QOSF_Task2 _final.ipynb

{
 "cells": [
  {
   "attachments": {
    "H_CNOTGate%20%281%29.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "seeing-learning",
   "metadata": {},
   "source": [
    "# QOSF Mentorship Screening Task 2\n",
    "\n",
    "## Question\n",
    "The bit-flip code and the sign-flip code (you can find a description of both here (https://en.wikipedia.org/wiki/Quantum_error_correction)) are two very simple circuits able to detect and fix the bit-flip and the sign-flip errors, respectively.\n",
    "    \n",
    "1) Build the following simple circuit to prepare the Bell state \n",
    "\n",
    "![H_CNOTGate%20%281%29.png](attachment:H_CNOTGate%20%281%29.png)\n",
    "\n",
    "2) Now add, right before the CNOT gate and for each of the two qubits, an arbitrary “error gate”. By error gate we mean that with a certain probability (that you can decide but must be non-zero for all the choices) you have a 1 qubit unitary which can be either the identity, or the X gate (bit-flip error) or the Z gate (sign-flip error).\n",
    "\n",
    "3) Encode each of the two qubits with a sign-flip or a bit-flip code, in such a way that **all the possible** choices for the error gates described in 2), occurring on the logical qubits, can be detected and fixed. Motivate your choice. This is the most non-trivial part of the problem, so do it with a lot of care!\n",
    "\n",
    "4) Test your solution by making many measurements over the final state and testing that the results are in line with the expectations.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "incomplete-refrigerator",
   "metadata": {},
   "source": [
    "### Importing necessary libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "acknowledged-foster",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.8/site-packages/qiskit/providers/ibmq/ibmqfactory.py:192: UserWarning: Timestamps in IBMQ backend properties, jobs, and job results are all now in local time instead of UTC.\n",
      "  warnings.warn('Timestamps in IBMQ backend properties, jobs, and job results '\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "# Importing standard Qiskit libraries\n",
    "from qiskit import QuantumCircuit, execute, Aer, IBMQ\n",
    "from qiskit.compiler import transpile, assemble\n",
    "from qiskit.tools.jupyter import *\n",
    "from qiskit.visualization import *\n",
    "from qiskit import *\n",
    "import numpy as np\n",
    "\n",
    "# Loading your IBM Q account(s)\n",
    "provider = IBMQ.load_account()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "intellectual-criminal",
   "metadata": {},
   "source": [
    "## Solution\n",
    "\n",
    "### Step 1 : Create a circuit that results in Bell State      $$\\lvert\\psi\\rangle =\\frac{\\lvert 00\\rangle +\\lvert 11\\rangle}{\\sqrt{2}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "funded-minnesota",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 327.252x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q=QuantumRegister(2,'q')\n",
    "c = ClassicalRegister(2)\n",
    "qc = QuantumCircuit(q,c)\n",
    "\n",
    "#Bell state\n",
    "\n",
    "qc.h(q[0])\n",
    "qc.cx(q[0],q[1])\n",
    "qc.measure(q[0:2],c[0:2])\n",
    "qc.draw('mpl')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "prescription-refrigerator",
   "metadata": {},
   "source": [
    "### Step 2 : Measure the probabilities of states $\\lvert00\\rangle$ and $\\lvert11\\rangle$\n",
    "\n",
    "- Both states should have equal probabilities of $50\\%$.\n",
    "- This is before introducing any error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "three-ground",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'00': 518, '11': 506}\n"
     ]
    },
    {
     "data": {
      "image/png": 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JktTjtDc0fw28NSL+ADgHeLTcPhh4sSMLkySpp+nXzv63AfOAncCzwMJy+3TgyQ6sS5KkHqddoZmZfxcRS4HRwKOZ+Up50TPAnI4uTpKknqS9e5pkZi2lWbNN237YYRVJktRDtfvmBhFxRUQ8FREvRsS4ctsnIuK9HV+eJEk9R3tvbnA1cB3wVSCaLHoO+GjHlSVJUs/T3j3NjwCXZuYdwJ4m7XXA5A6rSpKkHqi9oXk8sLyF9peB/gdfjiRJPVd7Q3MNMLWF9nOBFQdfjiRJPVd7Z89+AbgrIo6idE6zJiL+DPgrYHZHFydJUk/S3us0vx4R/YDPAkdRutHBc8BVmXl/J9QnSVKPcSDXac4F5kbEsUCfzNzS8WVJktTztDs098rM5zuyEEmSerr9hmZE/BKYkZnbI+JJIFvrm5mndGRxkiT1JEX2NB8AGpq8bzU0JUnqzfYbmpl5Y5P3N3RqNZIk9WDtvY3eTyPimBbaB0bETzusKkmSeqD23tzgLOCIFtqPBN520NVIktSDFZo9GxFN7wJ0SkRsa/K5L3AOsKEjC5MkqacpeslJLaUJQAk80sLyXcCVHVWUJEk9UdHQHEvptnlrgDcDv2mybDewJTMbO7g2SZJ6lEKhmZnPlt+2+6HVkiT1FkVubnA+8K+Z+XL5fasy87sdVpkkST1MkT3N7wDDgS3l961JSpOCJEnqlYrc3KBPS+8lSTrcGIKSJBVU9JxmIZ7TlCT1ZkXPaRbhOU1JUq/WrnOakiQdzgxESZIK8jpNSZIK8jpNSZIK8jpNSZIK6vIQjIgrImJtRLwUEUsjotXncEbEjIh4PCK2RsSuiPhVRFzbQr93R8SKiGgo//muzt0KSdLhqN2hGRFTI+K+iKgtv+Y1e95mW+teCNwBfBY4DXgceCgijmtllZ3AncB0YBLwGeDGiLiiyZg1wP3APwGnlv/8dkRUt3fbJElqS7tCMyLeD/wceCPwb+XXMOCJiPhAgSGuAe7JzLmZ+XRmXglsBC5vqXNmLs3Mb2bmU5m5NjP/EXgYaLp3ejXw75l5c3nMm4H55XZJkjpMe/c0bwbmZObMzLy+/HoHMIfSXmCrIuII4HRe+xDrR4Azi/zwiDit3HdBk+aaFsZ8uOiYkiQVVfQh1Hu9AfhWC+3fphScbTmW0uzazc3aNwNnt7ViRKwv/+x+wI2ZeXeTxcNbGXN4K2NdBlwGMGLECObPnw/AuHHjOProo1m2bBkAQ4YMYfLkySxcuBCAfv36MW3aNOrq6njhhRcAqKqqYvPmzcAJbZWvQ1RtbS07d+4EoLq6mvXr17NhwwYAJk6cSN++fVmxYgUAw4cPZ+zYsSxevBiA/v37U11dzZIlS9i1axcANTU1rF27lk2bNgEwadIkGhsbWblyJQAjR45k1KhRLFmyBIABAwZQVVXF4sWLaWhoAGDatGmsWrWKLVu2ADBlyhQaGhpYvXo1AKNHj2bYsGHU1tYCMHDgQKZOncqiRYvYs2cPANOnT+epp55i69atAFRWVrJjxw7WrFkDwJgxYxg8eDB1dXUADBo0iMrKShYsWEBmEhHMmDGDZcuWsX37dgCmTp3Ktm3bqK+vBw7u+7Ru3ToAxo8fT0VFBcuXLwdg6NChTJgwgUWLFgFQUVFBTU3NAf2eoKKdfxt0KNi4cWOHfJ/aEplZuKCI+AHwvcz8WrP2S4B3Z+YftbHuCGADMCMzFzZpvx54f2ZObGPdscAA4C3A54G/zMx55WW7gUsy874m/S8G5mZmm9+Mqqqq3PuPy8G49PaDHkI90Nyru7sCdRa/s71TR31nI2JpZla1tKy9N2x/CLglIqqAn5Xb3gKcD9ywn6GeBxopnQNtahiwqa0VM3Nt+e2TETGs/LPmlds2HciYkiS114HesH3fIc4mvgx8pbVBMnN3RCwFZlI6nLvXTOCBAnXs1YdXH1tZXB7j1mZjPt6OMSVJ2q+uvmH7bcC8iHgCeAz4CDACuBsgIu4r/8yLy5+vBNYCK8vrTweu5dXhfAewMCI+CXwPeBfwh8C0DqxbkqR2TwQ6KJl5f0QMAa6jdNnKcuDczHy23KX59Zp9KZ3DHAPsAZ4BPkk5ZMtjPh4R76M0e/emcp8LM3NJJ26KJOkw1O7QjIhBwB9RCrgjmi7LzJv2t35mfoVWDuNm5lnNPt8O3F5gzO9Q/LmfkiQdkHaFZkS8Bfgh0EDpEpANlPYYG4B6Snt6kiT1Su09X3krpdvUjQReAt5OaY+zltJhVEmSeq32huYpwF1ZurizEajIzM3AJ9j/JSeSJB3S2huau5u83wwcX36/k9IsWEmSeq32TgSqA84AVlG6Kfpnyjcb+ADwy44tTZKknqW9e5p/DTxXfn8d8BtKNzUYxGtvdiBJUq/Srj3NzKxt8v43lC49kSTpsHBANzeIiBOAk8ofV2Tmmo4rSZKknqm912kOAf4emAW88l/N8QNgdmZu7eD6JEnqMdp7TvNrwInA24Ajy6/pwFhgbseWJklSz9Lew7PnAP8tMxc3aXssIv4n8OOOK0uSpJ6nvXuavwF+30L7i4CHZiVJvVp7Q/Mm4PaIGLm3ofz+i3jfWUlSL7ffw7MR8SSQTZrGAvURsaH8ee99aIdSOucpSVKvVOScpo/ckiSJAqGZmTd2RSGSJPV0B3pzg7cDkygdtn0qM+d3ZFGSJPVE7b25wUjgX4DT+a970I6IiFrgXZn5XKsrS5J0iGvv7Nk7KT1H88TMHJ2Zo4Hx5bY7O7o4SZJ6kvYenp0JnJWZa/c2ZOaaiLgK+EmHViZJUg/T3j1NePXlJ221SZLUq7Q3NH8CfDkiRu9tiIjjgNtxT1OS1Mu1NzSvAv4AWBMRz0bEs8Az5barOro4SZJ6kvae09wKvBk4C3hTue3pzPRm7ZKkXq9waEZEX+B3QGVmPgo82mlVSZLUAxU+PJuZjcCzwBGdV44kST1Xe89p/h/gcxFxbGcUI0lST9bec5rXUnrKyYaIWE+zZ2tm5ikdVZgkST1Ne0PzO5SuyYxOqEWSpB6tUGhGxFHArcCfAK+jdE3mlZn5fOeVJklSz1L0nOaNwIeAHwLfAM4G/raTapIkqUcqenj2fODPM/ObABHxT8BjEdG3PKtWkqRer+ie5mjg/+39kJlPAHuAEZ1RlCRJPVHR0OwL7G7WtocDfIi1JEmHoqKhF8A/RkRDk7YjgbkR8eLehsyc1ZHFSZLUkxQNzXtbaPvHjixEkqSerlBoZuaHO7sQSZJ6ugN5CLUkSYclQ1OSpIIMTUmSCjI0JUkqyNCUJKkgQ1OSpIIMTUmSCjI0JUkqyNCUJKkgQ1OSpIIMTUmSCjI0JUkqyNCUJKkgQ1OSpIIMTUmSCjI0JUkqyNCUJKkgQ1OSpIIMTUmSCury0IyIKyJibUS8FBFLI+JtbfR9Y0T8c0T8KiIaI+KeFvp8KCKyhdeRnbohkqTDTpeGZkRcCNwBfBY4DXgceCgijmtllQrgeeBzwJI2hn4ReGPTV2a+1FF1S5IEXb+neQ1wT2bOzcynM/NKYCNweUudM7M+M6/KzHuAbW2Mm5m5qemr40uXJB3uuiw0I+II4HTgkWaLHgHOPMjh+0fEsxGxPiJ+EBGnHeR4kiS9Rr8u/FnHAn2Bzc3aNwNnH8S4K4HZwDLgaOAvgcciojIzVzfvHBGXAZcBjBgxgvnz5wMwbtw4jj76aJYtWwbAkCFDmDx5MgsXLgSgX79+TJs2jbq6Ol544QUAqqqq2Lx5M3DCQZSvnqq2tpadO3cCUF1dzfr169mwYQMAEydOpG/fvqxYsQKA4cOHM3bsWBYvXgxA//79qa6uZsmSJezatQuAmpoa1q5dy6ZNpQMhkyZNorGxkZUrVwIwcuRIRo0axZIlpTMRAwYMoKqqisWLF9PQ0ADAtGnTWLVqFVu2bAFgypQpNDQ0sHp16a/66NGjGTZsGLW1tQAMHDiQqVOnsmjRIvbs2QPA9OnTeeqpp9i6dSsAlZWV7NixgzVr1gAwZswYBg8eTF1dHQCDBg2isrKSBQsWkJlEBDNmzGDZsmVs374dgKlTp7Jt2zbq6+uBg/s+rVu3DoDx48dTUVHB8uXLARg6dCgTJkxg0aJFAFRUVFBTU3NAv6fSmR/1Nhs3buyQ71NbIjM7cROa/KCIEcAGYEZmLmzSfj3w/sycuJ/1fwA8n5kf2k+/vsAvgH/PzKva6ltVVZV7/3E5GJfeftBDqAeae3V3V6DO4ne2d+qo72xELM3MqpaWdeU5zeeBRmBYs/ZhQIedg8zMRqAWGN9RY0qSBF0Ympm5G1gKzGy2aCalWbQdIiICOIXSBCNJkjpMV57TBLgNmBcRTwCPAR8BRgB3A0TEfQCZefHeFSLi1PLbgcAr5c+7M3NFefmngZ8Bq8t9rqIUmi3OyJUk6UB1aWhm5v0RMQS4jtL1lMuBczPz2XKXlq7X/I9mn88DngXGlD8fA3wVGA78rtx/emY+0aHFS5IOe129p0lmfgX4SivLzmqhLfYz3seAj3VIcZIktcF7z0qSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBXU5aEZEVdExNqIeCkilkbE2/bTf0a530sRsSYiPnKwY0qSdCC6NDQj4kLgDuCzwGnA48BDEXFcK/3HAv9W7ncacAvw5Yh494GOKUnSgerqPc1rgHsyc25mPp2ZVwIbgctb6f8R4LnMvLLcfy5wL3DtQYwpSdIB6bLQjIgjgNOBR5otegQ4s5XValro/zBQFRGvO8AxJUk6IP268GcdC/QFNjdr3wyc3co6w4Eft9C/X3m8aO+YEXEZcFn5486IWFmkeO1zLPB8dxfRFb72se6uQOoQfmfb7/jWFnRlaPYImflV4KvdXcehKiJqM7Oqu+uQVIzf2Y7VlaH5PNAIDGvWPgzY1Mo6m1rpv6c8XhzAmJIkHZAuO6eZmbuBpcDMZotmUprx2pLFrfSvzcyXD3BMSZIOSFcfnr0NmBcRTwCPUZodOwK4GyAi7gPIzIvL/e8GPhoRtwN/B7wV+BBwUdEx1eE8tC0dWvzOdqDIzK79gRFXAH8FvBFYDnwsMxeWl80HyMyzmvSfAXwJmAw8B3w+M+8uOqYkSR2ly0NTkqRDlfeelSSpIENTkqSCDE1JkgoyNCVJKuiwuyOQ2i8iRgEnUrqZxCvAysz05hGSDjvOnlWbIuJyYDZQCfwe+E9gPfAz4HuZuTIi+mTmK91YpiR1CQ/PqlURMYTSc0q/T+ka2BpKj2ZrBC4G7oyISZn5SkRE91UqCaD89KcJEVHR3bX0Vu5pqlURcSXwgcysbmHZNEoPBR8JvDkzD4unKEg9WURcDdwMfAv4LvBz4DeZ2dikz0BKd1f7cWa+3B11Hsrc01RbdgNHR8QUgIioKD/DlMxcBLwfeAl4R/eVKKmJC4EnKM1B+B6l+3ffGhHTIuL15T5/CnzawDwwhqba8h1KE3+ujoijM7MhM3dHRB+AzPw18FtgVDfWKAmIiDcALwNzM/NtlJ4J+ffA/wAWAj+NiE8AVwNLuqvOQ52HZ9WiJuco/xi4AxhM6ZDPV4D/oBSU04G/BU7OzPpuKFNSWUS8EXgfsCIzH2627DTgkvLyQcDozNzQ9VUe+gxNtSkijgGOA84E3kXpXAiUnlcawLzMvKFbipP0KhHRH8jMfKnp5Lws/0MfETcD52bmad1V46HO6zT1GhExFPgz4OOUHva9i9Jh2EXAF4DXUTpn8qPMXNVNZUpqJjN37Q3LbLZHFBFHAe8Gvt4dtfUW7mnqNSLiHkqPYvtXYBulQ7MnAxOALcB1mek5EamHKM+I3dE8KJv1OZLSRKFvZObuLiuulzE09Srl/6XuoHQIZ2GTtuOAakrnRcYB783Mum4rVNI+EfF3lGbNPgE8m5kvtNDnmMz8bVfX1ts4e1bNTQLWUrrcBCgd5snMZzPzW8B5lA7VXtA95UlqKiIuAi4FvkjpRiS3RsS7IuKE8jnOvec67917+ZgOnHuaepXyl+sHwFGU7vrzTPNb5JVvevDnmXlq11coqamImEvpLl3/Fzgf+CBwArAS+DfgJ8BE4I7MPKK76uwt3NPUq2TmLuCvgf7AfcDFETE6IgbAvskEM4Dl3VelJICI6EfpyNBvM3NNZn4hM08GzgAWUArQbwFfBuZ1X6W9h3uaalH5MM4cYBalG7UvBn4DnA1sBC7JzCe7r0JJABExCBiWmb8q37Hr5aYTgiLiQuAbwNTM/EU3ldlrGJpqU/nyk3cCf0LplnnLgW9n5q+6sy5JrSvftSsyszEiLqV0aPao7q6rNzA0VZiPAJMOPRFxDdA3M2/t7lp6A0NTknqxiHgd0Oh/eDuGoSlJUkHOnpUkqSBDU5KkggxNSZIKMjQlSSrI0JQkqSBDU5Kkgv4/70/0w5pkW+sAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend = Aer.get_backend('qasm_simulator')\n",
    "job = execute(qc,backend,shots = 1024)\n",
    "result = job.result()\n",
    "counts = result.get_counts()\n",
    "print(counts)\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "controlled-princeton",
   "metadata": {},
   "source": [
    "## Background\n",
    "### Errors in qubits\n",
    "\n",
    "- Unlike classical bits there are two significant errors that could effect a qubit's performance.\n",
    "- They are\n",
    "    - Bit flip error\n",
    "    - Sign flip error\n",
    "\n",
    "- **Bit flip error** : It refers to the flipping of a qubit state from $\\lvert0\\rangle$ to $\\lvert1\\rangle$ and vice-versa.\n",
    "\n",
    "- **Sign/Phase flip error** : It refers to the change in relative sign between $\\lvert0\\rangle$ and $\\lvert1\\rangle$ during the transmission of a qubit.\n",
    " \n",
    "     - **Example** : A qubit in the state $\\lvert+\\rangle = \\frac{1}{\\sqrt{2}}(\\lvert0\\rangle + \\lvert1\\rangle)$ may be fliiped to the state $\\lvert-\\rangle = \\frac{1}{\\sqrt{2}}(\\lvert0\\rangle - \\lvert1\\rangle)$ ."
   ]
  },
  {
   "attachments": {
    "640px-Quantum_error_correction_of_phase_flip_using_three_qubits.svg.png": {
