find_Delta_best.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 9,
   "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",
    "from scipy.optimize import minimize\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": 2,
   "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": 169,
   "id": "183b23da",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of nodes 5\n",
      "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"
     ]
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "nodes_list_qubo = range(5, 25)\n",
    "random_cases = 20\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": 229,
   "id": "4d3e175a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-------- nq: 23 ------------\n"
     ]
    }
   ],
   "source": [
    "x0 = 5\n",
    "x1 = 42\n",
    "d0 = 0.87\n",
    "d1 = 0.5\n",
    "M = np.array([[1,x0,x0**2],[1,x1,x1**2],[0,1,2*x1]])\n",
    "b = np.linalg.inv(M) @ np.array([[d0],[d1],[0]])\n",
    "delta = lambda p: b[0] + b[1]*p + b[2]*p**2\n",
    "delta = lambda p:0.57\n",
    "delta_gamma = 0.55\n",
    "delta_beta = 0.55\n",
    "shots = 10000\n",
    "for nq in [23]:\n",
    "    print(f\"-------- nq: {nq} ------------\")\n",
    "    for case in [3]:\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",
    "# np.save(\"./Data/WMaxCut_cte.npy\", problems)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "id": "96258fc5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[350.70281444335575,\n",
       " 991.3398946663602,\n",
       " 723.5847030135471,\n",
       " 9024.607596804855,\n",
       " 450.56190996204305,\n",
       " 264.1874757844411,\n",
       " 811.3126206804442,\n",
       " 339.48678879009503,\n",
       " 2167.735708572315,\n",
       " 457.07400688716905,\n",
       " 1087.4683309522704,\n",
       " 321.4832110227126,\n",
       " 3394.431180485001,\n",
       " 339.0809606009105,\n",
       " 358.4689576805265,\n",
       " 458.8034379680872,\n",
       " 502.10505452006703,\n",
       " 777.1115147901048,\n",
       " 210.58653309923034,\n",
       " 1416.552491673724]"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nq = 20\n",
    "[2*nq*np.log(1-0.99)/np.log(1-problems[nq][case][\"results\"][\"probability\"]) for case in problems[nq].keys()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "id": "38d6dd00",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[348.94492935963774,\n",
       " 863.8000466078474,\n",
       " 983.4938003355121,\n",
       " 5831.264344612412,\n",
       " 736.210756730083,\n",
       " 374.58830487114443,\n",
       " 702.8152850066176,\n",
       " 709.3778682609907,\n",
       " 1387.4404402341625,\n",
       " 373.0121203506319,\n",
       " 1162.297311216224,\n",
       " 401.0625282914779,\n",
       " 2117.068514307012,\n",
       " 721.7083490946425,\n",
       " 401.4583940044128,\n",
       " 551.9854135076703,\n",
       " 485.51912172069206,\n",
       " 806.3112445916354,\n",
       " 279.20506190868474,\n",
       " 1788.5859436153446]"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nq = 23\n",
    "[nq*np.log(1-0.99)/np.log(1-problems[nq][case][\"results\"][\"probability\"]) for case in problems[nq].keys()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "id": "98cd572a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1760b4a60>]"
      ]
     },
     "execution_count": 197,
     "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": [
    "nqs = list(range(5,25))\n",
    "\n",
    "plt.plot(nqs, [np.mean([nq*np.log(1-0.99)/np.log(1-problems[nq][case][\"results\"][\"probability\"]) for case in problems[nq].keys() if problems[nq][case][\"results\"][\"probability\"] > 0]) for nq in nqs])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "c7623b94",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-------- nq: 17 ------------\n",
      "0.2659\n",
      "0.1153\n",
      "0.1057\n",
      "0.492\n",
      "0.2114\n",
      "0.2102\n",
      "0.3271\n",
      "0.1856\n",
      "0.4102\n",
      "0.1914\n",
      "0.0007\n",
      "0.3185\n",
      "0.1378\n",
