quantum_maxcut_algorithm_optimized.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "ae10007b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "System size: 15\n",
      "Number of iterations: 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'''\n",
    "(C) Renata Wong (CGU-CoIC, NCTS-NTU) 2023\n",
    "\n",
    "This is the accompanying code for the paper \n",
    "\"Bioinspired Quantum Oracle Circuits for Biomolecular Solutions of the Maximum Cut Problem\"\n",
    "by Weng-Long Chang, Renata Wong, Yu-Hao Chen, Wen-Yu Chung, Ju-Chin Chen, and Athanasios V. Vasilakos\n",
    "\n",
    "'''\n",
    "\n",
    "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister\n",
    "import numpy as np\n",
    "\n",
    "'''\n",
    "Create the quantum circuit for the 3-vertex example\n",
    "num_vertices = n = number of vertices\n",
    "num_enges = m = number of edges\n",
    "\n",
    "'''\n",
    "\n",
    "\n",
    "'''\n",
    "PLEASE FILL IN THE EDGE LIST FOR YOUR GRAPH IN THE LINE BELOW\n",
    "'''\n",
    "permanent_edge_list = [[0,1], [1,2]]\n",
    "\n",
    "# t is the maximum possible number of edges in a cut and is assumed to be known upfront\n",
    "t = 2\n",
    "\n",
    "\n",
    "\n",
    "num_vertices = len({x for l in permanent_edge_list for x in l})\n",
    "num_edges = len(permanent_edge_list)\n",
    "\n",
    "range_z = (num_edges * (num_edges + 3)) / 2  \n",
    "range_r = 2 * num_edges\n",
    "range_s = num_edges \n",
    "\n",
    "aux = QuantumRegister(1, 'aux')\n",
    "z_reg = QuantumRegister(range_z, 'z_reg')\n",
    "s_reg = QuantumRegister(range_s, 's_reg')\n",
    "r_reg = QuantumRegister(range_r, 'r_reg')\n",
    "x_reg = QuantumRegister(num_vertices, 'x_reg')\n",
    "readout = ClassicalRegister(num_vertices, 'out')\n",
    "qc = QuantumCircuit(x_reg, r_reg, s_reg, z_reg, aux, readout)\n",
    "\n",
    "\n",
    "system_size = qc.num_qubits\n",
    "print('System size:', system_size)\n",
    "\n",
    "\n",
    "'''\n",
    "Create r_matrix to store indices of the register r_reg \n",
    "'''\n",
    "r_matrix = [ [0 for j in range(2)] for i in range(num_edges)]\n",
    "rij = 0\n",
    "for i in range(num_edges):\n",
    "    for j in range(2):\n",
    "        r_matrix[i][j] = rij\n",
    "        rij += 1\n",
    "#print('r matrix', r_matrix)\n",
    "\n",
    "'''\n",
    "Create z_matrix to store indices of z_reg\n",
    "Note that i starts with index 1, not 0. \n",
    "'''\n",
    "\n",
    "z_matrix = [ [ 0 for j in range(num_edges + 1) ] for i in range(num_edges + 1) ]\n",
    "zij = 0\n",
    "for i in range(1, num_edges + 1):\n",
    "    for j in range(i + 1):\n",
    "        z_matrix[i][j] = zij\n",
    "        zij += 1\n",
    "#print('z matrix', z_matrix)\n",
    "        \n",
    "\n",
    "\n",
    "\n",
    "'''\n",
    "Define the EIIAC subcircuit\n",
    "'''\n",
    "\n",
    "sq = QuantumRegister(5,'sq')     \n",
    "sc = QuantumCircuit(sq, name='EIIAC')\n",
    "\n",
    "sc.x(sq[1])\n",
    "sc.ccx(sq[0], sq[1], sq[2])\n",
    "sc.x(sq[1])\n",
    "sc.x(sq[0])\n",
    "sc.ccx(sq[0], sq[1], sq[3])\n",
    "sc.x(sq[0])\n",
    "sc.x(sq[2])\n",
    "sc.x(sq[3])\n",
    "sc.ccx(sq[2], sq[3], sq[4])\n",
    "sc.x(sq[2])\n",
