QEC_project_5-1-3.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import (\n",
    "    QuantumRegister,\n",
    "    ClassicalRegister,\n",
    "    QuantumCircuit,\n",
    "    execute,\n",
    "    Aer\n",
    ")\n",
    "from qiskit.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dualcz(qc,i,j):\n",
    "    qc.h(i)\n",
    "    qc.cx(i,j)\n",
    "    qc.h(i)\n",
    "    \n",
    "    \n",
    "def build_extract_syndromes(qc):\n",
    "    # reset register 5 to be |0>\n",
    "\n",
    "    for i in range(4):\n",
    "        dualcz(qc,i,5)\n",
    "        qc.cz((i+1)%5, 5)\n",
    "        qc.cz((i+2)%5, 5)\n",
    "        dualcz(qc,(i+3)%5,5)\n",
    "        qc.measure([5],[i])\n",
    "        \n",
    "        \n",
    "def build_syndrome(qc, n):\n",
    "    qc.reset(qr[6])\n",
    "    qc.reset(qr[6])\n",
    "    qc.h(6)\n",
    "    dualcz(qc,(n)%5,5)\n",
    "    qc.cx(6,5)\n",
    "    qc.cx((1+n)%5,5)\n",
    "    qc.cx((2+n)%5,5)\n",
    "    qc.cx(6,5)\n",
    "    dualcz(qc,(3+n)%5,5)\n",
    "    qc.h(6)\n",
    "    qc.measure([5],[0])\n",
    "    qc.measure([6],[1])\n",
    "    \n",
    "    \n",
    "def build_circuit(qc):\n",
    "    build_syndrome(qc, 0)\n",
    "    qc.append(extract_syndrome).c_if(cr, 1)\n",
    "    qc.append(extract_syndrome).c_if(cr, 2)\n",
    "    qc.append(extract_syndrome).c_if(cr, 3)\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error syndrome and flag for syndrome 0 :  01\n",
      "Syndrome code:  0010\n",
      "Error detected and fixed.\n"
     ]
    }
   ],
   "source": [
    "# dual Control-Z: H CX H\n",
    "dualcz_reg = QuantumRegister(2)\n",
    "dczc = QuantumCircuit(dualcz_reg, name=\"dczc\")\n",
    "dczc.h(0)\n",
    "dczc.cx(0,1)\n",
    "dczc.h(0)\n",
    "\n",
    "dualcz = dczc.to_instruction()\n",
    "    \n",
    "# extract syndromes for two-bit [[5,1,3]] QEC scheme\n",
    "esr = QuantumRegister(5, 'q')\n",
    "esra = QuantumRegister(1, 'a')\n",
    "esrc = ClassicalRegister(4, 'c')\n",
    "esc = QuantumCircuit(esr, esra, esrc, name=\"esc\")\n",
    "\n",
    "for i in range(4):\n",
    "    esc.append(dualcz, [esr[i], esra[0]])\n",
    "    esc.cz(esr[(i+1)%5], esra[0])\n",
    "    esc.cz(esr[(i+2)%5], esra[0])\n",
    "    esc.append(dualcz, [esr[(i+3)%5], esra[0]])\n",
    "    esc.measure([esra[0]],[esrc[i]])\n",
    "\n",
    "extract_syndromes = esc.to_instruction()\n",
    "        \n",
    "# The full circuit\n",
    "\n",
    "\n",
    "def build_syndrome(qc, qr, anc, cr, n):\n",
    "\n",
    "    qc.h(anc[1])\n",
    "    qc.append(dualcz,[qr[(n)%5],anc[0]])\n",
    "    qc.cx(anc[1],anc[0])\n",
    "    qc.cx(qr[(1+n)%5],anc[0])\n",
    "    qc.cx(qr[(2+n)%5],anc[0])\n",
    "    qc.cx(anc[1],anc[0])\n",
    "    qc.append(dualcz,[qr[(3+n)%5],anc[0]])\n",
    "    qc.h(anc[1])\n",
    "    qc.measure([anc[0]],[cr[0]])\n",
    "    qc.measure([anc[1]],[cr[1]])\n",
    "    \n",
    "    return\n",
    "    \n",
    "    \n",
    "    \n",
    "simulator = Aer.get_backend('qasm_simulator')    \n",
    "\n",
    "qr = QuantumRegister(5, 'q')\n",
    "anc0 = QuantumRegister(2, 'a0')\n",
    "cr0 = ClassicalRegister(2, 'c0')\n",
    "\n",
    "def run_syndrome(qr, anc, cr, n):\n",
    "\n",
    "    syndrome = QuantumCircuit(qr, anc, cr)\n",
    "\n",
    "    build_syndrome(syndrome, qr, anc, cr, n)\n",
    "\n",
    "    job = execute(syndrome, simulator, shots=1)\n",
    "    result = job.result()\n",
    "    counts = result.get_counts(syndrome)\n",
    "\n",
    "    flags = ([*counts][0])\n",
    "    \n",
    "    print(\"Error syndrome and flag for syndrome\", n, \": \", flags)\n",
    "\n",
    "    if flags == '00':\n",
    "        if n == 3:\n",
    "            return 0\n",
    "        else:\n",
    "            return run_syndrome(qr, QuantumRegister(2, 'a' + str(n+1)), ClassicalRegister(2, 'c' + str(n+1)), n+1)\n",
    "    \n",
    "    else:\n",
    "        ancE = QuantumRegister(1, 'aE')\n",
    "        crE = ClassicalRegister(4, 'cE')\n",
