hQ4bAysoKo0aNgpmZGTIzMzFp0iS8+uqryM3NRV5eHtasWQO1Wo2RI0fi97//PaytrUXHlpQbqBuaCgsLE5qVV4QTEZFk3NMgIiLJWBpERCQZS4OIiCRjaRARkWQsDSIikoylQUREkrE0iIhIMpYGERFJxtIgIiLJWBpERCQZS4OIiCRjaRARkWQsDSIikoylQUREkrE0iIhIMpYGERFJxtIgIiLJ/g/LPUw7nBVLagAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 507.997x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = QuantumRegister(3,'q')\n",
    "c = ClassicalRegister(3,'c')\n",
    "qc = QuantumCircuit(q, c)\n",
    "qc.h(0)\n",
    "qc.h(1)\n",
    "qc.h(2)\n",
    "qc.barrier()\n",
    "qc.measure(q,c)\n",
    "\n",
    "qc.x(2).c_if(c, 3) # for the 011 case\n",
    "qc.x(2).c_if(c, 7) # for the 111 case\n",
    "\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "african-adams",
   "metadata": {},
   "source": [
    "## IPE\n",
    "\n",
    "The motivation for using the IPE algorithm is that QPE algorithm works fine for short depth circuits but when the circuit starts to grow, it doesn't work properly due to gate noise and decoherence times.\n",
    "\n",
    "The detailed explanation of how the algorithm works can be found in [Iterative Phase Estimation (IPE) Algorithm](https://qiskit.org/textbook/ch-labs/Lab04_IterativePhaseEstimation.html#2-iterative-phase-estimation-ipe-algorithm). To understand QPE in depth, you can see also [Ch.3.6 Quantum Phase Estimation](https://qiskit.org/textbook/ch-algorithms/quantum-phase-estimation.html).\n",
    "\n",
    "### IPE example with a 1-qubit gate for $U$\n",
    "\n",
    "We want to apply the IPE algorithm to estimate the phase for a 1-qubit operator $U$.  For example, here we use the $S$-gate.\n",
    "\n",
    "Let's apply the IPE algorithm to estimate the phase for $S$-gate.\n",
    "Its matrix is \n",
    "$$ S = \n",
    "\\begin{bmatrix}\n",
    "1 & 0\\\\\n",
    "0 & e^\\frac{i\\pi}{2}\\\\ \n",
    "\\end{bmatrix}$$\n",
    "\n",
    "That is, the $S$-gate adds a phase $\\pi/2$ to the state $|1\\rangle$, leaving unchanged the phase of the state $|0\\rangle$\n",
    "\n",
    "$$ S|1\\rangle = e^\\frac{i\\pi}{2}|1\\rangle $$\n",
    "\n",
    "In the following, we will use the notation and terms used in [Section 2 of lab 4](https://qiskit.org/textbook/ch-labs/Lab04_IterativePhaseEstimation.html#2-iterative-phase-estimation-ipe-algorithm) of the Qiskit textbook.\n",
    "\n",
    "Let's consider to estimate the phase $\\phi=\\frac{\\pi}{2}$ for the eigenstate $|1\\rangle$, we should find $\\varphi=\\frac{1}{4}$ (where $\\phi = 2 \\pi \\varphi$). Therefore to estimate the phase we need exactly 2 phase bits, i.e. $m=2$, since $1/2^2=1/4$. So $\\varphi=0.\\varphi_1\\varphi_2$.\n",
    "\n",
    "Remember from the theory that for the IPE algorithm, $m$ is also the number of iterations, so we need only $2$ iterations or steps.\n",
    "\n",
    "First, we initialize the circuit. IPE works with only 1 auxiliary qubit, instead of $m$ counting qubits of the QPE algorithm. Therefore, we need 2 qubits, 1 auxiliary qubit and 1 for the eigenstate of $U$-gate, and a classical register of 2 bits, for the phase bits $\\varphi_1$, $\\varphi_2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1b447171",
   "metadata": {},
   "outputs": [],
   "source": [
    "qubits = [5, 6]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b38d57c4",
   "metadata": {},
   "source": [
    "### Exercise #1.A - Conditional Reset\n",
    "\n",
    "Prepare the ground state for each of our qubits using three rounds of reset. \n",
    "\n",
    "First we'll do this with the conditional application of the $X$ gate based on a measurement. Use what you learned in the earlier presentation and about the `c_if` gate modifier to do this.\n",
    "\n",
