Screening-Task-2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task 2\n",
    "\n",
    "## Contents\n",
    "\n",
    "1. [Problem Statement](#problem-statement)\n",
    "2. [Implementation](#implementation)\n",
    "3. [Noise Model for the arbitrary error gates](#noise-model)\n",
    "4. [Circuit Layout without error correction code](#circuit-error)\n",
    "    - [Noise Channel](#noise-channel1)\n",
    "    - [Observation](#observation1)\n",
    "5. [Circuit Layout with error correction code](#circuit-shor)\n",
    "    - [Shor code](#shor)\n",
    "        - [Reason for using the Shor code](#reason)\n",
    "        - [Introduction](#introduction)\n",
    "    - [Shor Code Implementation](#shor-imp)\n",
    "        - [Encoding](#encoding)\n",
    "        - [Noise Channel](#noise-channel2)\n",
    "        - [Decoding](#decoding)\n",
    "        - [Observation](#observation2)\n",
    "6. [Conclusion](#conclusion)\n",
    "7. [References](#references)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='problem-statement'></a>\n",
    "## Problem Statement -\n",
    "\n",
    "1. Build the following simple circuit to prepare the Bell state: \n",
    "![Bell State](BellState.png \"Bell State\")\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",
    "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",
    "4. Test your solution by making many measurements over the final state and testing that the results are in line with the expectations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='implementation'></a>\n",
    "## Implementation\n",
    "\n",
    "In this project, I used qiskit to implement the circuit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister, Aer, execute\n",
    "from qiskit.providers.aer.noise import pauli_error\n",
    "from qiskit.providers.aer.noise import NoiseModel\n",
    "from qiskit.tools.visualization import plot_histogram\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='noise-model'></a>\n",
    "## Noise Model for the arbitrary error gates\n",
    "\n",
    "**pauli_error** function from qiskit used to generate bit flip operator with **p_error** error. Then Noise is generated using **NoiseModel** from qiskit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "p_error = 0.05\n",
    "bit_flip = pauli_error([('X', p_error), ('I', 1 - p_error)])\n",
    "noise_model = NoiseModel()\n",
    "noise_model.add_all_qubit_quantum_error(bit_flip, [\"id\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='circuit-error'></a>\n",
    "## Circuit Layout without error correction code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21afe14e508>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qr = QuantumRegister(2)\n",
    "cr = ClassicalRegister(2)\n",
    "circuit = QuantumCircuit(qr, cr)\n",
    "\n",
    "# For qr0\n",
    "circuit.h(qr[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21afe14e908>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit.barrier(qr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='noise-channel1'></a>\n",
    "### Noise Channel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21afe15c308>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit.id(qr[0])\n",
    "circuit.id(qr[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21afe15cb48>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit.barrier(qr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21afe14f908>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit.cx(qr[0], qr[1])\n",
    "circuit.measure(qr,cr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 520.833x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit.draw(output = 'mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "result = execute(circuit, backend = simulator, noise_model=noise_model, shots=2000).result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_histogram(result.get_counts(circuit))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Before applying Shor code \n",
      "--------------------------------------\n",
      "{'00': 981, '01': 40, '10': 48, '11': 931}\n"
     ]
    }
   ],
   "source": [
    "noisy_counts = result.get_counts()\n",
    "\n",
    "print(\"\\nBefore applying Shor code \")\n",
    "print(\"--------------------------------------\")\n",
    "print(noisy_counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='observation1'></a>\n",
    "### Observation\n",
    "\n",