     "image/png": 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W5xsEHJN3J6zjXYDKaBQ5AHwHuCzvTph1OweA1ilOC77MutnLaNcEM7NIzgE0MzMz6zIOAM3MzMy6jANAMzMzsy7jANDMzMysyzgANDMzM+syDgDNzMzMuowDQDMzM7Mu4wDQzMzMrMs4ADQzMzPrMg4AzczMzLqMA0AzMzOzLuMA0MzMzKzLOAA0MzMz6zIOAM3MzMy6jANAMzMzsy7jANDMzMysywzJuwNmGVkRWDPvTsR4AHgq705Yx9uJYp/bZwFX5N0Js25X5JOEWT2uQQHW3Lw7UsNQ4HvAynl3xDrafsBXgKfz7kiEFYBRwIV5d8SsmzkAtE6xELAXMCPvjtQwDngk705YxxsLXA8clndHIpwOjMm7E2bdzjmAZmZmZl3GAaCZmZlZl0kzBTwIeAiYBHyYQR9OBO4ALsvgvcwse/sCU4GeOl83FzgXuCjzHpmZWUPSBIA9wOooifeNDPrwOPA1HACaFdVFwI3ABpSCuYOAS4EPytqNBJYClkNB4xTgvpb10szMEmvWIpCF0AXgI8HPeBD4HfBalbYXASeh1ZH/bFJ/zCy9mcAzwGrB/88CzqR/8AfwJvA8cCcKDh8CnmtNF83MrB7NyAHcCLgXeBX4KvAlYDZwP9Bbpf17wOVoBWcnGo5GQk5GF8UhweMpwLbB82btYPPg8Q4GBn+V5gJ3A/9pao/M0usBNgN+hAYilgB+C5wGfBqNaJt1rKxHABcFrgSOQx+k0JnBz7oSWBdN+5abBpwPHENx67jVaz5Uj+sQNAL6F2A6sDP63SyJguOzgFOBnwHv59HRLncCsDwqHxPmtPagMhWvAV8OvrcWcCQwD3i77PUjgWHoGL++Bf3N0ybB480J28/AI4DtYhLwLXT+fafs++HxfQZwU/C949HsTrXPzBvAF1vQ30YMAfYBjkb1Ev+Mbmp2RoMRs4Dd0L/5NyhP/a08OmpWNEOAPjTNW+ksNF00f5XnhqPRvmoJ4YPQB3G7jPqYt2VR0HcRyocqN7vi/5dGifIPo0Ck6M4BPpd3J6p4i3R37EsBH0PHbh+6oO2LblSWLGs3H8p93RJ4N2h7HTAZWJXqx3y5ccBLKfqXxmiyyc8tNwYdu33AFlWenwgsXPG9i3C9N4DDURHwVjgEjWjVawSa4t8Knaf7UHH18PgeUdZ2KRQwnh20m031z0wtp5NfkLgwuhG/Gv27yj0LjK9oeyrwL4q/yxDA9yl2/cc42xE/s2A5qxUALoBGsO6NeO0dKEBcsMpz30FTo+1uWXRn/PUaz1cGgKEvoN/fck3oU5Y6LQAMnYqO67/FtBsDzAnafryO92/3AHBb9G+eSf9gIHQOAwPAtTLuQ7tqhwAwtAga5e6jNOJby4lBu6QjwqG8AsCFUJ7qj9GgQ6XKADC0Ezru12te1zLhANDqkmUOYC+6MPw3os2LaCSw2gjCNGAHdAJqV/OjPS6PRHkk9fgVmoL5I/GjSZa9ML8tLgDcBE13zQJuaWqPimWz4PFuBp6kJ6BFXJWLvB5sdqcsc5uh4GgGWswTJfzM3NDUHmWjBw0w/BqdZ/vqeO3lwB7AxQy8yTFrW1kGgOFw+qsRbV4JHteo8twzaIRw9wz71GoHoe2+Tk35+p8B9wAHZtYjS2JhSitcp8e0DQOhu+iuu9Xe4PFt4DPB12eBI9AI0P35dMsyFh7ft1F7tgK05Vw4LTq9mR3KyOfQ9e7wlK+/DOVufyerDtn/DEcpBIehfNPTUIqBNVmWAWB4ZzQzos2s4LFa/iBoFHD/rDrUYmPQtO8RDb7PMWjxyOiGe2RJTaY06nF3TNvwAjm9mR0qmFHAOsF/v4pyvT6GgsKtUE7YTVVfWb/N0UX6FNoj76rTJD2+N0ajah8QP1KYtx4UuH0TTW+n9RNge2CZDPpksiLwD5RPuimKSb6GzsM/p/7i81aHLAPAMNk7ahVv+FytxPDfoxy4dTPqUyvtANxO42UvXkLTkDs03CNLKrzo3UH07jajKQVC05vZoYLZGBiKbuC+jAK0b6G81S3RCbzePLBaXkGpJAehfFprnTQj4XdQurEvqk3QcRWVn57EDLSwaWrDPTLQWoDr0IrySoNQlYwTWtqjLpNlABiOWEXlVoR3X7VGt2agPI19s+pUC00Brsrova4J3s9aI7yYxY1ibYQWQc1EF75uUT7tXW2E/0UGLnBZHK2crtcjaFW8td4m6ML7LkpFiZL0M1MEPjcX01eIH009EFXKsCZoxk4gUUO24XNR08TT0EKIQ2PaFc0ElGCchcfR3Y813wKUclJnoynNWnYLHu+mvY7NRkVd7AejhU+VTkajhWl+T/Uk6Ft2JgeP/6F60f7QEGDt4L/bIQCcgK4pWXic9ijX1Q62T9BmKFod/Ksm96UrZRkAhkWMkwSA70a0uRWNFE4K/jutNWjdNN3LwEqo0HVcIeu3iS/RMRhNkz+KRlKKZBBaAFDvKudmSzPaBLro9aDjd3miT+6fDh6np/xZzSjPUs0glEydhdGUyl/cWOX5eWjxUrl10YpgF88tORiNeDTbfMAvU742DPTfQJ/xWiaiC/NMNCpcr/nQ9p/Hp3htvd5HpV22RzllUWYDjxGfJzgWTScXLRAcis5l7VIKZoGE7X4K/LCZHUlgPMVPdahblgFgOAUUVcIkrB/2dkSblVA9t3802J9HgBUafI+kBgPXogUgcVMnr6AdU6KsilYSf5zGkpabIdwR4JK8O1LhmZSvC0tZ3Ixy2moZS2mBUlypmFreQ+VSmm0U8PeM3mt9dJ74kOQX+29Sqnu3CrANOoHeGbzHbuji+TgqrfFKlfcILYV2bRiPPtNnMTBPc3lgTxT0jkY3jpcx8GZseWDH4N8zDJ1jlgR+UdZmBCr5sUrw//egY73Rz+EvaE3A82XSFd9ekNKo3qFEn8dORJ+b20g3wjsTLXY7J8Vr6zUYpRRcSvWR6nIPoyD45Yg2C6HyT1Mo3rn5KHSOSVuFotVuoHTMRTkG7ciSp44L/iDbADAM2KJGrMIim/+MaLM/WgzS6OjBXFT0s1X+jYr9JvmZcW3GoerzrzfaqSaYhXI1W/m7TSLttGE46hG3iGEjGl/12Edrfm9hoeoshL+fe0m2VeF2qJbnI8H/v4tyBE9A04p3om3z3kJB2xMowKs2RbceCkB/jD7PV6AaoruUtVkEBZWfRVvxjQUuBPZDC6nCUibroEK5UynNQByLRoDDAHAF4K9oBO2b6O99CipN9Uka+53OpDV/+w9IFwBORsHSO8ADMW17g8fpKX5O6H1adw55Gh0ncT8v3OYxqt0K6GaziOfmmejvX7Rzcy1/JD4AnIvqMLbLv6mtZLkI5PbgMSoAXCJ4rJVAPxRdFFpxZ5i168luK7tt6fx9ZYtgDMlzmdpp1WOWwhHSJLlem6NVkmeUfe95NMr3Otpp4evoZvF5NK1zXvCaj1Z5v0lov9a30cjGpWi/1vIAZxm0enX14P/fQiPxU4K2oT2Dn1uefnJ82f/3oBvPJ9AI1zwUPB6K/vafiP3Xt7fw+L4d3UDUMpbSDi/VUgKKKMtz83Zo5ao17lTiZ25+gQJ4a4IsA8B/oxPCRDQFVWkUmlZ5EOVZVLMNOtFPz7BfrXIl6v/YBt9nfpSv8peGe2RxwlpmM4ifuu8NHqc3sT9FMQHl8e0FbBh8743ge5VfGwAHoLv061AAVm2qrY/quwT9AuWEHVzluWvoP+r2XvC4WNn37kM3nWFO6hD094T+KSD/Ar6Bgs1d0NTvbErT+puhwKay7zPR6OfWVfrXSZKu6i3/zMTVzCyKG9DfttGyQj1oBDluKtmSeRsF1M/UeP48dANmTZL1KuDvoPyondAfr9yn0In+uIjX74uqrbfjKsDn0UXwMBorBn0ICv6ez6JTFim86N1J9K4HY+iu+n/HUVpUc1nwuB7Re6HOBv4QtI8aQar0OMrpW6fKcy8mfI+haP/btVCgF44YlO/3+gs0Wvg1lIPYh6aO90PTS+FORlMYuB/3Y3T2TidpRsJvJ/ozUyTvo9Gm76GbmrT2QgMd92XRKQP02VoNfQ53QeeB89FofDtsMdh1hqCTZ63dPA5CSbSrlX1v1eB7R0e87yLobrudi78uDjxH6SRZTdRJc2NUgmGxiDZ5Owdtq1Q0b6HFQ/W4Ax3Lx8S02zZo9x7pV9eOY2CtvGZp1WrjerxA9ZXjI9F0a/mK/wno911ZcHfP4PsTy743Gf1dfoS2lCJ47KP/+SZccTg/2nHgUBQsPouC3X2C1+yd/J+U2OGUFsU02yHod1GP8uN7aEzbu4O2R9bftf85HfhiA69PYyS62dg1os2zlPLUK62CbspXyrhfWfo+7bMCuJqV0UIca5Fm1AH8KbqwHokCuuHogrQPcHXE6/ZAF4FGd9LI00todOFatENCPYsF1kUJ6FOIXoVm2RhJadQprtzQJsHjXUTvFGLRBlX53vrB96PODVFOQ+eMwynNHAwve34hdG5ZAwVGT6EFPzejup0voAvP9ejmbHUGGozqQ16bso9Ft2nweBfRN6ijKY0UZrXzS6vMQAt57kOf4XrqAk5E17TPoyDSrCNkmQNY7i60cm4/dPLdkfgT/P605+KPSrehGlqXoVGG4dHNGYoS469Av7Pbmto7G4FG4w6kNJr3FgN3p+lBpTGWpVQT7eXge3GjJFbdppRKQYE+G8ejFcM/Lft+WC+08vw0uMr3x6KRq/K0kU+ghTrD0cjfIijIrKzD9z76mz6DRnd+gm5Ul6potz86ZjrJIHQsr4hWUEPt43tk8P0vUho0eIt0q43z9E9UWusUNFpWLVe93GA07TsdzWwVrfSVWUOaMQKYxjropPuHvDuSkavQdO5J6KJzHsrrC3OTxqGaZNuhaa1H0CjTv1re0+6yBtp0PBTm8oQ7uJxB6Sbkx5Sm8t8O2q6IFjq8h1a8tmOuap5eQsV4r0SjMIeiwOvLlBZuTKWUp3UICsBPQDXOwkLcp6A8oQvRApQL0N/uz2j6eAxaYfz54PUnA19FqShnoJut4cH7HUOp5FS44vg6VArmRVT+5wWy2+WnKM6glNP5WvAVHt8foGN/HhodPb/sdeFnZlrweBJaWNMubkOjzj9EK77PR8fNE8HzY1AKzhQ0ePEGmiLPqq6mWVuLywFM43TSV68vuvXQyMLfUbL5nODxYXTy3LD2Swupk3IAW8k5gJqu7UHTiFuhlbiVwtGm8CscZVqg4vvlf+uhKBdwC/qP3q1K6TwV7ie6RPCzNwjep5oRKADaCo0eNqroOYCtlkcOYDWror/LfcCrqObce2gHpp+jNJ524hxAq0sRRgCHo6nPrOo0Fc3dwdc38+6IWQHMJbrQ8AxKo4HlonYPmk31PM5Hyv77ueDxv1QvR1PuA9pjj1trzCNoBDhuEZhZR2pWDmA9dkQjI2n2lDSz9jCUYtxwmpkZ6QLAuSh5Os0ekNVsQ2cs/jCzgbYG/oSCv21QIn27LR4wM+s4ae7I+4BFSbYvaBJfwqU1zDrVdXjrLDOzwkk7BVwtRyctB39mZmZmLVSEHEAzMzMzayEnZVun+AD4LsXdn3Q+VJzYrJlmohI3J+TdkQhr0dl7K5u1BQeA1il2RHXgimynvDtgHe/nqLRW2j2rW+ESvPDPLHcOAK1T3BN8mXW7U/LugJkVn3MAzczMzLqMA0AzMzOzLuMA0MzMzKzLOAA0MzMz6zIOAM3MzMy6jANAMzMzsy7jANDMzMysyzgANDMzM+syDgDNzMzMuowDQDMzM7Mu4wDQzMzMrMs4ADQzMzPrMg4AzczMzLqMA0AzMzOzLuMA0MzMzKzLOAA0MzMz6zJD8u6AWUZ2ArbJuxMxrgD+kncnrKPNB5wM9OTdkQgzgW8Bs/LuiFk3cwBoneK3wJEU96IyEjgXWDjvjlhH+zKwHPDHnPsRZRdgX+CXeXfErJs5ALROMRc4G5iRd0dqGAcclncnrCs8DJyZdycirJ53B8zMOYBmZmZmXSdtALhYhsP/ZyAAAAp7SURBVH1YABia4fuZmZmZWYQ0AeBg4FmU05SFk4BDMnovMzMzM4uRNgAcBgzPqA+XAV8ABmX0fmZmZmYWoVmLQHqBz6Pl/oOCn/Mz4K4qbf8aPL8pcFOT+mNmZmZmgWYEgAcBBwJbA08F31sJBXpnAD+paD8PuACVBXAAWDyLAbsBOwKrAOOBPYEfoID+CuD3KNg3M7PWGAtMRefmNYElgD7gq8AD6Nx8CfBOXh20Yst6FfA6wInA1ygFfwCPA/sBPwK2qPK6c1BtqDEZ98fSG4GCvEeBtdAI7nooSP8+sCUK6ncHnkQBfDs6F7gfeLrs60ngXuDKsnbrBd97tKLt34Pv79y6LptlbjLRx/cOZW3PBu6j+mfm6tZ1uWv1oELaT6Lz8PnAxijYOwfYBLgYmBK0ORhX/LCMDEF3GQtVee564E2qH2yDgBeBW2q87+3AAVl00Bq2InAPKia7XMVz5wCfq/jeRqj22HnA/M3uXA1v0djCpMPRcf0WsGxEu+FBmz7gVJLvuDAOeKmB/tVjNPBGi36WxTsc+F6LftYh6EY7reFoxKgPzdZEHd9HBO3eIfozU+l04ItpO9jlxgPXoRvxVSue+z4Da42uDtwKXAUs0vTeNWZldB2xFsnyrmBZNLr3KJrWrdQHPIHuVJav8vw02ncUqZMsgE4uD6Ht1Z5J8JrbgQ3RNMQlTetZc60YPN4A/Cei3YKURqrPQwWozTrFeHQDATonRx3fywWPNxL9mbFsDEPnp9lo5O+RBK95GF2XRwDXUOwtAq3FsgwAN0GjfFGjHC8GbTat8tzFaKpxlQz7ZPWbhkb+DkBBe1LvARugC0g73t1vHjzeGNOuFx3Db6KpY7NOEn4OXkY380na/q153bEyJ6Ep3e2BOXW87kNgK+AV4Lgm9MvaVJYBYDiC8npEm/C5lao89w4KPPbJsE9Wn82BNdAinjTeRwtGvo1GEtvFspRGM6bHtN0seLyF6iPdZu0sPL5vIvoGcAlgYvDf05vZIQM0MDIVzZKlOe/MRak7BwDLZNivLKyOFoLeiv6dj6K0ibzSibpGlgFgeMH/MKLN7Iq2laYBe+OdQfJyFHAs0X/DOE8Cl6Paju0ivOi9Rvy0Sth2etN6Y5af3uAxriJDOIvzGlooYs11OBoBbCS393XgNODQTHqUjU+jfPPdUZ50DwoCfwjcBiycX9c6XzMCwKickfC5WgHgDcAsYJusOmWJLQ6sC1yawXudA+yawfu0ShjU3Uz0qMdiKFEZHABa51mO0mKOuAAw6WfGGjcMrcKelsF7TUMVN4qwKngFlEdda1OJtdAKZ2uSLA+CJCswwxNFraHdeeiA8GKQ1tsITWvOyuC97kMXk1EZvFcr9AaPcRe9MM/1dbRIxqyThEFdkvy/8qlia6610GK8lzN4r/+iUduJcQ1b4BvET/NOQeXlrAmyLAQdJqVGvWf43HsRbc5DF9dxROcTxpmfYi4omUcx7r4q9aKp33Vj2o0DJiRo9wbwCfrXg2ymtL/TJSmtSl+VgWUUym0dPN5OujycHuJ/b1mYn2IeY90sHGFvtqWob4FAuU2Cx3dRnblahlAaCb85xc8ZjPLQWvH7qEdRz81boWtm3O9rPKpQENfuHRRY5X2DPiVhuz3Jf6vY++nAke4sA8Cw2njUMvPwuXcj2jwRPL8SutCmtTTwqwZe3yyPUczAdAI6+S0X024cCpQ+GdNuWeCbjXcrsbR5o+FIxuto5DLK2sHj9JQ/az5ac0z20LxtHi2dbSkdP820GOnTOMoXOL0Z0W4yuiC/Qbr8v2HAHsDHU7y2mR6n+gLFvC2Czrtx546wzt9GMe1WQcfJXg32q1FLJWw3ldLNSV42orHc+I5RqxD0scH3L4p47blBmx9EtNkKeAHXK2q1A4BfJ2hXrRB0NY/R2tVmaQtB/xodk3EXzXCbpT40JVMvF4LuXu1QCHoZSsd33A3qr4J2l6X4OeBC0PXahmQ7rFQrBF3NdcQHia1wPaVjLuoryfXGUshyuPve4HF8RJslgseo/Kl9cYHdPPyL7O5+50N3oy9m9H7NlDSXKVz1+Dpe9WidJzy+Xwb+GdO2N3ic3qzOWD//olRmLQsTg/fM23kJ2ryNdjGxJsgyALwDLSBYPKLNeJSfUutiOxbtPnF2hv2yZG5BU7tRAXxSU1Bu0Oy4hjlbklIydFwA2Bs8uv6fdaLy6d+oXKclKQUj05vZIfufJ9B1M4sUgnVRQehWzUZEOQ+4NqbNIXg2o2myDADfQNuATUQniUqLoqmFq6m9mmkq8AA64K21ZgNXAP+XwXt9iWzKyTRbeS2zf8S07Q0epzerM2Y56g0ek94IJfnMWHYuQefVRhXp3DwP1QG8iIE3He+iNAEPBjVR1iuejkLJw5+v8twBKMg4KuL1+6IcM8vHd4CvUj2AT2pbFOz/LosONVk46nEr8bsehNPj05vZIbMcLAl8JPjvpPX/4nYKsWydiGoBrt7Ae6yF9hD+WSY9ysYMVAR6NTTadziwH1pEWMRFnB0l65WCz6Ep3IvRMPMvUZS/P9pebGe0OXU1H0UHwSUZ98mS+w9KIL8M3enPrPP1KwFnAZ+iPaZJe4PHuFIW5TuFOP/POk358Z10JNz1/1rrbeBg4PdoAUe9JdIWR+f1rwIfZNu1TDxKfO1Jy1gzah7dAqwZvPcvgTNRbaI1gL9EvG4f4A+UyslYPk5GJVVuQytXk1oD5YH+Fm3tU3SLU8plujWmbThVfDse9bDOEwaAccd3+f6/aer/WWMuRulR96AyZ0lNCF5zN9HXYOsyzaoV9hpa6p/UUFST6LPN6Y7VoQ9YD005PICm7C+g9ojeSDR0fyDwtaBtUY1ASdALoHSDsLjoasH3ngCeDb63AqV81vC4HIWKQX+IR0CsvX0E1fxcHuVeQ/XjeziwProZ3L3s9Wuilf6Po5kfa40dUamXe1FpoV9Re7HdMJRHdzRwArq5N/ufohSLnYIqnU/PuR8mc9F0wxXA8ahu45/RXeTyaJR2FBo5mAL8FdgQeDKPztZhSVRVfi7aoSSslzYJ2ACNQIcB4DZoVPM9NJIN+rzsghKUvQeqtbMdUcpG+fE9FB3fH1Ba7T4eFW2eCzxN6TOzPvo8XIgDwFbqQ8Hc9ejcfAxwJRq9/Sj62x2Apok/gYrbT0E382b9FCUA3BdNHfqCWiw3osBuVXTB2AIt8JiEAsAb0ehfO9T7AwV9X0jY9oxmdsQsZ0lHg54h+WfGWudetJPKCujcvAm6OZ+LRnAfAL6L/n5mVRUhAFwE2A4FElZMjwRfZmZWHE8Dp+TdCWtPRQgAdwXuRCtQzaxxs9BuOx5RL44t8+6AmVm5NAHgHJT/9G5GfVgMOCmj9zIzTQFtnncnzMysuNKOAG4W3ySxb2f4XmZmZmYWoxl1AM3MzMyswBwAmpmZmXWZIiwCMcvC05RqlxVRD/CvvDthHe8/qPhvkRedjES1Q80sR4Pim5i1hcWApfLuRIxngVfz7oR1vLUp9uzOHLRK3czMzMzMzMzMzMzMzMzMzMzMzMzMzMzMzMzMzMzMzMzMzMzMrFv9P2VsdPrwFm/JAAAAAElFTkSuQmCC"
    },
    "Quantum_error_correction_of_bit_flip_using_three_qubits.png": {
     "image/png": 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"
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   "cell_type": "markdown",
   "id": "celtic-ordinance",
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   "source": [
    "### Basic error correcting codes \n",
    "- Two basic error correcting codes are **The bit flip code** and  **the sign flip code**\n",
    "#### 1) The bit flip code:\n",
    "   - This is a 3 qubit circuit that makes use of 2 ancillary qubits to correct 1 qubit. The circuit is as follows :\n",
    "\n",
    "   ![Quantum_error_correction_of_bit_flip_using_three_qubits.png](attachment:Quantum_error_correction_of_bit_flip_using_three_qubits.png)\n",
    "   \n",
    "\n",
    "   - The code works by first using CNOT gates to transfer the computational state of the main qubit to the other ancillary qubits. Then if an error occurs the first qubits state will be flipped. To correct the bit flip CNOT gates are applied to the ancillary qubits again and then a toffoli gate is applied to the first qubit which will correct its state. \n",
    "\n",
    "   - For example let’s say the main qubits state was 0. CNOT gates will be applied to the ancillary qubits which will leave them unchanged since the main qubits state was 0. \n",
    "\n",
    "   - Next a bit flip occurs which flips the main qubits state to 1. After the bit flip CNOT gates are applied to the ancillary qubits which will flip their states to 1 since the main qubits state is 1. \n",
    "\n",
    "   - Then a toffoli gate is applied to the main qubit which will flip the state of the qubit since the ancillary qubits states are 1. This flips the state of the main qubit to 0 thus correcting the error. \n",
    "   \n",
    "#### 2) The sign/phase flip code:\n",