    "Keep in mind that if you implement comnditional reset yourself, you will have to add additional classical registers to the circuit to store the meaurement result in. You will then have to modify the analysis code later on to ignore those preparation results using `marginal_counts` function supplied by Qiskit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "67e5bfb3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def reset_conditional(qc, q, reset_reg):\n",
    "    qc.barrier(q)\n",
    "    qc.measure(q, reset_reg)\n",
    "    qc.x(q).c_if(reset_reg, 1)\n",
    "    qc.barrier(q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "800f6f49",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 678.093x686.28 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def reset_conditional(qc, q, reset_reg):\n",
    "    qc.barrier(q)\n",
    "    qc.measure(q, reset_reg)\n",
    "    qc.x(q).c_if(reset_reg, 1)\n",
    "    qc.barrier(q)\n",
    "\n",
    "qr = QuantumRegister(2)\n",
    "reset_reg0 = ClassicalRegister(1, \"reset_reg0\")\n",
    "reset_reg1 = ClassicalRegister(1, \"reset_reg1\")\n",
    "cr0 = ClassicalRegister(1, \"reset_result0\")\n",
    "cr1 = ClassicalRegister(1, \"reset_result1\")\n",
    "\n",
    "qc_reset = QuantumCircuit(qr, reset_reg0, reset_reg1, cr0, cr1)\n",
    "reset_conditional(qc_reset, qr[0], reset_reg0)\n",
    "reset_conditional(qc_reset, qr[1], reset_reg1)\n",
    "\n",
    "qc_reset.measure(0, cr0)\n",
    "qc_reset.measure(1, cr1)\n",
    "\n",
    "qc_reset = transpile(qc_reset, backend_real, initial_layout=qubits)\n",
    "qc_reset.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e0055edb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Hint use qiskit.result.marginal_counts to remove the first three classical register results\n",
    "# from your counts\n",
    "def pad_counts(counts):\n",
    "    new_counts = {}\n",
    "    for k, v in counts.items():\n",
    "        if len(k) < 4:\n",
    "            for _ in range(4-len(k)):\n",
    "                k = \"0\"+k\n",
    "        new_counts[k] = v\n",
    "    return new_counts\n",
    "\n",
    "def remove_reset_results(counts):\n",
    "    return marginal_counts(pad_counts(counts), indices=[0, 1])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "64faf6b6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reset job id: c6crc0u42htbamp4td7g\n",
      "The results of your reset circuit are {'00': 976, '01': 12, '10': 12}\n"
     ]
    }
   ],
   "source": [
    "reset_job = run_openqasm3(qc_reset, backend_real, verbose=False)\n",
    "print(f\"Reset job id: {reset_job.job_id()}\")\n",
    "reset_result = reset_job.result()\n",
    "reset_counts = remove_reset_results(reset_result.get_counts(0))\n",
    "print(f\"The results of your reset circuit are {reset_counts}\")\n",
    "assert reset_counts[\"00\"] > 700"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a689191",
   "metadata": {},
   "source": [
    "### Exercise #1.B - Qubit Initialization\n",
    "\n",
    "To best initialize the qubit oftentimes multiple rounds of reset are required to drive the qubit as close as possible to the ground state which is determined by the readout errors, gate errors, and thermal populations of the system.\n",
    "\n",
    "Below implement the `init` operation using three rounds of the builtin `QuantumCircuit.reset`, this handles the extra measurement bit required for you and is also more efficient in hardware."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c0e50013",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 617.893x565.88 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def init(qc, qr):\n",
    "    \"\"\"Implement a qubit initialization using three rounds of qubit reset.\"\"\"\n",