    "sc.x(sq[3])\n",
    "\n",
    "    \n",
    "eiiac = sc.to_instruction()\n",
    "\n",
    "\n",
    "    \n",
    "    \n",
    "'''\n",
    "Initialize the system and set it in a uniform superpostion\n",
    "'''\n",
    "\n",
    "for qubit in s_reg:\n",
    "    qc.x(qubit)\n",
    "\n",
    "for qubit in x_reg:\n",
    "    qc.h(qubit)\n",
    "    \n",
    "qc.x(aux)\n",
    "qc.h(aux)\n",
    "    \n",
    "#qc.barrier()\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "'''\n",
    "NOTE: There will always be an even number of solutions, since under maximum cut 101 is the same as 010.\n",
    "For Fig. 1 in the paper, we set the number of solutions to 2.\n",
    "\n",
    "YOU MAY NEED TO ADJUST THE NUMBER OF SOLUTIONS.\n",
    "'''\n",
    "\n",
    "num_solutions = 2 \n",
    "num_runs = int(np.ceil(np.pi * np.sqrt((2**num_vertices) / num_solutions)) / 4)\n",
    "print('Number of iterations:', num_runs)\n",
    "\n",
    "\n",
    "\n",
    "'''\n",
    "Amplitude amplification\n",
    "'''    \n",
    "\n",
    "for run in range(num_runs):\n",
    "\n",
    "    # Apply EIIAC \n",
    "    # It is assumed that the two vertices in the x_reg share an edge\n",
    "    \n",
    "    \n",
    "    edge_list = permanent_edge_list.copy()\n",
    "    \n",
    "    for index, edge in enumerate(edge_list):\n",
    "        [index_v1, index_v2] = edge\n",
    "        cfe_qubits = []\n",
    "        cfe_qubits += [x_reg[index_v1]]\n",
    "        cfe_qubits += [x_reg[index_v2]]\n",
    "        cfe_qubits += [r_reg[k] for k in range(2*index, 2*index+2)]\n",
    "        cfe_qubits += [s_reg[index]]\n",
    "        qc.append(eiiac, cfe_qubits)\n",
    "        #qc.barrier()\n",
    "        \n",
    "\n",
    "    \n",
    "    # Apply INO\n",
    "    if t > 0:\n",
    "        qc.cx(s_reg[0], z_reg[1])\n",
    "    \n",
    "    # Apply PNO\n",
    "    if t < num_edges:\n",
    "        qc.x(s_reg[0])\n",
    "        qc.cx(s_reg[0], z_reg[0])\n",
    "        qc.x(s_reg[0])\n",
    "\n",
    "        \n",
    "        \n",
    "    # Apply CIO and CPO\n",
    "    for i in range(1, num_edges):\n",
    "        for j in reversed(range(i+1)):\n",
    "            if j+1 <= t and num_edges-i+j == t:\n",
    "                qc.ccx(s_reg[i], z_reg[z_matrix[i][j]], z_reg[z_matrix[i+1][j+1]])\n",
    "            if j <= t and num_edges-i+j-1 == t:\n",
    "                qc.x(s_reg[i])\n",
    "                qc.ccx(s_reg[i], z_reg[z_matrix[i][j]], z_reg[z_matrix[i+1][j+1]])\n",
    "                qc.x(s_reg[i])\n",
    "     \n",
    "    \n",
    "    \n",
    "    '''\n",
    "    Which qubit of register z_reg is used here depends on how many edges are there in the cut.\n",
    "    For the example in Fig. 1 we expect 2 edges, and therefore we choose qubit 2 (counting from 0, 1, 2, etc.).\n",
    "    This qubit should be in the state 1.\n",
    "    \n",
    "    YOU MAY NEED TO ADJUST THE CONTROL QUBIT IN THE CX GATE.\n",
    "    '''\n",
    "    \n",
    "    #qc.barrier()\n",
    "    \n",
    "    qc.cx(z_reg[z_matrix[num_edges][t]], aux)\n",
    "    \n",
    "    #qc.barrier()\n",
    "    \n",
    "    \n",
    "\n",
    "    '''\n",
