large_qubit-systems_experimentation_code.ipynb

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   "source": [
    "# Quantum Error Correction Project\n",
    "## Philippe Noël, Alaisha Sharma, Nicolas Weninger\n",
    "### File #4: Large qubit-systems error correction experimentation"
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "import os\n",
    "import sys\n",
    "\n",
    "from qutip import *\n",
    "\n",
    "from qiskit import QuantumProgram\n",
    "import Qconfig\n",
    "from qiskit.tools.visualization import plot_histogram, plot_state\n",
    "from qiskit.backends import local_backends, remote_backends\n",
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister\n",
    "\n",
    "assert sys.version_info >= (3,5), \"Only Python 3.5 or greater supported.\"\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import display, HTML, Image"
   ]
  },
  {
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   "metadata": {},
   "source": [
    "The 9-qubit error correction scheme is promising because it can detect and correct both bit flips and phase flips (one of each) that could even occur on the same qubit. The circuit below error corrects for three logical qubits by mapping each one to its own 9-qubit error correction scheme. If we could successfully run this circuit then we could be able to perform both bit flip and phase flip error correction for a 3-qubit Deutsch-Josza circuit. Unfortunately, Python itself starts to slow down on computations involving more than 20 qubits (20 qubits means $2^{20}$ possible states and for this scheme we need to use 27 qubits). Although we would not be able to run this circuit it is interesting to think about possible optimizations that might allow error correction of a larger number of logical qubits."
   ]
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    "# 9 qubits times three\n",
    "n = 27\n",
    "\n",
    "# Circuit to large to run on local quantum simulator\n",
    "qpL = QuantumProgram()\n",
    "\n",
    "# Quantum register\n",
    "q = qpL.create_quantum_register(\"q\", n) \n",
    "# Classical register\n",
    "c = qpL.create_classical_register(\"c\", n) \n",
    "\n",
    "# LargeExperiment circuit\n",
    "large_exp27 = qpL.create_circuit(\"LargeExperiment27\", [q], [c])\n",
    "\n",
    "# Arbitrary states \n",
    "large_exp27.h(q[0])\n",
    "large_exp27.h(q[9])\n",
    "large_exp27.h(q[18])\n",
    "\n",
    "# Encoding state 1\n",
    "large_exp27.cx(q[0],q[3])\n",
    "large_exp27.cx(q[0],q[6])\n",
    "\n",
    "large_exp27.h(q[0])\n",
    "large_exp27.h(q[3])\n",
    "large_exp27.h(q[6])\n",
    "\n",
    "large_exp27.cx(q[0],q[1])\n",
    "large_exp27.cx(q[0],q[2])\n",
    "\n",
    "large_exp27.cx(q[3],q[4])\n",
    "large_exp27.cx(q[3],q[5])\n",
    "\n",
    "large_exp27.cx(q[6],q[7])\n",
    "large_exp27.cx(q[6],q[8])\n",
    "\n",
    "# Encoding state 2\n",
    "large_exp27.cx(q[9],q[12])\n",
    "large_exp27.cx(q[9],q[15])\n",
    "\n",
    "large_exp27.h(q[9])\n",
    "large_exp27.h(q[12])\n",
    "large_exp27.h(q[15])\n",
    "\n",
    "large_exp27.cx(q[9],q[10])\n",
    "large_exp27.cx(q[9],q[11])\n",
    "\n",
    "large_exp27.cx(q[12],q[13])\n",
    "large_exp27.cx(q[12],q[14])\n",