    "        \n",
    "        extract = QuantumCircuit(qr, ancE, crE)\n",
    "        extract.append(extract_syndromes, [qr[0], qr[1], qr[2], qr[3], qr[4], ancE[0]], [crE[0], crE[1], crE[2], crE[3]])\n",
    "        \n",
    "        job = execute(extract, simulator, shots=1)\n",
    "        result = job.result()\n",
    "        counts = result.get_counts(extract)\n",
    "        \n",
    "        syndrome_code = ([*counts][0])\n",
    "        \n",
    "        print(\"Syndrome code: \", syndrome_code)\n",
    "        \n",
    "        fixer = QuantumCircuit(qr)\n",
    "        \n",
    "        if flags == '10':\n",
    "            \n",
    "            if syndrome_code == '0001':\n",
    "                fixer.x(qr[0])\n",
    "            if syndrome_code == '1011':\n",
    "                fixer.x(qr[0])\n",
    "                fixer.z(qr[0])\n",
    "            if syndrome_code == '1010':\n",
    "                fixer.z(qr[0])\n",
    "            if syndrome_code == '1000':\n",
    "                fixer.x(qr[1])\n",
    "            if syndrome_code == '1101':\n",
    "                fixer.x(qr[1])\n",
    "                fixer.z(qr[1])\n",
    "            if syndrome_code == '0101':\n",
    "                fixer.z(qr[1])\n",
    "            if syndrome_code == '1100':\n",
    "                fixer.x(qr[2])\n",
    "            if syndrome_code == '1110':\n",
    "                fixer.x(qr[2])\n",
    "                fixer.z(qr[2])\n",
    "            if syndrome_code == '0010':\n",
    "                fixer.z(qr[2])\n",
    "            if syndrome_code == '0110':\n",
    "                fixer.x(qr[3])\n",
    "            if syndrome_code == '1111':\n",
    "                fixer.x(qr[3])\n",
    "                fixer.z(qr[3])\n",
    "            if syndrome_code == '1001':\n",
    "                fixer.z(qr[3])\n",
    "            if syndrome_code == '0011':\n",
    "                fixer.x(qr[4])\n",
    "            if syndrome_code == '0111':\n",
    "                fixer.x(qr[4])\n",
    "                fixer.z(qr[4])\n",
    "            if syndrome_code == '0100':\n",
    "                fixer.z(qr[4])\n",
    "                \n",
    "        else:\n",
    "            \n",
    "            if n == 0:\n",
    "                \n",
    "                if syndrome_code == '0001':\n",
    "                    fixer.x(qr[0])\n",
    "                if syndrome_code == '0100':\n",
    "                    fixer.x(qr[3])\n",
    "                    fixer.z(qr[2])\n",
    "                if syndrome_code == '0110':\n",
    "                    fixer.x(qr[3])\n",
    "                if syndrome_code == '1000':\n",
    "                    fixer.x(qr[2])\n",
    "                    fixer.x(qr[3])\n",
    "                    fixer.z(qr[2])\n",
    "                if syndrome_code == '1001':\n",
    "                    fixer.x(qr[0])\n",
    "                    fixer.x(qr[1])\n",
    "                if syndrome_code == '1010':\n",
    "                    fixer.x(qr[2])\n",
    "                    fixer.x(qr[3])\n",
    "                if syndrome_code == '1100':\n",
    "                    fixer.x(qr[3])\n",
    "                    fixer.x(qr[4])\n",
    "                    fixer.z(qr[3])\n",
    "                \n",
    "            if n == 1:\n",
    "                \n",
    "                if syndrome_code == '0011':\n",
    "                    fixer.x(qr[4])\n",
    "                if syndrome_code == '0100':\n",
    "                    fixer.x(qr[1])\n",
    "                    fixer.x(qr[2])\n",
    "                if syndrome_code == '0101':\n",
    "                    fixer.x(qr[3])\n",
    "                    fixer.x(qr[4])\n",
    "                if syndrome_code == '0110':\n",
    "                    fixer.x(qr[0])\n",
    "                    fixer.x(qr[4])\n",
    "                    fixer.z(qr[4])\n",
    "                if syndrome_code == '1000':\n",
    "                    fixer.x(qr[1])\n",