    "  - In essence this error is equivalent to a Z-gate. However as said before it can be corrected using the phase flip code.  The phase flip code works identically to the bit flip code in that it first transfers the state of the main qubit to the ancillary qubits using CNOT gates. Next all qubits are put in to superposition using a Hadamard gate. \n",
    "\n",
    "  - After this a phase flip error will occur on the main qubit which will effect its phase. After this a Hadamard gate is applied to all qubits again which will take them out of superposition since two Hadamard gates applied leave the state of the qubits unchanged.\n",
    "\n",
    "  - However because the main qubits phase was changed it will not be in it’s previous state but flipped from 1 to 0 or vice versa. Because this has altered the computational state of the qubit we can correct this using CNOT gates and a Toffoli gate where the main qubit is the target and the control qubits are the ancillary qubits.\n",
    "  - The circuit diagram is shown below ![640px-Quantum_error_correction_of_phase_flip_using_three_qubits.svg.png](attachment:640px-Quantum_error_correction_of_phase_flip_using_three_qubits.svg.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dependent-person",
   "metadata": {},
   "source": [
    "### Step 3 : To encode the qubits in using the above error correcting codes\n",
    "\n",
    "- Note: The errors must me introduced after the **H** gate and before the **CNOT** gate.\n",
    "\n",
    "**Assumptions :**\n",
    "\n",
    "- Since the first qubit will be in the superposition state $\\lvert q_0\\rangle = \\frac{1}{\\sqrt{2}}(\\lvert0\\rangle + \\lvert1\\rangle)$, there will be no significance of introducing bit flip error i.e, **X** gate. Therefore we can encode the first qubit using sign flip code.\n",
    "- Now, considering the state of second qubit, it will be in $\\lvert q_1\\rangle = \\lvert 0\\rangle$ state and the effect of sign flip i.e, **Z** gate could be neglected. Hence we can encode it using bit flip code."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "included-performer",
   "metadata": {},
   "source": [
    "### Step 4 : Create an error_gate function\n",
    "\n",
    "- To apply an error gate to the both qubits randomly from the set of **{I, X, Z}** gates, we can create an error_gate() function.\n",
    "- The arguments are a quantum circuit and the qubit to which the gate must be applied."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "second-empire",
   "metadata": {},
   "outputs": [],
   "source": [
    "def error_gate(circuit,qubit):\n",
    "    s = np.random.randint(0,3)\n",
    "    if s == 0 :\n",
    "        circuit.i(qubit)\n",
    "    if s == 1 :\n",
    "        circuit.x(qubit)\n",
    "    if s == 2 :\n",
    "        circuit.z(qubit)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adapted-woman",
   "metadata": {},
   "source": [
    "- Another way of creating error_gate() function using numpy.random.choice() method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "advance-weekend",
   "metadata": {},
   "outputs": [],
   "source": [
    "def error_gates(circuit,qubit):\n",
    "    error_gates_list = ['i','x','z']\n",
    "    d = np.random.choice(error_gates_list)\n",
    "    if d == 'i' :\n",
    "        circuit.i(qubit)\n",
    "    if d == 'x' :\n",
    "        circuit.x(qubit)\n",
    "    if d == 'z' :\n",
    "        circuit.z(qubit)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "technological-howard",
   "metadata": {},
   "source": [
    "### Step 5 : Construct the error correcting circuit \n",
    "- First we create a quantum circuit of 2 logical qubits, 4 ancilla qubits (2 for each of logical qubits) and two classical bits.\n",
    "- Apply the **H** gate to the first qubit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "american-product",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x133f6998630>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Create Quantum and Classical Registers\n",
    "q = QuantumRegister(2,'logical_qubits')\n",
    "a = QuantumRegister(4,'ancilla_qubits')\n",
    "c = ClassicalRegister(2)\n",
    "\n",
    "#Initialize the circuit with above registers\n",
    "circ = QuantumCircuit(q,a,c)\n",
    "circ.h(q[0])\n",
    "circ.barrier()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reasonable-falls",
   "metadata": {},
   "source": [
    "- Encode the first qubit in sign flip and second qubit in bit flip code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "married-toner",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x133f6a6b0b8>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#encoding for q0 and q1 - sign flip & bit flip respectively\n",
    "circ.cx(q[0],a[0])\n",
    "circ.cx(q[0],a[1])\n",
    "circ.cx(q[1],a[2])\n",
    "circ.cx(q[1],a[3])\n",
    "circ.h(q[0])\n",
    "circ.h(a[0])\n",
    "circ.h(a[1])\n",
    "circ.barrier()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "worth-hollow",
   "metadata": {},
   "source": [
    "- Introduce error gates randomly from the set **{I, X, Z}** using error_gate() function\n",
    "- Decode the qubits, apply **CX** gate, measure and draw the circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "hawaiian-tobacco",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1583.26x445.48 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#introducing error gates to both qubits randomly\n",
    "error_gate(circ,0)\n",
    "error_gate(circ,1)\n",
    "circ.barrier()\n",
    "\n",
    "\n",
    "#decoding for q0 and q1 - sign flip and bit flip respectively\n",
    "circ.h(q[0])\n",
    "circ.h(a[0])\n",
    "circ.h(a[1])\n",
    "circ.cx(q[0],a[0])\n",
    "circ.cx(q[0],a[1])\n",
    "circ.cx(q[1],a[2])\n",
    "circ.cx(q[1],a[3])\n",
    "circ.ccx(a[1],a[0],q[0])\n",
    "circ.ccx(a[3],a[2],q[1])\n",