    "As we can observe approx. 5% of the 2000 shots are distributed between 01 and 10 states. It's because the [noise channel](#noise-channel1) either bit flips the state of the qubit, with probability 0.05 or leaves it unchanged."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='circuit-shor'></a>\n",
    "## Circuit Layout with error correction code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21afe14f848>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qr = QuantumRegister(18)\n",
    "cr = ClassicalRegister(2)\n",
    "circuit = QuantumCircuit(qr, cr)\n",
    "\n",
    "# For qr0\n",
    "circuit.h(qr[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21aff350148>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit.barrier(qr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='shor'></a>\n",
    "### Shor code\n",
    "<a id='reason'></a>\n",
    "#### Reason for using the Shor code\n",
    "\n",
    "In the third point of the [problem statement](#problem-statement) it is mentioned that *the two qubits has to be encoded in such a way that **all the possible choices** for the error gates described in the second point can be detected and fixed*. Since the Shor code is a combination of bit flip and phase flip codes, so its a perfert choice to detect and fix all the possible choices for the error gates.\n",
    "<a id='introduction'></a>\n",
    "#### Introduction\n",
    "\n",
    "The Shor code is a 9 qubit circuit that requires 8 ancillary qubits to correct 1 qubit. \n",
    "\n",
    "Essentially, the Shor code is a combination of bit flip and phase flip codes. We first encode a qubit using the encoding procedure of the phase flip code: $\\left|0\\right\\rangle → \\left|+ + +\\right\\rangle, \\left|1\\right\\rangle → \\left|− − −\\right\\rangle$. This is followed by encoding each of these 3 qubits according to the bit flip encoding procedure:\n",
    "$$\\left|+\\right\\rangle → \\frac{1}{\\sqrt{2}}\\big[\\left|000\\right\\rangle + \\left|111\\right\\rangle\\big]$$\n",
    "$$\\left|-\\right\\rangle → \\frac{1}{\\sqrt{2}}\\big[\\left|000\\right\\rangle - \\left|111\\right\\rangle\\big]$$\n",
    "\n",
    "Thus the final codewords are:\n",
    "$$\\left|0\\right\\rangle → \\left|0_{L}\\right\\rangle = \\frac{1}{2\\sqrt{2}}\\big[\\left|000\\right\\rangle + \\left|111\\right\\rangle\\big]\\big[\\left|000\\right\\rangle + \\left|111\\right\\rangle\\big]\\big[\\left|000\\right\\rangle + \\left|111\\right\\rangle\\big]$$\n",
    "$$\\left|0\\right\\rangle → \\left|0_{L}\\right\\rangle = \\frac{1}{2\\sqrt{2}}\\big[\\left|000\\right\\rangle - \\left|111\\right\\rangle\\big]\\big[\\left|000\\right\\rangle - \\left|111\\right\\rangle\\big]\\big[\\left|000\\right\\rangle - \\left|111\\right\\rangle\\big]$$\n",
    "\n",
    "To show that the Shor code can correct any quantum error on a single qubit, we first show that it detects and corrects the following errors :-\n",
    "\n",
    "- Bit flip error on a single qubit.\n",
    "- Phase flip error on a single qubit.\n",
    "- Combined bit and phase flip error on a single qubit.\n",
    "\n",
    "![Shor Code](ShorCode.png \"Shor Code\")\n",
    "\n",
    "The 1st, 4th and 7th qubits are for the sign flip code, while the three group of qubits $(1,2,3), (4,5,6),$ and $(7,8,9)$ are designed for the bit flip code. \n",
    "\n",
    "If a bit flip error happens to a qubit, the syndrome analysis will be performed on each set of states $(1,2,3), (4,5,6),$ and $(7,8,9),$ then correct the error.\n",
    "\n",
    "If the three bit flip group $(1,2,3), (4,5,6),$ and $(7,8,9)$ are considered as three inputs, then the Shor code circuit can be reduced as a sign flip code. This means that the Shor code can also repair sign flip error for a single qubit.\n",
    "\n",
    "The Shor code also can correct for any arbitrary errors (both bit flip and sign flip) to a single qubit. If an error is modeled by a unitary transform U, which will act on a qubit $\\left|\\psi\\right\\rangle$ , then $U$ can be described in the form\n",
    "\n",
    "$$U=c_{0}I+c_{1}\\sigma _{x}+c_{2}\\sigma _{y}+c_{3}\\sigma _{z}$$\n",
    "\n",
    "where $c_{0}, c_{1}, c_{2},$ and $c_{3}$ are complex constants, I is the identity, and the Pauli matrices are given by\n",
    "\n",
    "$$\\sigma _{x}={\\biggl (}{\\begin{matrix}0&1\\\\1&0\\end{matrix}}{\\biggr )};\n",
    "\\sigma _{y}={\\biggl (}{\\begin{matrix}0&-i\\\\i&0\\end{matrix}}{\\biggr )};\n",
    "\\sigma _{z}={\\biggl (}{\\begin{matrix}1&0\\\\0&-1\\end{matrix}}{\\biggr )}$$\n",
    "\n",