    "                if syndrome_code == '1010':\n",
    "                    fixer.x(qr[4])\n",
    "                    fixer.z(qr[3])\n",
    "                if syndrome_code == '1100':\n",
    "                    fixer.x(qr[3])\n",
    "                    fixer.x(qr[4])\n",
    "                    fixer.z(qr[3])\n",
    "                \n",
    "            if n == 2:\n",
    "                \n",
    "                if syndrome_code == '0001':\n",
    "                    fixer.x(qr[0])\n",
    "                if syndrome_code == '0010':\n",
    "                    fixer.x(qr[0])\n",
    "                    fixer.x(qr[4])\n",
    "                if syndrome_code == '0011':\n",
    "                    fixer.x(qr[0])\n",
    "                    fixer.x(qr[1])\n",
    "                    fixer.z(qr[0])\n",
    "                if syndrome_code == '0101':\n",
    "                    fixer.x(qr[0])\n",
    "                    fixer.z(qr[4])\n",
    "                if syndrome_code == '0110':\n",
    "                    fixer.x(qr[0])\n",
    "                    fixer.x(qr[4])\n",
    "                    fixer.x(qr[4])\n",
    "                if syndrome_code == '1010':\n",
    "                    fixer.x(qr[2])\n",
    "                    fixer.x(qr[3])\n",
    "                if syndrome_code == '1100':\n",
    "                    fixer.x(qr[2])\n",
    "                \n",
    "            if n == 3:\n",
    "                \n",
    "                if syndrome_code == '0001':\n",
    "                    fixer.x(qr[3])\n",
    "                    fixer.x(qr[4])\n",
    "                    fixer.z(qr[4])\n",
    "                if syndrome_code == '0010':\n",
    "                    fixer.x(qr[1])\n",
    "                    fixer.z(qr[0])\n",
    "                if syndrome_code == '0011':\n",
    "                    fixer.x(qr[0])\n",
    "                    fixer.x(qr[1])\n",
    "                    fixer.z(qr[0])\n",
    "                if syndrome_code == '0101':\n",
    "                    fixer.x(qr[3])\n",
    "                    fixer.x(qr[4])\n",
    "                if syndrome_code == '0110':\n",
    "                    fixer.x(qr[3])\n",
    "                if syndrome_code == '1000':\n",
    "                    fixer.x(qr[1])\n",
    "                if syndrome_code == '1001':\n",
    "                    fixer.x(qr[0])\n",
    "                    fixer.x(qr[1])\n",
    "                \n",
    "                \n",
    "        return 1\n",
    "\n",
    "error_detected = run_syndrome(qr, anc0, cr0, 0)\n",
    "\n",
    "if error_detected:\n",
    "    print(\"Error detected and fixed.\")\n",
    "else:\n",
    "    print(\"No error detected.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Syndrome 1 Extraction Circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">        ┌───────┐                                   \n",
       "q_0: |0>┤0      ├───────────────────────────────────\n",
       "        │       │                                   \n",
       "q_1: |0>┤       ├───────■───────────────────────────\n",
       "        │       │       │                           \n",
       "q_2: |0>┤       ├───────┼────■──────────────────────\n",
       "        │  dczc │       │    │       ┌───────┐      \n",
       "q_3: |0>┤       ├───────┼────┼───────┤0      ├──────\n",
       "        │       │       │    │       │       │      \n",
       "q_4: |0>┤       ├───────┼────┼───────┤  dczc ├──────\n",
       "        │       │┌───┐┌─┴─┐┌─┴─┐┌───┐│       │┌─┐   \n",
       "a_0: |0>┤1      ├┤ X ├┤ X ├┤ X ├┤ X ├┤1      ├┤M├───\n",
       "        └─┬───┬─┘└─┬─┘└───┘└───┘└─┬─┘└─┬───┬─┘└╥┘┌─┐\n",
       "a_1: |0>──┤ H ├────■──────────────■────┤ H ├───╫─┤M├\n",
       "          └───┘                        └───┘   ║ └╥┘\n",
       " c_0: 0 ═══════════════════════════════════════╩══╬═\n",
       "                                                  ║ \n",
       " c_1: 0 ══════════════════════════════════════════╩═\n",
