LR-QAOA.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e5f7eb43",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Libraries needed \n",
    "pip install docplex # CPLEX solver\n",
    "pip install qiskit\n",
    "pip install qiskit_aer \n",
    "pip install openqaoa-core\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d848cde4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import defaultdict\n",
    "from copy import copy\n",
    "from docplex.mp.model import Model\n",
    "import networkx as nx\n",
    "import itertools\n",
    "\n",
    "\n",
    "from qiskit import QuantumCircuit\n",
    "from qiskit_aer import Aer\n",
    "from qiskit.circuit import ParameterVector\n",
    "\n",
    "from openqaoa.problems import FromDocplex2IsingModel\n",
    "\n",
    "backend = Aer.get_backend(\"qasm_simulator\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b8c19e16",
   "metadata": {},
   "outputs": [],
   "source": [
    "def MaxCut(G):\n",
    "    \"\"\"\n",
    "    Input:\n",
    "        G: Networkx graph\n",
    "    Output:\n",
    "        mdl: Docplex model\n",
    "    \"\"\"\n",
    "    # MIS model as a QUBO problem\n",
    "    mdl = Model('MaxCut')\n",
    "    num_vertices = G.number_of_nodes()\n",
    "    x = {i: mdl.binary_var(name=f\"x_{i}\") for i in range(num_vertices)}\n",
    "    cost = 0\n",
    "    for i, j in G.edges:\n",
    "        if nx.is_weighted(G):\n",
    "            cost += - G[i][j][\"weight\"] * (x[i] * (1 - x[j]) + x[j] * (1 - x[i]))\n",
    "        else:\n",
    "            cost += - (x[i] * (1 - x[j]) + x[j] * (1 - x[i]))\n",
    "    mdl.minimize(cost)\n",
    "    return mdl\n",
    "\n",
    "def cost_maxcut(bitstring, weights):\n",
    "    cost = 0\n",
    "    for i, j in weights.keys():\n",
    "        if bitstring[i] + bitstring[j] in [\"10\",\"01\"]:\n",
    "            cost += weights[i,j]\n",
    "    return cost\n",
    "\n",
    "def objective_MaxCut(samples_dict, G, optimal_solution):\n",
    "    if nx.is_weighted(G):\n",
    "        weights = {(i,j):(G[i][j][\"weight\"] if len(G[i][j]) != 0 else 1) for i, j in G.edges}\n",
    "    else:\n",
    "        weights = {(i,j):(G[i][j] if len(G[i][j]) != 0 else 1) for i, j in G.edges}\n",
    "    optimal_cost = cost_maxcut(optimal_solution, weights)\n",
    "    results = []\n",
    "    probability = 0\n",
    "    for bitstring, counts in samples_dict.items():\n",
    "        cost = cost_maxcut(bitstring, weights)\n",
    "        r  = cost / optimal_cost\n",
    "        if np.abs(cost - optimal_cost) < 1e-8: # If the approximation ratio is 1 means the bitstring is the optimal solution\n",
    "            probability += counts\n",
    "        if optimal_cost - cost < 0:\n",
    "            print(f\"There is a better cost than that of CPLEX by {optimal_cost - cost}!\")\n",
    "        results.append([cost, r, counts])\n",
    "    results = np.array(results)\n",
    "    shots = np.sum(results[:,2])\n",
    "    mean_r = np.sum(results[:,0] * results[:,2])/(shots * optimal_cost)\n",
    "    probability /= shots\n",
    "    return {\"results\":np.array(results), \"optimal_cost\":optimal_cost, \"r\":mean_r, \"probability\":probability}\n",
    "\n",
    "def qaoa_circ(hamiltonian, gammas, betas, n_qubits, shots):\n",
    "    p = len(gammas)\n",
    "    qc = QuantumCircuit(n_qubits)\n",
    "    qc.h(range(n_qubits))\n",
    "    for ii in range(p):\n",
    "        for qbits, value in hamiltonian.items():\n",
    "            if len(qbits) == 1:\n",
    "                qc.rz(2*gammas[ii]*float(value), qbits[0])\n",
    "        for qbits, value in hamiltonian.items():\n",
    "            if len(qbits) == 2:\n",
    "                qc.rzz(2*gammas[ii]*float(value), *qbits)\n",
    "        qc.rx(-2*betas[ii], range(n_qubits))\n",
    "    qc = qc.reverse_bits()\n",
    "    qc.measure_all()\n",
    "    probs = backend.run(qc, shots=shots).result().get_counts()\n",
    "    return probs\n",
    "\n",
    "def mitigated(samples, G, hamming=1):\n",
    "    weights = {(i,j):(G[i][j][\"weight\"] if len(G[i][j]) != 0 else 1) for i, j in G.edges}\n",
    "    change = {\"0\":\"1\", \"1\":\"0\"}\n",
    "    new_samples = defaultdict(int)\n",
    "    nq = G.number_of_nodes()\n",
    "    combinations = list(itertools.combinations(range(nq), hamming))\n",
    "    for string, count in samples.items():\n",
    "        best_cost = cost_maxcut(string, weights)\n",
    "        best_string = string\n",
    "        for comb in combinations:\n",
    "            new_string = \"\".join((change[i] if n in comb else i) for n, i in enumerate(string))\n",