      "0.342\n",
      "0.1393\n",
      "0.095\n",
      "0.201\n",
      "0.4117\n",
      "0.1101\n",
      "0.2705\n",
      "-------- nq: 18 ------------\n",
      "0.1732\n",
      "0.185\n",
      "0.2195\n",
      "0.3052\n",
      "0.1601\n",
      "0.429\n",
      "0.1954\n",
      "0.1865\n",
      "0.2202\n",
      "0.3522\n",
      "0.0824\n",
      "0.0829\n",
      "0.1369\n",
      "0.2477\n",
      "0.1532\n",
      "0.1483\n",
      "0.0956\n",
      "0.3252\n",
      "0.2291\n",
      "0.1796\n"
     ]
    }
   ],
   "source": [
    "shots = 10000\n",
    "delta_0 = 0.8\n",
    "\n",
    "\n",
    "for nq in range(17,19):\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",
    "        sol = minimize(cost_function, x0 = delta_0, method = \"COBYLA\", bounds=[(0.3, 2)], args=(hamiltonian, problems[nq][case][\"G\"],problems[nq][case][\"sol\"], p), options={\"maxiter\":20})\n",
    "        delta = sol.x[0]\n",
    "        gammas = np.arange(1, p+1) * delta/p\n",
    "        betas = np.arange(1, p+1)[::-1] * delta/p\n",
    "        problems[nq][case][\"samples\"] = qaoa_circ(hamiltonian, gammas, betas, nq, shots)\n",
    "        problems[nq][case][\"delta\"] = delta\n",
    "        problems[nq][case][\"results\"] = objective_MaxCut(problems[nq][case][\"samples\"],\n",
    "                                                            problems[nq][case][\"G\"],\n",
    "                                                            problems[nq][case][\"sol\"])\n",
    "        print(problems[nq][case][\"results\"][\"probability\"])\n",
    "# np.save(\"./Data/WMaxCut_cte.npy\", problems)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "eb8a7cb0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-------- nq: 19 ------------\n",
      "probability:0.3482 || delta\"0.5333333333333333\n",
      "probability:0.1733 || delta\"0.5555555555555556\n",
      "probability:0.0452 || delta\"0.4222222222222222\n",
      "probability:0.0687 || delta\"0.5555555555555556\n",
      "probability:0.1492 || delta\"0.5555555555555556\n",
      "probability:0.0497 || delta\"0.4666666666666667\n",
      "probability:0.2157 || delta\"0.5555555555555556\n",
      "probability:0.1125 || delta\"0.5333333333333333\n",
      "probability:0.0723 || delta\"0.5111111111111111\n",
      "probability:0.1955 || delta\"0.5777777777777777\n",
      "probability:0.2422 || delta\"0.5777777777777777\n",
      "probability:0.1265 || delta\"0.6\n",
      "probability:0.0366 || delta\"0.4444444444444445\n",
      "probability:0.2589 || delta\"0.5555555555555556\n",
      "probability:0.2299 || delta\"0.5555555555555556\n",
      "probability:0.3167 || delta\"0.5333333333333333\n",
      "probability:0.1216 || delta\"0.5333333333333333\n",
      "probability:0.031 || delta\"0.4444444444444445\n",
      "probability:0.2521 || delta\"0.5555555555555556\n",
      "probability:0.0592 || delta\"0.5555555555555556\n"
     ]
    }
   ],
   "source": [
    "shots = 10000\n",
    "\n",
    "deltas = np.linspace(0.3, 0.65, 15)\n",
    "for nq in [19]:\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",
    "        best_probability = 0\n",
    "        for nn, delta in enumerate(deltas):\n",
    "            gammas = np.arange(1, p+1) * delta/p\n",
    "            betas = np.arange(1, p+1)[::-1] * delta/p\n",
    "            samples = qaoa_circ(hamiltonian, gammas, betas, nq, shots)\n",
    "            results = objective_MaxCut(samples, problems[nq][case][\"G\"], problems[nq][case][\"sol\"])\n",
    "            if results[\"probability\"] > best_probability:\n",
    "                problems[nq][case][\"samples\"] = samples\n",
    "                problems[nq][case][\"results\"] = results\n",
    "                problems[nq][case][\"delta\"] = delta\n",
    "                best_probability = results[\"probability\"] \n",
    "        print(f'probability:{problems[nq][case][\"results\"][\"probability\"]} || delta{problems[nq][case][\"delta\"]}')\n",
    "# np.save(\"./Data/WMaxCut_cte.npy\", problems)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "a41c436e",