       "                                                    </pre>"
      ],
      "text/plain": [
       "<qiskit.visualization.text.TextDrawing at 0x13a78ceb8>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Error Syndrome Extraction Circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">        ┌───────┐                                                            »\n",
       "q_0: |0>┤0      ├────────────────────────────────────────────────────────────»\n",
       "        │       │                  ┌───────┐                                 »\n",
       "q_1: |0>┤       ├─■────────────────┤0      ├─────────────────────────────────»\n",
       "        │       │ │                │       │                  ┌───────┐      »\n",
       "q_2: |0>┤       ├─┼──■─────────────┤       ├─■────────────────┤0      ├──────»\n",
       "        │  dczc │ │  │ ┌───────┐   │       │ │                │       │      »\n",
       "q_3: |0>┤       ├─┼──┼─┤0      ├───┤  dczc ├─┼──■─────────────┤       ├─■────»\n",
       "        │       │ │  │ │       │   │       │ │  │ ┌───────┐   │  dczc │ │    »\n",
       "q_4: |0>┤       ├─┼──┼─┤  dczc ├───┤       ├─┼──┼─┤0      ├───┤       ├─┼──■─»\n",
       "        │       │ │  │ │       │┌─┐│       │ │  │ │  dczc │┌─┐│       │ │  │ »\n",
       "a_0: |0>┤1      ├─■──■─┤1      ├┤M├┤1      ├─■──■─┤1      ├┤M├┤1      ├─■──■─»\n",
       "        └───────┘      └───────┘└╥┘└───────┘      └───────┘└╥┘└───────┘      »\n",
       " c_0: 0 ═════════════════════════╩══════════════════════════╬════════════════»\n",
       "                                                            ║                »\n",
       " c_1: 0 ════════════════════════════════════════════════════╩════════════════»\n",
       "                                                                             »\n",
       " c_2: 0 ═════════════════════════════════════════════════════════════════════»\n",
       "                                                                             »\n",
       " c_3: 0 ═════════════════════════════════════════════════════════════════════»\n",
       "                                                                             »\n",
       "«     ┌───────┐                              \n",
       "«q_0: ┤0      ├────────────────■─────────────\n",
       "«     │       │                │ ┌───────┐   \n",
       "«q_1: ┤       ├────────────────┼─┤0      ├───\n",
       "«     │       │                │ │       │   \n",
       "«q_2: ┤       ├────────────────┼─┤       ├───\n",
       "«     │  dczc │   ┌───────┐    │ │       │   \n",
       "«q_3: ┤       ├───┤0      ├────┼─┤  dczc ├───\n",
       "«     │       │   │       │    │ │       │   \n",
       "«q_4: ┤       ├───┤  dczc ├─■──┼─┤       ├───\n",
       "«     │       │┌─┐│       │ │  │ │       │┌─┐\n",
       "«a_0: ┤1      ├┤M├┤1      ├─■──■─┤1      ├┤M├\n",
       "«     └───────┘└╥┘└───────┘      └───────┘└╥┘\n",
       "«c_0: ══════════╬══════════════════════════╬═\n",
       "«               ║                          ║ \n",
       "«c_1: ══════════╬══════════════════════════╬═\n",
       "«               ║                          ║ \n",
       "«c_2: ══════════╩══════════════════════════╬═\n",
       "«                                          ║ \n",
       "«c_3: ═════════════════════════════════════╩═\n",
       "«                                            </pre>"
      ],
      "text/plain": [
       "<qiskit.visualization.text.TextDrawing at 0x1119752b0>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qr = QuantumRegister(5, 'q')\n",
    "anc = QuantumRegister(1, 'a')\n",
    "cr = ClassicalRegister(4, 'c')\n",
    "        \n",
    "extract = QuantumCircuit(qr, anc, cr)\n",
    "extract.append(extract_syndromes, [qr[0], qr[1], qr[2], qr[3], qr[4], anc[0]], [cr[0], cr[1], cr[2], cr[3]])\n",
    "        \n",
    "extract.decompose().draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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