    "circ.barrier()\n",
    "\n",
    "#bell state and measurement\n",
    "circ.cx(q[0],q[1])\n",
    "circ.measure(q[0:2],c)\n",
    "circ.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "coral-investing",
   "metadata": {},
   "source": [
    "- Simulate the above circuit using *qasm_simulatior* and observe the probabilities of $\\lvert 00\\rangle$ and $\\lvert 11\\rangle$ in the bell state\n",
    "- These probabilities are obtained after inctroducing, detecting and correcting the errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "talented-reminder",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#histogram\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "job = execute(circ,backend)\n",
    "counts = job.result().get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "basic-converter",
   "metadata": {},
   "source": [
    "- The above histogram plot shows the equal probabilities of $\\lvert 00\\rangle$ and $\\lvert 11\\rangle$ similar to the circuit before introducing any error. Hence, the proposed circuit can detect and correct the errors introduced as in the assumptions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "minus-nitrogen",
   "metadata": {},
   "source": [
    "#### We will, now simulate the circuit for different combinations of error gates \n",
    "   (other than the above case)\n",
    "\n",
    "- Case I : **X** gate  to both qubits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "foreign-video",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1583.26x445.48 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Create Quantum and Classical Registers\n",
    "q = QuantumRegister(2,'logical_qubits')\n",
    "a = QuantumRegister(4,'ancilla_qubits')\n",
    "c = ClassicalRegister(2)\n",
    "\n",
    "#Initialize the circuit with above registers\n",
    "circ = QuantumCircuit(q,a,c)\n",
    "circ.h(q[0])\n",
    "circ.barrier()\n",
    "\n",
    "#encoding for q0 and q1 - sign flip & bit flip respectively\n",
    "circ.cx(q[0],a[0])\n",
    "circ.cx(q[0],a[1])\n",
    "circ.cx(q[1],a[2])\n",
    "circ.cx(q[1],a[3])\n",
    "circ.h(q[0])\n",
    "circ.h(a[0])\n",
    "circ.h(a[1])\n",
    "circ.barrier()\n",
    "\n",
    "#introducing error gates to both qubits randomly\n",
    "error_gate(circ,0)\n",
    "error_gate(circ,1)\n",
    "circ.barrier()\n",
    "\n",
    "#decoding for q0 and q1 - sign flip and bit flip respectively\n",
    "circ.h(q[0])\n",
    "circ.h(a[0])\n",
    "circ.h(a[1])\n",
    "circ.cx(q[0],a[0])\n",
    "circ.cx(q[0],a[1])\n",
    "circ.cx(q[1],a[2])\n",
    "circ.cx(q[1],a[3])\n",
    "circ.ccx(a[1],a[0],q[0])\n",
    "circ.ccx(a[3],a[2],q[1])\n",
    "circ.barrier()\n",
    "\n",
    "#bell state and measurement\n",
    "circ.cx(q[0],q[1])\n",
    "circ.measure(q[0:2],c)\n",
    "circ.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "atmospheric-donor",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#histogram\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "job = execute(circ,backend)\n",
    "counts = job.result().get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "advised-drive",
   "metadata": {},
   "source": [
    "- Case II : **I** gate  to $q_0$ and  **Z** gate to $q_1$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "closed-verse",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1583.26x445.48 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Create Quantum and Classical Registers\n",
    "q = QuantumRegister(2,'logical_qubits')\n",
    "a = QuantumRegister(4,'ancilla_qubits')\n",
    "c = ClassicalRegister(2)\n",
    "\n",
    "#Initialize the circuit with above registers\n",
    "circ = QuantumCircuit(q,a,c)\n",
    "circ.h(q[0])\n",
    "circ.barrier()\n",
    "\n",
    "#encoding for q0 and q1 - sign flip & bit flip respectively\n",
    "circ.cx(q[0],a[0])\n",
    "circ.cx(q[0],a[1])\n",
    "circ.cx(q[1],a[2])\n",
    "circ.cx(q[1],a[3])\n",
    "circ.h(q[0])\n",
    "circ.h(a[0])\n",
    "circ.h(a[1])\n",
    "circ.barrier()\n",
    "\n",
    "#introducing error gates to both qubits randomly\n",
    "error_gate(circ,0)\n",
    "error_gate(circ,1)\n",
    "circ.barrier()\n",
    "\n",
    "#decoding for q0 and q1 - sign flip and bit flip respectively\n",
    "circ.h(q[0])\n",
    "circ.h(a[0])\n",
    "circ.h(a[1])\n",
    "circ.cx(q[0],a[0])\n",
    "circ.cx(q[0],a[1])\n",
    "circ.cx(q[1],a[2])\n",
    "circ.cx(q[1],a[3])\n",
    "circ.ccx(a[1],a[0],q[0])\n",
    "circ.ccx(a[3],a[2],q[1])\n",
    "circ.barrier()\n",
    "\n",
    "#bell state and measurement\n",
    "circ.cx(q[0],q[1])\n",
    "circ.measure(q[0:2],c)\n",
    "circ.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "recovered-observer",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#histogram\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "job = execute(circ,backend)\n",
    "counts = job.result().get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "harmful-biography",
   "metadata": {},
   "source": [
    "- Case III : **I** gate  to $q_0$ and  **X** gate to $q_1$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "desirable-hybrid",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1583.26x445.48 with 1 Axes>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Create Quantum and Classical Registers\n",
    "q = QuantumRegister(2,'logical_qubits')\n",
    "a = QuantumRegister(4,'ancilla_qubits')\n",
    "c = ClassicalRegister(2)\n",
    "\n",
    "#Initialize the circuit with above registers\n",
    "circ = QuantumCircuit(q,a,c)\n",
    "circ.h(q[0])\n",
    "circ.barrier()\n",
    "\n",
    "#encoding for q0 and q1 - sign flip & bit flip respectively\n",
    "circ.cx(q[0],a[0])\n",
    "circ.cx(q[0],a[1])\n",
    "circ.cx(q[1],a[2])\n",
    "circ.cx(q[1],a[3])\n",