   "metadata": {},
   "outputs": [
    {
     "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",
    "nqs = range(5,17)\n",
    "for nq in nqs:\n",
    "    ax.plot([problems[nq][case][\"delta\"] for case in problems[nq].keys()], [problems[nq][case][\"results\"][\"optimal_cost\"] for case in problems[nq].keys()], marker=\"o\", linewidth=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e96d8896",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "id": "c80813e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 9.79839299e-01],\n",
       "       [-2.76113952e-02],\n",
       "       [ 3.28707085e-04]])"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = np.array([[1,5,25],[1,42,1764],[0,1,84]])\n",
    "p = np.linalg.inv(M) @ np.array([[0.85],[0.4],[0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "id": "818e9e09",
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "unsupported operand type(s) for +: 'dict' and 'dict'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[171], line 2\u001b[0m\n\u001b[1;32m      1\u001b[0m nqs \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mlist\u001b[39m(\u001b[38;5;28mrange\u001b[39m(\u001b[38;5;241m5\u001b[39m,\u001b[38;5;241m10\u001b[39m))\n\u001b[0;32m----> 2\u001b[0m plt\u001b[38;5;241m.\u001b[39mplot(nqs, [np\u001b[38;5;241m.\u001b[39mmean([problems[nq][case][\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mdelta\u001b[39m\u001b[38;5;124m\"\u001b[39m] \u001b[38;5;28;01mfor\u001b[39;00m case \u001b[38;5;129;01min\u001b[39;00m problems[nq]\u001b[38;5;241m.\u001b[39mkeys()]) \u001b[38;5;28;01mfor\u001b[39;00m nq \u001b[38;5;129;01min\u001b[39;00m nqs])\n\u001b[1;32m      3\u001b[0m x \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mlist\u001b[39m(\u001b[38;5;28mrange\u001b[39m(\u001b[38;5;241m5\u001b[39m,\u001b[38;5;241m20\u001b[39m)) \u001b[38;5;241m+\u001b[39m [\u001b[38;5;241m42\u001b[39m] \u001b[38;5;241m+\u001b[39m [\u001b[38;5;241m44\u001b[39m]\n\u001b[1;32m      5\u001b[0m y \u001b[38;5;241m=\u001b[39m [np\u001b[38;5;241m.\u001b[39mmean([problems[nq][case][\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mdelta\u001b[39m\u001b[38;5;124m\"\u001b[39m] \u001b[38;5;28;01mfor\u001b[39;00m case \u001b[38;5;129;01min\u001b[39;00m problems[nq]\u001b[38;5;241m.\u001b[39mkeys()]) \u001b[38;5;28;01mfor\u001b[39;00m nq \u001b[38;5;129;01min\u001b[39;00m nqs] \u001b[38;5;241m+\u001b[39m [\u001b[38;5;241m0.4\u001b[39m, \u001b[38;5;241m0.39\u001b[39m]\n",
      "Cell \u001b[0;32mIn[171], line 2\u001b[0m, in \u001b[0;36m<listcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m      1\u001b[0m nqs \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mlist\u001b[39m(\u001b[38;5;28mrange\u001b[39m(\u001b[38;5;241m5\u001b[39m,\u001b[38;5;241m10\u001b[39m))\n\u001b[0;32m----> 2\u001b[0m plt\u001b[38;5;241m.\u001b[39mplot(nqs, [\u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mmean\u001b[49m\u001b[43m(\u001b[49m\u001b[43m[\u001b[49m\u001b[43mproblems\u001b[49m\u001b[43m[\u001b[49m\u001b[43mnq\u001b[49m\u001b[43m]\u001b[49m\u001b[43m[\u001b[49m\u001b[43mcase\u001b[49m\u001b[43m]\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mdelta\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mfor\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mcase\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;129;43;01min\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mproblems\u001b[49m\u001b[43m[\u001b[49m\u001b[43mnq\u001b[49m\u001b[43m]\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mkeys\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m \u001b[38;5;28;01mfor\u001b[39;00m nq \u001b[38;5;129;01min\u001b[39;00m nqs])\n\u001b[1;32m      3\u001b[0m x \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mlist\u001b[39m(\u001b[38;5;28mrange\u001b[39m(\u001b[38;5;241m5\u001b[39m,\u001b[38;5;241m20\u001b[39m)) \u001b[38;5;241m+\u001b[39m [\u001b[38;5;241m42\u001b[39m] \u001b[38;5;241m+\u001b[39m [\u001b[38;5;241m44\u001b[39m]\n\u001b[1;32m      5\u001b[0m y \u001b[38;5;241m=\u001b[39m [np\u001b[38;5;241m.\u001b[39mmean([problems[nq][case][\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mdelta\u001b[39m\u001b[38;5;124m\"\u001b[39m] \u001b[38;5;28;01mfor\u001b[39;00m case \u001b[38;5;129;01min\u001b[39;00m problems[nq]\u001b[38;5;241m.\u001b[39mkeys()]) \u001b[38;5;28;01mfor\u001b[39;00m nq \u001b[38;5;129;01min\u001b[39;00m nqs] \u001b[38;5;241m+\u001b[39m [\u001b[38;5;241m0.4\u001b[39m, \u001b[38;5;241m0.39\u001b[39m]\n",