    "As per the problem statement we have a Bell State, and an arbitrary “error gate” is added right before the CNOT gate and for each of the two qubits. Therefore to detect and fix the error we have taken 18 qubits to encode 2 qubits (qr0 and qr9, which are in Bell State)\n",
    "<a id='shor-imp'></a>\n",
    "### Shor Code Implementation\n",
    "<a id='encoding'></a>\n",
    "#### Encoding\n",
    "\n",
    "The Shor code works by first taking the computational state of the main qubit and transferring it to two other qubits, let's call them target qubit (For qr0 it's qr3 and qr6, and for it's qr12 and qr15 ). These qubits are used for correcting phase errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21aff653408>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For qr0\n",
    "circuit.cx(qr[0],qr[3])\n",
    "circuit.cx(qr[0],qr[6])\n",
    "# For qr9\n",
    "circuit.cx(qr[9],qr[12])\n",
    "circuit.cx(qr[9],qr[15])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After this these qubits are put in to superposition using a Hadamard gate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21aff653ec8>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For qr0\n",
    "circuit.h(qr[0])\n",
    "circuit.h(qr[3])\n",
    "circuit.h(qr[6])\n",
    "# For qr9\n",
    "circuit.h(qr[9])\n",
    "circuit.h(qr[12])\n",
    "circuit.h(qr[15])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next the states of the main qubits (qr0, qr9) as well as the target qubits (qr3, qr6, qr12, qr15) use CNOT gates to transfer their states to ancillary qubits responsible for correcting bit flips."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21aff651888>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For qr0\n",
    "circuit.cx(qr[0],qr[1])\n",
    "circuit.cx(qr[0],qr[2])\n",
    "# For qr9\n",
    "circuit.cx(qr[9],qr[10])\n",
    "circuit.cx(qr[9],qr[11])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21aff658488>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For qr0\n",
    "circuit.cx(qr[3],qr[4])\n",
    "circuit.cx(qr[3],qr[5])\n",
    "# For qr9\n",
    "circuit.cx(qr[12],qr[13])\n",
    "circuit.cx(qr[12],qr[14])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21aff65a2c8>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For qr0\n",
    "circuit.cx(qr[6],qr[7])\n",
    "circuit.cx(qr[6],qr[8])\n",
    "# For qr9\n",
    "circuit.cx(qr[15],qr[16])\n",
    "circuit.cx(qr[15],qr[17])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21aff651f88>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit.barrier(qr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='noise-channel2'></a>\n",
    "#### Noise Channel\n",
    "\n",
    "After this a bit flip or phase flip (it this case we have taken bit flip error) will occur with a certain probalility on the main qubits (qr0, qr9). Noise Model has been created [before](#noise-model)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21aff65aec8>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit.id(qr[0])\n",
    "circuit.id(qr[9])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21aff65d448>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit.barrier(qr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 714.849x1167.88 with 1 Axes>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='decoding'></a>\n",
    "#### Decoding\n",
    "\n",
    "Next the previous step is repeated. Toffoli gates are then applied to the main qubits as well as the target qubits where the control qubits are the auxiliary qubits responsible for phase correction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21affcc7c48>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For qr0\n",
    "circuit.cx(qr[0],qr[1])\n",
    "circuit.cx(qr[0],qr[2])\n",
    "# For qr9\n",
    "circuit.cx(qr[9],qr[10])\n",
    "circuit.cx(qr[9],qr[11])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21affcd2fc8>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For qr0\n",
    "circuit.cx(qr[3],qr[4])\n",
    "circuit.cx(qr[3],qr[5])\n",
    "# For qr9\n",
    "circuit.cx(qr[12],qr[13])\n",
    "circuit.cx(qr[12],qr[14])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21affcd20c8>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For qr0\n",
    "circuit.cx(qr[6],qr[7])\n",
    "circuit.cx(qr[6],qr[8])\n",
    "# For qr9\n",
    "circuit.cx(qr[15],qr[16])\n",
    "circuit.cx(qr[15],qr[17])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21aff9411c8>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For qr0\n",