    "circ.h(q[0])\n",
    "circ.h(a[0])\n",
    "circ.h(a[1])\n",
    "circ.barrier()\n",
    "\n",
    "#introducing error gates to both qubits randomly\n",
    "error_gate(circ,0)\n",
    "error_gate(circ,1)\n",
    "circ.barrier()\n",
    "\n",
    "#decoding for q0 and q1 - sign flip and bit flip respectively\n",
    "circ.h(q[0])\n",
    "circ.h(a[0])\n",
    "circ.h(a[1])\n",
    "circ.cx(q[0],a[0])\n",
    "circ.cx(q[0],a[1])\n",
    "circ.cx(q[1],a[2])\n",
    "circ.cx(q[1],a[3])\n",
    "circ.ccx(a[1],a[0],q[0])\n",
    "circ.ccx(a[3],a[2],q[1])\n",
    "circ.barrier()\n",
    "\n",
    "#bell state and measurement\n",
    "circ.cx(q[0],q[1])\n",
    "circ.measure(q[0:2],c)\n",
    "circ.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "simple-pension",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#histogram\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "job = execute(circ,backend)\n",
    "counts = job.result().get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "individual-building",
   "metadata": {},
   "source": [
    "- Case IV : **Z** gate  to $q_0$ and  **I** gate to $q_1$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "confidential-shore",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1583.26x445.48 with 1 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Create Quantum and Classical Registers\n",
    "q = QuantumRegister(2,'logical_qubits')\n",
    "a = QuantumRegister(4,'ancilla_qubits')\n",
    "c = ClassicalRegister(2)\n",
    "\n",
    "#Initialize the circuit with above registers\n",
    "circ = QuantumCircuit(q,a,c)\n",
    "circ.h(q[0])\n",
    "circ.barrier()\n",
    "\n",
    "#encoding for q0 and q1 - sign flip & bit flip respectively\n",
    "circ.cx(q[0],a[0])\n",
    "circ.cx(q[0],a[1])\n",
    "circ.cx(q[1],a[2])\n",
    "circ.cx(q[1],a[3])\n",
    "circ.h(q[0])\n",
    "circ.h(a[0])\n",
    "circ.h(a[1])\n",
    "circ.barrier()\n",
    "\n",
    "#introducing error gates to both qubits randomly\n",
    "error_gate(circ,0)\n",
    "error_gate(circ,1)\n",
    "circ.barrier()\n",
    "\n",
    "#decoding for q0 and q1 - sign flip and bit flip respectively\n",
    "circ.h(q[0])\n",
    "circ.h(a[0])\n",
    "circ.h(a[1])\n",
    "circ.cx(q[0],a[0])\n",
    "circ.cx(q[0],a[1])\n",
    "circ.cx(q[1],a[2])\n",
    "circ.cx(q[1],a[3])\n",
    "circ.ccx(a[1],a[0],q[0])\n",
    "circ.ccx(a[3],a[2],q[1])\n",
    "circ.barrier()\n",
    "\n",
    "#bell state and measurement\n",
    "circ.cx(q[0],q[1])\n",
    "circ.measure(q[0:2],c)\n",
    "circ.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "acute-community",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#histogram\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "job = execute(circ,backend)\n",
    "counts = job.result().get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "lightweight-bulletin",
   "metadata": {},
   "source": [
    "- Case V : **I** gate  to $q_0$ and  **I** gate to $q_1$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "recorded-agent",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XKIABAAAAAADAr1EAAwAAAAAAgF/7/zvF16eKzqxlAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1583.26x445.48 with 1 Axes>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Create Quantum and Classical Registers\n",
    "q = QuantumRegister(2,'logical_qubits')\n",
    "a = QuantumRegister(4,'ancilla_qubits')\n",
    "c = ClassicalRegister(2)\n",
    "\n",
    "#Initialize the circuit with above registers\n",
    "circ = QuantumCircuit(q,a,c)\n",
    "circ.h(q[0])\n",
    "circ.barrier()\n",
    "\n",
    "#encoding for q0 and q1 - sign flip & bit flip respectively\n",
    "circ.cx(q[0],a[0])\n",
    "circ.cx(q[0],a[1])\n",
    "circ.cx(q[1],a[2])\n",
    "circ.cx(q[1],a[3])\n",
    "circ.h(q[0])\n",
    "circ.h(a[0])\n",
    "circ.h(a[1])\n",
    "circ.barrier()\n",
    "\n",
    "#introducing error gates to both qubits randomly\n",
    "error_gate(circ,0)\n",
    "error_gate(circ,1)\n",
    "circ.barrier()\n",
    "\n",
    "#decoding for q0 and q1 - sign flip and bit flip respectively\n",
    "circ.h(q[0])\n",
    "circ.h(a[0])\n",
    "circ.h(a[1])\n",
    "circ.cx(q[0],a[0])\n",
    "circ.cx(q[0],a[1])\n",
    "circ.cx(q[1],a[2])\n",
    "circ.cx(q[1],a[3])\n",
    "circ.ccx(a[1],a[0],q[0])\n",
    "circ.ccx(a[3],a[2],q[1])\n",
    "circ.barrier()\n",
    "\n",
    "#bell state and measurement\n",
    "circ.cx(q[0],q[1])\n",
    "circ.measure(q[0:2],c)\n",
    "circ.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "special-edwards",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#histogram\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "job = execute(circ,backend)\n",
    "counts = job.result().get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "approximate-marker",
   "metadata": {},
   "source": [
    "- Case VI : **X** gate  to $q_0$ and  **I** gate to $q_1$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "great-funds",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1583.26x445.48 with 1 Axes>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Create Quantum and Classical Registers\n",
    "q = QuantumRegister(2,'logical_qubits')\n",
    "a = QuantumRegister(4,'ancilla_qubits')\n",
    "c = ClassicalRegister(2)\n",
    "\n",
    "#Initialize the circuit with above registers\n",
    "circ = QuantumCircuit(q,a,c)\n",
    "circ.h(q[0])\n",
    "circ.barrier()\n",
    "\n",
    "#encoding for q0 and q1 - sign flip & bit flip respectively\n",
    "circ.cx(q[0],a[0])\n",
    "circ.cx(q[0],a[1])\n",
    "circ.cx(q[1],a[2])\n",
    "circ.cx(q[1],a[3])\n",
    "circ.h(q[0])\n",
    "circ.h(a[0])\n",
    "circ.h(a[1])\n",
    "circ.barrier()\n",
    "\n",
    "#introducing error gates to both qubits randomly\n",
    "error_gate(circ,0)\n",