    "            new_cost = cost_maxcut(new_string, weights)\n",
    "            if new_cost >= best_cost:\n",
    "                best_string = new_string\n",
    "                best_cost = new_cost\n",
    "        new_samples[best_string] += count\n",
    "    return new_samples\n",
    "\n",
    "def random_sampler(num_samples, n_qubits):\n",
    "    random_samples = defaultdict(int)\n",
    "    for i in range(num_samples):\n",
    "        random_samples[\"\".join(str(i) for i in np.random.choice([0,1], n_qubits))] += 1\n",
    "    return random_samples"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5930df7",
   "metadata": {},
   "source": [
    "# W-MaxCut problems"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df06d2b8",
   "metadata": {},
   "source": [
    "# $p = N_q$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "183b23da",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of nodes 5\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of nodes 6\n",
      "number of nodes 7\n",
      "number of nodes 8\n",
      "number of nodes 9\n",
      "number of nodes 10\n",
      "number of nodes 11\n",
      "number of nodes 12\n",
      "number of nodes 13\n",
      "number of nodes 14\n",
      "number of nodes 15\n",
      "number of nodes 16\n",
      "number of nodes 17\n",
      "number of nodes 18\n",
      "number of nodes 19\n",
      "number of nodes 20\n",
      "number of nodes 21\n",
      "number of nodes 22\n",
      "number of nodes 23\n",
      "number of nodes 24\n",
      "number of nodes 25\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "nodes_list_qubo = range(5, 26)\n",
    "random_cases = 10\n",
    "prob = 1\n",
    "problems = {}\n",
    "# Generate graphs with the above condition for different number of nodes\n",
    "for nodes in nodes_list_qubo: \n",
    "    print(f\"number of nodes {nodes}\")\n",
    "    problems[nodes] = {}\n",
    "    for kk in range(random_cases):\n",
    "        problems[nodes][kk] = defaultdict(dict)\n",
    "        G = nx.Graph()\n",
    "        G.add_nodes_from(range(nodes))\n",
    "        for i in range(nodes - 1):\n",
    "            for j in range(i+1, nodes):\n",
    "                if np.random.rand() < prob:\n",
    "                    w = round(np.random.rand(), 3)\n",
    "                    G.add_weighted_edges_from([[i,j,w]])\n",
    "        problems[nodes][kk][\"G\"] = G\n",
    "        mdl = MaxCut(G)\n",
    "        problems[nodes][kk][\"qubo\"] = MaxCut(G)\n",
    "        mdl.solve() # solve the problem using CLPEX\n",
    "        problems[nodes][kk][\"n_iterations_cplex\"] = mdl.get_solve_details().nb_iterations\n",
    "        problems[nodes][kk][\"time_cplex\"] = mdl.get_solve_details().deterministic_time\n",
    "        problems[nodes][kk][\"real_time_cplex\"] = mdl.get_solve_details().time\n",
    "        problems[nodes][kk][\"sol\"] = \"\".join(str(round(mdl.solution.get_value(var))) for var in mdl.iter_binary_vars())\n",
    "        problems[nodes][kk][\"ising_hamiltonian\"] = FromDocplex2IsingModel(mdl).ising_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c7623b94",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-------- nq: 5 ------------\n",
      "-------- nq: 6 ------------\n",
      "-------- nq: 7 ------------\n",
      "-------- nq: 8 ------------\n",
      "-------- nq: 9 ------------\n",
      "-------- nq: 10 ------------\n",
      "-------- nq: 11 ------------\n",
      "-------- nq: 12 ------------\n",
      "-------- nq: 13 ------------\n",
      "-------- nq: 14 ------------\n",
      "-------- nq: 15 ------------\n",
      "-------- nq: 16 ------------\n",
      "-------- nq: 17 ------------\n",
      "-------- nq: 18 ------------\n",
      "-------- nq: 19 ------------\n",
      "-------- nq: 20 ------------\n",
      "-------- nq: 21 ------------\n",
      "-------- nq: 22 ------------\n",
      "-------- nq: 23 ------------\n",
      "-------- nq: 24 ------------\n",
      "-------- nq: 25 ------------\n"
     ]
    }
   ],
   "source": [
    "shots = 10000\n",
    "delta_beta = 0.5\n",
    "delta_gamma = 0.5\n",
    "\n",
    "for nq in problems.keys():\n",
    "    if nq > 25:\n",
    "        break\n",
    "    print(f\"-------- nq: {nq} ------------\")\n",
    "    for case in problems[nq].keys():\n",
    "        problems[nq][case][\"shots\"] = shots\n",
    "        ising_hamiltonian = problems[nq][case][\"ising_hamiltonian\"]\n",
    "        max_weight = max(ising_hamiltonian.weights) # Normalization\n",