    "    qc.barrier(qr)\n",
    "    qc.reset(qr)\n",
    "    qc.reset(qr)\n",
    "    qc.reset(qr)\n",
    "    qc.barrier(qr)\n",
    "    \n",
    "\n",
    "    \n",
    "qr = QuantumRegister(2)\n",
    "cr0 = ClassicalRegister(1, \"reset_result0\")\n",
    "cr1 = ClassicalRegister(1, \"reset_result1\")\n",
    "\n",
    "qc_init = QuantumCircuit(qr, cr0, cr1)\n",
    "\n",
    "init(qc_init, qr)\n",
    "\n",
    "qc_init.measure(0, cr0)\n",
    "qc_init.measure(1, cr1)\n",
    "\n",
    "qc_init = transpile(qc_init, backend_real, initial_layout=qubits)\n",
    "qc_init.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "8655a204",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Qubit init job id: c6crcae42htbamp4tdmg\n",
      "The results of your reset circuit are {'0 0': 989, '0 1': 4, '1 0': 7}\n"
     ]
    }
   ],
   "source": [
    "init_job = run_openqasm3(qc_init, backend_real, verbose=False)\n",
    "print(f\"Qubit init job id: {init_job.job_id()}\")\n",
    "init_result = init_job.result()\n",
    "init_counts = init_result.get_counts()\n",
    "print(f\"The results of your reset circuit are {init_counts}\")\n",
    "assert init_counts[\"0 0\"] > 900"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8095d4c3",
   "metadata": {},
   "source": [
    "## Exercise #1.c - Compare your initialization results against your reset\n",
    "\n",
    "Did you do better? Why might that be?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b2bbedb9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "With the initialization circuit we prepared the ground state 13 more times than in the reset circuit.\n"
     ]
    }
   ],
   "source": [
    "delta_counts = init_counts[\"0 0\"] - reset_counts[\"00\"]\n",
    "print(f\"With the initialization circuit we prepared the ground state {delta_counts} more times than in the reset circuit.\"\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dominican-camcorder",
   "metadata": {},
   "source": [
    "## IPE - First step\n",
    "\n",
    "Now we build the quantum circuit for the first step, that is, the first iteration of the algorithm, to estimate the least significant phase bit $\\varphi_m$, in this case $\\varphi_2$. For the first step we have 4 sub-steps:\n",
    "- qubit initialization\n",
    "- initialization\n",
    "- application of the Controlled-$U$ gates\n",
    "- measure of the auxiliary qubit in x-basis\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "d88e5f2c",
   "metadata": {},
   "outputs": [],
   "source": [
    "nq = 2\n",
    "m = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "6b35938a",
   "metadata": {},
   "outputs": [],
   "source": [
    "qr = QuantumRegister(2,'q')\n",
    "c0 = ClassicalRegister(1,'c0')\n",
    "c1 = ClassicalRegister(1, 'c1')\n",
    "qc_S = QuantumCircuit(qr, c0, c1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51a30ec6",
   "metadata": {},
   "source": [
    "### Exercise 2. - Qubit Initialization\n",
    "\n",
    "Before we begin using our qubits we must initialize them. Use the `init` function you wrote earlier to initialize the qubits in in qc_S below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "e76b7324",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 387.452x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def init_ipe_circuit(qc):\n",
    "    \"\"\"Initialize the qubits in your IPE circuit.\"\"\"\n",
    "    init(qc, [0, 1])\n",
    "\n",
    "init_ipe_circuit(qc_S)\n",
    "qc_S.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a043b28a",
   "metadata": {},
   "source": [
    "### Exercise 3. Eigenstate Initialization\n",
    "\n",