    "error_gate(circ,1)\n",
    "circ.barrier()\n",
    "\n",
    "#decoding for q0 and q1 - sign flip and bit flip respectively\n",
    "circ.h(q[0])\n",
    "circ.h(a[0])\n",
    "circ.h(a[1])\n",
    "circ.cx(q[0],a[0])\n",
    "circ.cx(q[0],a[1])\n",
    "circ.cx(q[1],a[2])\n",
    "circ.cx(q[1],a[3])\n",
    "circ.ccx(a[1],a[0],q[0])\n",
    "circ.ccx(a[3],a[2],q[1])\n",
    "circ.barrier()\n",
    "\n",
    "#bell state and measurement\n",
    "circ.cx(q[0],q[1])\n",
    "circ.measure(q[0:2],c)\n",
    "circ.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "married-james",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#histogram\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "job = execute(circ,backend)\n",
    "counts = job.result().get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "italic-gates",
   "metadata": {},
   "source": [
    "- Case VII : **Z** gate  to $q_0$ and  **Z** gate to $q_1$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "individual-aruba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1583.26x445.48 with 1 Axes>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Create Quantum and Classical Registers\n",
    "q = QuantumRegister(2,'logical_qubits')\n",
    "a = QuantumRegister(4,'ancilla_qubits')\n",
    "c = ClassicalRegister(2)\n",
    "\n",
    "#Initialize the circuit with above registers\n",
    "circ = QuantumCircuit(q,a,c)\n",
    "circ.h(q[0])\n",
    "circ.barrier()\n",
    "\n",
    "#encoding for q0 and q1 - sign flip & bit flip respectively\n",
    "circ.cx(q[0],a[0])\n",
    "circ.cx(q[0],a[1])\n",
    "circ.cx(q[1],a[2])\n",
    "circ.cx(q[1],a[3])\n",
    "circ.h(q[0])\n",
    "circ.h(a[0])\n",
    "circ.h(a[1])\n",
    "circ.barrier()\n",
    "\n",
    "#introducing error gates to both qubits randomly\n",
    "error_gate(circ,0)\n",
    "error_gate(circ,1)\n",
    "circ.barrier()\n",
    "\n",
    "#decoding for q0 and q1 - sign flip and bit flip respectively\n",
    "circ.h(q[0])\n",
    "circ.h(a[0])\n",
    "circ.h(a[1])\n",
    "circ.cx(q[0],a[0])\n",
    "circ.cx(q[0],a[1])\n",
    "circ.cx(q[1],a[2])\n",
    "circ.cx(q[1],a[3])\n",
    "circ.ccx(a[1],a[0],q[0])\n",
    "circ.ccx(a[3],a[2],q[1])\n",
    "circ.barrier()\n",
    "\n",
    "#bell state and measurement\n",
    "circ.cx(q[0],q[1])\n",
    "circ.measure(q[0:2],c)\n",
    "circ.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "going-initial",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#histogram\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "job = execute(circ,backend)\n",
    "counts = job.result().get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "thousand-consciousness",
   "metadata": {},
   "source": [
    "- Case VIII : **X** gate  to $q_0$ and  **Z** gate to $q_1$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "indian-equation",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1583.26x445.48 with 1 Axes>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Create Quantum and Classical Registers\n",
    "q = QuantumRegister(2,'logical_qubits')\n",
    "a = QuantumRegister(4,'ancilla_qubits')\n",
    "c = ClassicalRegister(2)\n",
    "\n",
    "#Initialize the circuit with above registers\n",
    "circ = QuantumCircuit(q,a,c)\n",
    "circ.h(q[0])\n",
    "circ.barrier()\n",
    "\n",
    "#encoding for q0 and q1 - sign flip & bit flip respectively\n",
    "circ.cx(q[0],a[0])\n",
    "circ.cx(q[0],a[1])\n",
    "circ.cx(q[1],a[2])\n",
    "circ.cx(q[1],a[3])\n",
    "circ.h(q[0])\n",
    "circ.h(a[0])\n",
    "circ.h(a[1])\n",
    "circ.barrier()\n",
    "\n",
    "#introducing error gates to both qubits randomly\n",
    "error_gate(circ,0)\n",
    "error_gate(circ,1)\n",
    "circ.barrier()\n",
    "\n",
    "#decoding for q0 and q1 - sign flip and bit flip respectively\n",
    "circ.h(q[0])\n",
    "circ.h(a[0])\n",
    "circ.h(a[1])\n",
    "circ.cx(q[0],a[0])\n",
    "circ.cx(q[0],a[1])\n",
    "circ.cx(q[1],a[2])\n",
    "circ.cx(q[1],a[3])\n",
    "circ.ccx(a[1],a[0],q[0])\n",
    "circ.ccx(a[3],a[2],q[1])\n",
    "circ.barrier()\n",
    "\n",
    "#bell state and measurement\n",
    "circ.cx(q[0],q[1])\n",
    "circ.measure(q[0:2],c)\n",
    "circ.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "sunset-colon",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#histogram\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "job = execute(circ,backend)\n",
    "counts = job.result().get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "attachments": {
    "circuit-kl8akfr7.png": {
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    },
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     "image/jpeg": 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    "- Hence, for all the combinations of error gates the proposed circuit could detect and correct the errors.\n",
    "\n",
    "## Miscellaneous\n",
    "\n",
    "- The simulation of the circuit using real quantum device **ibmq_16_melbourne** has shown the following result ![ibmq_melbourne_task2.jpg](attachment:ibmq_melbourne_task2.jpg)\n",
    "- Transpiled circuit\n",
    "![circuit-kl8akfr7.png](attachment:circuit-kl8akfr7.png)"
   ]
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   "source": [
    "## References\n",
    "- Quantum Computing UK, https://quantumcomputinguk.org/tutorials/quantum-error-correction-bit-flip-code-in-qiskit\n",
    "- Quantum Computing UK, https://quantumcomputinguk.org/tutorials/quantum-error-correction-phase-flip-code-in-qiskit\n",
    "- Wikipedia contributors. (2021, February 3). Quantum error correction. In Wikipedia, The Free Encyclopedia. https://en.wikipedia.org/w/index.php?title=Quantum_error_correction&oldid=1004616288"
   ]
  }
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