    "        hamiltonian = {tuple(i) : w / max_weight for i, w in zip(ising_hamiltonian.terms, ising_hamiltonian.weights) if abs(w) > 1e-9}\n",
    "        p = nq # The number of qubits equal to the number of layers in QAOA\n",
    "        gammas = np.arange(1, p+1) * delta_gamma/p\n",
    "        betas = np.arange(1, p+1)[::-1] * delta_beta/p\n",
    "        problems[nq][case][\"samples\"] = qaoa_circ(hamiltonian, gammas, betas, nq, shots)\n",
    "        problems[nq][case][\"results\"] = objective_MaxCut(problems[nq][case][\"samples\"],\n",
    "                                                            problems[nq][case][\"G\"],\n",
    "                                                            problems[nq][case][\"sol\"])\n",
    "        problems[nq][case][\"samples_mitig\"] = mitigated(problems[nq][case][\"samples\"], problems[nq][case][\"G\"])\n",
    "        problems[nq][case][\"results_mitig\"] = objective_MaxCut(problems[nq][case][\"samples_mitig\"],\n",
    "                                                                    problems[nq][case][\"G\"],\n",
    "                                                                    problems[nq][case][\"sol\"])\n",
    "np.save(\"./Data/WMaxCut_cte.npy\", problems)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "523ad4d8",
   "metadata": {},
   "outputs": [],
   "source": [
    "problems = np.load(\"WMaxCut_cte.npy\", allow_pickle=True).item()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b0deb462",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x312d79090>"
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     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "colors=plt.get_cmap(\"turbo\")\n",
    "nqs = list(problems.keys())\n",
    "nq_min = 5\n",
    "nq_max = 30\n",
    "nqs = np.arange(5, 26)\n",
    "for nq in nqs:\n",
    "    ax.plot(len(problems[nq])*[nq], [problems[nq][case][\"results\"][\"probability\"] for case in problems[nq].keys()], marker=\"o\", linewidth=0, markersize=2, color=colors((nq-nq_min)/(nq_max-nq_min)))\n",
    "for nq in nqs:\n",
    "    ax.plot([nq], np.mean([problems[nq][case][\"results\"][\"probability\"] for case in problems[nq].keys()]), marker=\"o\", linewidth=0, markeredgecolor=\"black\", color=colors((nq-nq_min)/(nq_max-nq_min)), markersize=6)\n",
    "ax.plot([], [], marker=\"o\", linewidth=0, markersize=2, color=\"black\", label=\"case\")\n",
    "ax.plot([], [], marker=\"o\", linewidth=0, markeredgecolor=\"black\", color=\"white\", markersize=6, label =r\"mean $\\Delta_{\\gamma,\\beta}=0.5$\")\n",
    "ax.plot(nqs, [2/2**(i/2) for i in nqs], color=\"black\", linestyle=\"--\", label=r\"$2/2^{N_q/2}$\")\n",
    "ax.plot(nqs, [2/2**(i) for i in nqs], color=\"black\", linestyle=\":\", label=r\"$2/2^{N_q}$\")\n",
    "\n",
    "ax.set_ylabel(r\"probability($x^*$)\")\n",
    "ax.set_xlabel(r\"$N_q,p$\")\n",
    "ax.set_yscale(\"log\")\n",
    "ax.set_xticks([5,10,15,20,25])\n",
    "ax.legend()\n",
    "# fig.savefig(\"probability_WMaxCut_LRQAOA.pdf\", transparent=True, bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "1a886933",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x17819f790>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "colors=plt.get_cmap(\"turbo\")\n",
    "nqs = list(problems.keys())\n",
    "nq_min = 5\n",
    "nq_max = 30\n",
    "nqs = np.arange(5, 26)\n",
    "for nq in nqs:\n",
    "    ax.plot(len(problems[nq])*[nq], [problems[nq][case][\"results\"][\"r\"] for case in problems[nq].keys()], marker=\"o\", linewidth=0, markersize=2, color=colors((nq-nq_min)/(nq_max-nq_min)))\n",
    "for nq in nqs:\n",
    "    ax.plot([nq], np.mean([problems[nq][case][\"results\"][\"r\"] for case in problems[nq].keys()]), marker=\"o\", linewidth=0, markeredgecolor=\"black\", color=colors((nq-nq_min)/(nq_max-nq_min)))\n",
    "ax.plot([], [], marker=\"o\", linewidth=0, markersize=2, color=\"black\", label=\"case\")\n",
    "ax.plot([], [], marker=\"o\", linewidth=0, markeredgecolor=\"black\", color=\"white\", markersize=6, label =r\"mean $\\Delta_{\\gamma,\\beta}=0.5$\")\n",
    "ax.plot([5, 25], [0.878, 0.878], color=\"black\", linestyle=\"--\", label=r\"GW\")\n",
    "\n",
    "ax.set_ylabel(\"r\")\n",
    "ax.set_xlabel(r\"$N_q, p$\")\n",
    "ax.set_xticks([5,10,15,20,25])\n",
    "ax.set_yticks([0.8, 0.85, 0.9, 0.95, 1])\n",
    "ax.legend()\n",
    "# fig.savefig(\"WMaxCut_LRQAOA_r.pdf\", transparent=True, bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d62cc879",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "cplex_env",
   "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": "3.10.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}