    "The initialization consists of application the Hadamard gate to the auxiliary qubit and the preparation of the eigenstate $|1\\rangle$. Complete this below by filling in the function.\n",
    "\n",
    "**hint**: To prepare the $|1>$ state recall how we corrected for an inadverdent $|1>$ in our conditional qubit reset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "classified-pipeline",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 447.652x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def initialize_eigenstate(qc):\n",
    "    \"\"\"Initialize the eigenstate and prepare our ancilla qubit\"\"\"\n",
    "    qc.h(0)\n",
    "    qc.x(1)\n",
    "\n",
    "initialize_eigenstate(qc_S)\n",
    "    \n",
    "qc_S.draw('mpl')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "pacific-momentum",
   "metadata": {},
   "source": [
    "#### Application of the Controlled-$U$ gates\n",
    "\n",
    "Then we have to apply $2^t$ times the Controlled-$U$ operators (see also in the docs [Two qubit gates](https://qiskit.org/documentation/tutorials/circuits/3_summary_of_quantum_operations.html#Two-qubit-gates)), that, in this example, is the Controlled-$S$ gate ($CS$ for short).\n",
    "\n",
    "To implement $CS$ in the circuit, since $S$ is a phase gate, we can use the controlled phase gate $\\text{CP}(\\theta)$, with $\\theta=\\pi/2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "5d9cc23c",
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = 1 * np.pi / 2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "410d3936-190e-4950-80bc-8902ea7f6bac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKoAAAB7CAYAAADkFBsIAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAIK0lEQVR4nO3dW0xU+R3A8e8MC8KWrcWQYsSIIowKkUHxFmK51OqiL9h4t0yiIdGI2kTb6kOD7Ut5IJPGtMHGpgYTH2iUkE2aGFI2wiBC6rWD2rqjQURdBNSyLlRQYfow67AoF+mGc85v+H2SCXBgwm/CN+fMmXDmb/P7/X6Usji72QMo9SE0VCWChqpE0FCVCBqqEkFDVSJoqEoEDVWJoKEqETRUJYKGqkTQUJUIGqoSQUNVImioSgQNVYmgoSoRNFQlgoaqRNBQlQgaqhJBQ1UiaKhKBA1ViaChKhE0VCWChqpE0FCVCBqqEkFDVSJoqEoEDVWJoKEqETRUJYKGqkTQUJUIGqpAgwPQ3wsDr8yexDiWDnVwcBC3201ycjKRkZE4nU48Hg8LFixgz549Zo9nuL4XcOdzqPsjXPwT1P4BblTB8zazJ5t8H5k9wFgKCwupqqqiuLiYjIwMGhsb2bFjB11dXRw+fNjs8QzV8xSu/RVe9w3f/uw+PGuBRZ9C/GJzZjOCZUOtqKjg9OnT1NXVkZ2dDUBubi7Xr1+nqqqKpUuXmjyhcfx+uPk3eN0/0jcDH/79d4iZDR/HGDqaYSx76C8pKSEvLy8Y6VtJSUmEh4eTlpYGQGtrK9nZ2TgcDhYvXszFixfNGHdSdT+C3mcEoxyRHx57jZrIeJYM9dGjR9y6dYstW7a89722tjZSU1OZNm0aAHv37mXbtm34fD5OnjzJ9u3befVq/LMMm80m5vbzwt+M+3j8fj81n10zfdaJ3j6UZUMFmDlz5rDtL1++xOPxBA/7T58+paGhgcLCQgAyMzOZNWsWtbW1xg48ycJsYYy3EqjNZiPMHmbQRMaz5HPU2NhYAHw+Hxs2bAhuLy0tpb29nYyMDCCwd42LiwvuXQHmzZvHgwcPxv0dkpaA7bwHzZ+N/3M/+jQd/+/lPK6JsGSoiYmJpKWlUVJSwowZM4iPj6eyspLz588DBEOdKmITYVp04LXTsZ6nzk43aiLjWfLQb7fbOXfuHKmpqezbt4/du3cTGxvL/v37CQsLC55IzZkzh46ODvr7h06H79+/T0JCglmjTwq7HVI3gM0GjPK0bu5K+H6coWMZyiZpGXSXy4XX66W5uTm4bd26dWzcuJGioiIaGxvZvHkzra2tREREmDjp5PjqS7h3Ef7zcGhb5HSYtxJmLf4m5BAlKtRFixaxatUqysvLg9taWlrYtWsXT548ISIigrKysvde0go1L7vh0l8Cn6/5RWgH+pYln6OOpKenB5/PR1FR0bDtiYmJ1NfXmzSVOaJ+MPT5VIgUBIUaHR3NwMCA2WMok1jyZEqpd2moSgQNVYmgoSoRNFQlgoaqRNBQlQgaqhJBQ1UiaKhKBA01BNXV1ZGQkEBOTg75+fn09Q2/dNXtdnPjxo1R7//48WPWr19PZmYmq1ev5tChQwB4vV5KS0sndfbRaKghyuVyUVdXR2ZmJpWVlcHtg4ODXLp0iSVLlox635qaGgoKCrhw4QINDQ10dnZy8+ZNnE4nTU1NplwdoaGGuPT09OA1aBDYKyYlJQGBPW9MTAw5OTkkJCSQn58PgMfjIT8/n8jISADCw8MJCwtcj5WcnDzm3niyaKghrr6+HofDEfz67t27zJ07F4CsrCxWrFgRfO+EEydO4Pf76e3tJTo6GoDm5ma6urpISUkBAv9WeefOHcMfh4Yaos6cOUNubi7d3d3BPeW7WlpaSExMBODhw4fEx8fj9XpxOp0APH/+nAMHDnDq1CnD5h6NhhqiXC4XtbW1lJWVBQ/bEDh0t7a2AnD79m1SU1MZGBjAbg+kUFNTw9q1a3nz5g0FBQW43e5hl623tLSwcOFCQx8LaKhTjtPpxOfzAUOh9vf309nZSXt7O1evXmXZsmWcO3eOK1eucOTIEXJycmhqagICl7Cnp6cbPreoa6bUkM/dgY8/+eXE7+t2u1mzZs2IZ/5nz55l69atI97P6/VSXV3N0aNHJ/5LvyMNVajvEqpEeuhXImioSgQNVYmgoSoRNFQlgoaqRNBQlQgaqhJBQ1UiaKhKBA1ViaChKhE0VCWCpUPVRXvf999uuNcw9PXztsASlKHO0u84rYv2DvEPwhcX4NE/h2+/fhY+iYP0nwaW+AlVlv1/1IqKCnbu3Dls0V6ATZs2UVVVxeXLl1m+fLmJExrLVwdtV0f5pg2+NwNWusBu6V3P/8+yh/4PXbT32LFjOBwO7Hb7sOvXQ8mrXnh4fYwf8AcW9e3wGTaS4SwZ6kQW7c3Ly6O6upqsrCyjxzTMky8Ch/4x2aD9tiHjmMKyocL4i/ZCYKHet5f8ToTZqypP5PbbX/9u/Hcn8cO1f9wyfdYptbr0txft/bZ3F+2dKr7qfTruH3VwcIDurzsMmsh4lnzqbcSivRY9hxxR39fQ8GfGXLDXbg/jZwfW8KuTch7XRFhyj/qhi/ZOFZGfwOyxHrINoqZDnPHvC2EYS+5RARwOB7W1tcO2uVwuUlJSiIqKMmkq8zh+DG9ew5N/fbPh7TMBP3wcA0s2QVi4WdNNPsu+jjqSkRbtLS4upry8nK6uLqKjo4mKisLj8TB//nwTJ508Lzrgy1vQ9wI+ioAfLoDYxMBS6aFMTKg9PT1Mnz6d48ePc/DgQbPHUQYTE6qa2kL8gKFChYaqRNBQlQgaqhJBQ1UiaKhKBA1ViaChKhE0VCWChqpE0FCVCBqqEkFDVSJoqEoEDVWJoKEqETRUJYKGqkTQUJUIGqoSQUNVImioSgQNVYmgoSoRNFQlgoaqRNBQlQj/A08ZhshjQJjAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 206.852x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cu_circ = QuantumCircuit(2)\n",
    "cu_circ.cp(theta,0,1)\n",
    "cu_circ.draw('mpl')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9e49bfb-b699-4219-8133-08190551daeb",
   "metadata": {},
   "source": [
    "Let's apply $2^t$ times $\\text{CP}(\\pi/2)$. Since for the first step $t=m-1$, and $m=2$, we have $2^t=2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "tender-variation",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 688.452x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for _ in range(2**(m-1)):\n",
    "    qc_S.cp(theta,0,1)\n",
    "qc_S.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "continued-worst",
   "metadata": {},
   "source": [
    "## Exercise 5 - Measure in x-basis\n",
    "\n",
    "Finally, we perform the measurenment of the auxiliary qubit in x-basis. Fill out the function to perform the x_measure and then apply it. \n",
    "\n",
    "\n",
    "In this way we obtain the phase bit $\\varphi_2$ and store it in the classical bit $c_0$.\n",
    "\n",
    "**hint**: The eigenvectors of the Hadamard gate are the basis vectors of the x-basis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "considerable-sense",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 808.852x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def x_measurement(qc, qubit, cbit):\n",
    "    \"\"\"Measure 'qubit' in the X-basis, and store the result in 'cbit'\"\"\"\n",
    "    qc.h(qubit)\n",
    "    qc.measure(qubit, cbit)\n",
    "    \n",
    "x_measurement(qc_S, qr[0], c0)\n",
    "qc_S.draw('mpl')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "lasting-difference",
   "metadata": {},
   "source": [
    "### Subsequent steps (2nd step)\n",
    "\n",
    "Now we build the quantum circuit for the other remaining steps, in this example, only the second one.\n",
    "In these steps we have 4 sub-steps: the 3 sub-steps as in the first step and, in the middle, the additional step of the phase correction\n",
    "- initialization with reset\n",
    "- phase correction\n",
    "- application of the Control-$U$ gates\n",
    "- measure of the auxiliary qubit in x-basis\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46f486e4",
   "metadata": {},
   "source": [
    "## Exercise 6 - Reset the auxiliary qubit\n",
    "\n",
    "As we want to perform an iterative algorithm in the same circuit, we need to reset the auxiliary qubit $q0$ after the measument gate and initialize it again as before to recycle the qubit. \n",
    "\n",
    "Use the builtin `qc.reset` operation to perform a reset of qubit 0 followed by the hadamard operation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "123e4313-366a-4ea4-b672-7b30cbdccc15",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 929.252x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def reset_auxiliary(qc):\n",
    "    qc.reset(0)\n",
    "    qc.h(0)\n",