    "\n",
    "large_exp27.cx(q[15],q[16])\n",
    "large_exp27.cx(q[15],q[17])\n",
    "\n",
    "# Encoding state 3\n",
    "large_exp27.cx(q[18],q[21])\n",
    "large_exp27.cx(q[18],q[24])\n",
    "\n",
    "large_exp27.h(q[18])\n",
    "large_exp27.h(q[21])\n",
    "large_exp27.h(q[24])\n",
    "\n",
    "large_exp27.cx(q[18],q[19])\n",
    "large_exp27.cx(q[18],q[20])\n",
    "\n",
    "large_exp27.cx(q[21],q[22])\n",
    "large_exp27.cx(q[21],q[23])\n",
    "\n",
    "large_exp27.cx(q[24],q[25])\n",
    "large_exp27.cx(q[24],q[26])\n",
    "\n",
    "# Bit flip detection and correction 1\n",
    "large_exp27.cx(q[0],q[1])\n",
    "large_exp27.cx(q[0],q[2])\n",
    "large_exp27.ccx(q[1],q[2],q[0])\n",
    "\n",
    "large_exp27.cx(q[3],q[4])\n",
    "large_exp27.cx(q[3],q[5])\n",
    "large_exp27.ccx(q[4],q[5],q[3])\n",
    "\n",
    "large_exp27.cx(q[6],q[7])\n",
    "large_exp27.cx(q[6],q[8])\n",
    "large_exp27.ccx(q[7],q[8],q[6])\n",
    "\n",
    "# Bit flip detection and correction 2\n",
    "large_exp27.cx(q[9],q[10])\n",
    "large_exp27.cx(q[9],q[11])\n",
    "large_exp27.ccx(q[10],q[11],q[9])\n",
    "\n",
    "large_exp27.cx(q[12],q[13])\n",
    "large_exp27.cx(q[12],q[14])\n",
    "large_exp27.ccx(q[13],q[14],q[12])\n",
    "\n",
    "large_exp27.cx(q[15],q[16])\n",
    "large_exp27.cx(q[15],q[17])\n",
    "large_exp27.ccx(q[16],q[17],q[15])\n",
    "\n",
    "# Bit flip detection and correction 3\n",
    "large_exp27.cx(q[18],q[19])\n",
    "large_exp27.cx(q[18],q[20])\n",
    "large_exp27.ccx(q[19],q[20],q[18])\n",
    "\n",
    "large_exp27.cx(q[21],q[22])\n",
    "large_exp27.cx(q[21],q[23])\n",
    "large_exp27.ccx(q[22],q[23],q[21])\n",
    "\n",
    "large_exp27.cx(q[24],q[25])\n",
    "large_exp27.cx(q[24],q[26])\n",
    "large_exp27.ccx(q[25],q[26],q[24])\n",
    "\n",
    "# Phase flip detection 1\n",
    "large_exp27.h(q[0])\n",
    "large_exp27.h(q[3])\n",
    "large_exp27.h(q[6])\n",
    "\n",
    "large_exp27.cx(q[0],q[3])\n",
    "large_exp27.cx(q[0],q[6])\n",
    "\n",
    "# Phase flip correction 1\n",
    "large_exp27.ccx(q[3],q[6],q[0])\n",
    "\n",
    "# Phase flip detection 2\n",
    "large_exp27.h(q[9])\n",
    "large_exp27.h(q[12])\n",
    "large_exp27.h(q[15])\n",
    "\n",
    "large_exp27.cx(q[9],q[12])\n",
    "large_exp27.cx(q[9],q[15])\n",
    "\n",
    "# Phase flip correction 2\n",
    "large_exp27.ccx(q[12],q[15],q[9])\n",
    "\n",
    "# Phase flip detection 3\n",
    "large_exp27.h(q[18])\n",
    "large_exp27.h(q[21])\n",
    "large_exp27.h(q[24])\n",
    "\n",
    "large_exp27.cx(q[18],q[21])\n",
    "large_exp27.cx(q[18],q[24])\n",
    "\n",
    "# Phase flip correction 3\n",
    "large_exp27.ccx(q[21],q[24],q[18])\n",
    "\n",
    "# Add measurement \n",
    "large_exp27.measure(q[0], c[0])\n",
    "large_exp27.measure(q[9], c[9])\n",
    "large_exp27.measure(q[18], c[18])\n",
    "\n",
    "# Execute circuit\n",
    "results = qpL.execute(\"LargeExperiment27\", shots = 50)\n",
    "\n",
    "# Plot measurement results\n",
    "print(\"Measurement after gate without errors:\")\n",
    "plot_histogram(results.get_counts(\"LargeExperiment27\"))"
   ]
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