    "    Uncomputing CIO, CPO, PNO, INO, and EIIAC, \n",
    "    '''\n",
    "    \n",
    "    # uncompute CIO and CPO\n",
    "    for i in range(1, num_edges):\n",
    "        for j in reversed(range(i+1)):\n",
    "            if j+1 <= t and num_edges-i+j == t:\n",
    "                qc.ccx(s_reg[i], z_reg[z_matrix[i][j]], z_reg[z_matrix[i+1][j+1]])\n",
    "            if j <= t and num_edges-i+j-1 == t:\n",
    "                qc.x(s_reg[i])\n",
    "                qc.ccx(s_reg[i], z_reg[z_matrix[i][j]], z_reg[z_matrix[i+1][j+1]])\n",
    "                qc.x(s_reg[i])\n",
    "                \n",
    "\n",
    "    # Uncompute PNO\n",
    "    if t < num_edges:\n",
    "        qc.x(s_reg[0])\n",
    "        qc.cx(s_reg[0], z_reg[0])\n",
    "        qc.x(s_reg[0])\n",
    "    \n",
    "    # Uncompute INO\n",
    "    if t > 0:\n",
    "        qc.cx(s_reg[0], z_reg[1])\n",
    "\n",
    "    # Uncompute EIIAC\n",
    "    index = len(edge_list) - 1\n",
    "    for edge in reversed(edge_list):\n",
    "        [index_v1, index_v2] = edge\n",
    "        cfe_qubits = []\n",
    "        cfe_qubits += [x_reg[index_v1]]\n",
    "        cfe_qubits += [x_reg[index_v2]]\n",
    "        cfe_qubits += [r_reg[k] for k in range(2*index, 2*index+2)]\n",
    "        cfe_qubits += [s_reg[index]]\n",
    "        index -= 1\n",
    "        qc.append(eiiac.inverse(), cfe_qubits)\n",
    "    \n",
    "    \n",
    "    \n",
    "    \n",
    "    '''\n",
    "    Diffusion operations\n",
    "    '''\n",
    "\n",
    "    qc.barrier()\n",
    "    \n",
    "    for qubit in x_reg:\n",
    "        qc.h(qubit)\n",
    "        qc.x(qubit)\n",
    "        \n",
    "    qc.h(x_reg[len(x_reg) - 1])\n",
    "    multiplexer = [x_reg[i] for i in range(len(x_reg) - 1)]\n",
    "    qc.mcx(multiplexer, x_reg[len(x_reg) - 1])\n",
    "    qc.h(x_reg[len(x_reg) - 1])\n",
    "    \n",
    "    for qubit in x_reg:\n",
    "        qc.x(qubit)\n",
    "        qc.h(qubit)\n",
    "\n",
    "    #qc.barrier()\n",
    "          \n",
    "\n",
    "        \n",
    "        \n",
    "        \n",
    "            \n",
    "'''\n",
    "Measurement \n",
    "'''\n",
    "\n",
    "cuts = []\n",
    "\n",
    "for i in range(len(x_reg)):\n",
    "    cuts.append(x_reg[i])\n",
    "\n",
    "# Reverse the order in which the output is shown so that it can be read from left to right.\n",
    "cuts.reverse()\n",
    "\n",
    "\n",
    "qc.measure(cuts, readout)\n",
    "\n",
    "from qiskit import Aer, execute\n",
    "from qiskit.visualization import plot_histogram\n",
    "from qiskit.providers.aer import QasmSimulator, StatevectorSimulator\n",
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "result = execute(qc, backend = simulator, shots = 1024).result()\n",
    "counts = result.get_counts()\n",
    "\n",
    "\n",
    "# Uncomment to save the output\n",
    "#plot_histogram(counts).savefig('example.svg')\n",
    "plot_histogram(counts)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "2eafe5aa",
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 1635.88x987.28 with 1 Axes>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3b283935",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}