    "\n",
    "reset_auxiliary(qc_S)\n",
    "qc_S.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fcd145b2-870e-42a9-9178-df21a77b2354",
   "metadata": {},
   "source": [
    "#### Phase correction (for step 2)\n",
    "As seen in the theory, in order to extract the phase bit $\\varphi_{1}$, we perform a phase correction of $-\\pi\\varphi_2/2$.\n",
    "Of course, we need to apply the phase correction in the circuit only if the phase bit $\\varphi_2=1$, i.e. we have to apply the phase correction of $-\\pi/2$ only if the classical bit $c_0$ is 1.\n",
    "\n",
    "So, after the reset we apply the phase gate $P(\\theta)$ with phase $\\theta=-\\pi/2$ conditioned by the classical bit $c_0$ ($=\\varphi_2$) using the `c_if` method.\n",
    "So as we saw in the first part of this tutorial, we have to use the `c_if` method with a value of 1, as $1_{10} = 001_{2}$ (the subscripts $_{10}$ and $_2$ indicate the decimal and binary representations)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "shaped-fluid",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 989.452x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc_S.p(-np.pi/2,0).c_if(c0, 1)\n",
    "qc_S.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "moving-vertical",
   "metadata": {},
   "source": [
    "#### Application of the Control-$U$ gates and x-measurement (for step 2)\n",
    "\n",
    "We apply the $CU$ operations as we did in the first step. For the second step we have $t=m-2$, hence $2^t=1$. So we apply $\\text{CP}(\\pi/2)$ once. And then we perform the x-measurment of the qubit $q_0$, storing the result, the phase bit $\\varphi_1$, in the bit $c_1$ of classical register."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "thrown-galaxy",
   "metadata": {},
   "outputs": [],
   "source": [
    "## 2^t c-U operations (with t=m-2)\n",
    "for _ in range(2**(m-2)):\n",
    "    qc_S.cp(theta,0,1)\n",
    "\n",
    "x_measurement(qc_S, qr[0], c1) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "supported-speaking",
   "metadata": {},
   "source": [
    "Et voilà, we have our final circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "former-plain",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1230.25x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc_S.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "falling-ballot",
   "metadata": {},
   "source": [
    "Let's execute the circuit with the `qasm_simulator`, the simulator without noise that run locally."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "d8282f97",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'0 1': 1024}"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "count = execute(qc_S, backend_sim).result().get_counts()\n",
    "count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "included-jesus",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "count0 = remove_reset_results(execute(qc_S, backend_sim).result().get_counts())\n",
    "\n",
    "key_new = [str(int(key,2)/2**m) for key in list(count0.keys())]\n",
    "count1 = dict(zip(key_new, count0.values()))\n",
    "\n",
    "fig, ax = plt.subplots(1,2)\n",
    "plot_histogram(count0, ax=ax[0])\n",
    "plot_histogram(count1, ax=ax[1])\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dried-tribute",
   "metadata": {},
   "source": [
    "In the picture we have the same histograms but on the left we have on the x-axis the string with phase bits $\\varphi_1$, $\\varphi_2$ and on the right the actual phase $\\varphi$ in decimal representation.\n",
    "\n",
    "As we expected we have found $\\varphi=\\frac{1}{4}=0.25$ with a $100\\%$ probability."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4523a67b",