    "circuit.ccx(qr[2],qr[1],qr[0])\n",
    "circuit.ccx(qr[5],qr[4],qr[3])\n",
    "circuit.ccx(qr[8],qr[7],qr[6])\n",
    "# For qr9\n",
    "circuit.ccx(qr[11],qr[10],qr[9])\n",
    "circuit.ccx(qr[14],qr[13],qr[12])\n",
    "circuit.ccx(qr[17],qr[16],qr[15])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After this Hadamard gates are applied to the main qubits as well as the target qubits to bring them out of superposition."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21affcd2508>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For qr0\n",
    "circuit.h(qr[0])\n",
    "circuit.h(qr[3])\n",
    "circuit.h(qr[6])\n",
    "# For qr9\n",
    "circuit.h(qr[9])\n",
    "circuit.h(qr[12])\n",
    "circuit.h(qr[15])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then CNOT gates are applied to the target qubits where the control qubits are the main qubits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21affcac3c8>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For qr0\n",
    "circuit.cx(qr[0],qr[3])\n",
    "circuit.cx(qr[0],qr[6])\n",
    "# For qr9\n",
    "circuit.cx(qr[9],qr[12])\n",
    "circuit.cx(qr[9],qr[15])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally a toffoli gate is applied to the main qubits which are controlled by the target qubits. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21affcac248>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For qr0\n",
    "circuit.ccx(qr[6],qr[3],qr[0])\n",
    "# For qr9\n",
    "circuit.ccx(qr[15],qr[12],qr[9])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21affcbd248>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit.barrier(qr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x21affca70c8>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit.cx(qr[0], qr[9])\n",
    "circuit.measure([qr[0],qr[9]],cr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1377.05x1167.88 with 1 Axes>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit.draw(output = 'mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "result = execute(circuit, backend = simulator, noise_model=noise_model, shots=2000).result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_histogram(result.get_counts(circuit))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "After applying Shor code\n",
      "--------------------------------------\n",
      "{'00': 1003, '11': 997}\n"
     ]
    }
   ],
   "source": [
    "corrected_counts = result.get_counts()\n",
    "\n",
    "print(\"\\nAfter applying Shor code\")\n",
    "print(\"--------------------------------------\")\n",
    "print(corrected_counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='observation2'></a>\n",
    "### Observation\n",
    "\n",
    "As we can see the errors has been corrected and the  qubits (qr0 and qr9 in this case) are perfectly entangled."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_histogram([noisy_counts, corrected_counts], legend=['noisy', 'corrected'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='conclusion'></a>\n",
    "## Conclusion\n",
    "\n",
    "Quantum error correction code is a vital part of the quantum computing pipeline. The noise generated in this task can be a combination of bit flip and phase flip errors. To detect and correct the noise generated, the shor code was used. It's a combination of bit flip and phase flip code. The shor code is not very efficient with respect to the time complexity and number of gates. But it works fine as per the problem statement. Quantum error correction is only one part of a much-needed effort to make effecient quantum computer, but it is an important part that can help make a big difference.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='references'></a>\n",
    "## References\n",
    "\n",
    "- https://en.wikipedia.org/wiki/Quantum_error_correction\n",
    "- https://www.cs.umd.edu/class/fall2018/cmsc657/projects/group_4.pdf\n",
    "- https://www.cse.iitk.ac.in/users/amitks/quantum/report_pranav_samik.pdf\n",
    "- https://qiskit.org/documentation/tutorials/simulators/3_building_noise_models.html\n",
    "- https://qiskit.org/documentation/stubs/qiskit.providers.aer.noise.pauli_error.html\n",
    "- https://quantumcomputinguk.org/tutorials/quantum-error-correction-shor-code-in-qiskit"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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 },
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}