   "metadata": {},
   "source": [
    "## Now lets run on real hardware"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "6b93a18f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1684.33x1167.88 with 1 Axes>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc_S_backend = transpile(qc_S, backend_real, initial_layout=qubits, optimization_level=3)\n",
    "qc_S_backend.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "dadf82ca",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IPE job id: c6crdvnalsooemjqei6g\n"
     ]
    }
   ],
   "source": [
    "real_ipe_job = run_openqasm3(qc_S_backend, backend_real, verbose=False)\n",
    "print(f\"IPE job id: {real_ipe_job.job_id()}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "8b11c2df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "real_counts0 = remove_reset_results(real_ipe_job.result().get_counts())\n",
    "real_key_new = [str(int(key,2)/2**m) for key in list(real_counts0.keys())]\n",
    "real_counts1 = dict(zip(real_key_new, real_counts0.values()))\n",
    "\n",
    "fig, ax = plt.subplots(1,2)\n",
    "plot_histogram(real_counts0, ax=ax[0])\n",
    "plot_histogram(real_counts1, ax=ax[1])\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7c4f3fe",
   "metadata": {},
   "source": [
    "## Exercise 7 - Try estimating the phase of another Gate\n",
    "Now that we have estimated the phase of the $S$ gate, lets try finding the phase of another gate. Lets this by using that fact that we implemented IPE for `S` using the $P(\\theta)$ gate. Choose a new instance of the $P$ gate that can be estimated with two bits of precision and rerun.\n",
    "\n",
    "Solution - Modify $\\theta$ and rerun"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c11b301d",
   "metadata": {},
   "source": [
    "## Exercise 8 (Stretch goal) - Adding an extra bit of precision\n",
    "Now that we have mastered IPE for two bits of precision, lets try adding a third bit. Modify the code of this exercise to add another round of IPE.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "together-projector",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td><code>qiskit-terra</code></td><td>0.19.0</td></tr><tr><td><code>qiskit-aer</code></td><td>0.8.2</td></tr><tr><td><code>qiskit-ignis</code></td><td>0.6.0</td></tr><tr><td><code>qiskit-ibmq-provider</code></td><td>0.18.0</td></tr><tr><td><code>qiskit-aqua</code></td><td>0.9.4</td></tr><tr><td><code>qiskit</code></td><td>0.28.0</td></tr><tr><th>System information</th></tr><tr><td>Python version</td><td>3.9.5</td></tr><tr><td>Python compiler</td><td>Clang 10.0.0 </td></tr><tr><td>Python build</td><td>default, May 18 2021 12:31:01</td></tr><tr><td>OS</td><td>Darwin</td></tr><tr><td>CPUs</td><td>8</td></tr><tr><td>Memory (Gb)</td><td>32.0</td></tr><tr><td colspan='2'>Sat Nov 20 23:04:34 2021 AST</td></tr></table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div style='width: 100%; background-color:#d5d9e0;padding-left: 10px; padding-bottom: 10px; padding-right: 10px; padding-top: 5px'><h3>This code is a part of Qiskit</h3><p>&copy; Copyright IBM 2017, 2021.</p><p>This code is licensed under the Apache License, Version 2.0. You may<br>obtain a copy of this license in the LICENSE.txt file in the root directory<br> of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.<p>Any modifications or derivative works of this code must retain this<br>copyright notice, and modified files need to carry a notice indicating<br>that they have been altered from the originals.</p></div>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import qiskit.tools.jupyter\n",
    "%qiskit_version_table\n",
    "%qiskit_copyright"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}