      "File \u001b[0;32m~/anaconda3/envs/cplex_env/lib/python3.10/site-packages/numpy/core/fromnumeric.py:3504\u001b[0m, in \u001b[0;36mmean\u001b[0;34m(a, axis, dtype, out, keepdims, where)\u001b[0m\n\u001b[1;32m   3501\u001b[0m     \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m   3502\u001b[0m         \u001b[38;5;28;01mreturn\u001b[39;00m mean(axis\u001b[38;5;241m=\u001b[39maxis, dtype\u001b[38;5;241m=\u001b[39mdtype, out\u001b[38;5;241m=\u001b[39mout, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[0;32m-> 3504\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43m_methods\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_mean\u001b[49m\u001b[43m(\u001b[49m\u001b[43ma\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43maxis\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43maxis\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdtype\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mdtype\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m   3505\u001b[0m \u001b[43m                      \u001b[49m\u001b[43mout\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mout\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/anaconda3/envs/cplex_env/lib/python3.10/site-packages/numpy/core/_methods.py:118\u001b[0m, in \u001b[0;36m_mean\u001b[0;34m(a, axis, dtype, out, keepdims, where)\u001b[0m\n\u001b[1;32m    115\u001b[0m         dtype \u001b[38;5;241m=\u001b[39m mu\u001b[38;5;241m.\u001b[39mdtype(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mf4\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m    116\u001b[0m         is_float16_result \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mTrue\u001b[39;00m\n\u001b[0;32m--> 118\u001b[0m ret \u001b[38;5;241m=\u001b[39m \u001b[43mumr_sum\u001b[49m\u001b[43m(\u001b[49m\u001b[43marr\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43maxis\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdtype\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mout\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkeepdims\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mwhere\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mwhere\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    119\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(ret, mu\u001b[38;5;241m.\u001b[39mndarray):\n\u001b[1;32m    120\u001b[0m     \u001b[38;5;28;01mwith\u001b[39;00m _no_nep50_warning():\n",
      "\u001b[0;31mTypeError\u001b[0m: unsupported operand type(s) for +: 'dict' and 'dict'"
     ]
    }
   ],
   "source": [
    "nqs = list(range(5,10))\n",
    "plt.plot(nqs, [np.mean([problems[nq][case][\"delta\"] for case in problems[nq].keys()]) for nq in nqs])\n",
    "x = list(range(5,20)) + [42] + [44]\n",
    "\n",
    "y = [np.mean([problems[nq][case][\"delta\"] for case in problems[nq].keys()]) for nq in nqs] + [0.4, 0.39]\n",
    "# p = np.polyfit(x, y, 2)\n",
    "tq = np.arange(5,43)\n",
    "x0 = 5\n",
    "x1 = 42\n",
    "d0 = 0.87\n",
    "d1 = 0.4\n",
    "M = np.array([[1,x0,x0**2],[1,x1,x1**2],[0,1,2*x1]])\n",
    "p = np.linalg.inv(M) @ np.array([[d0],[d1],[0]])\n",
    "plt.plot(tq, p[0] + p[1]*tq + p[2]*tq**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "523ad4d8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# problems = np.load(\"WMaxCut_cte.npy\", allow_pickle=True).item()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "id": "1d8f91ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x17e0ab6d0>]"
      ]
     },
     "execution_count": 174,
     "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": [
    "nqs = list(range(5,16))\n",
    "\n",
    "plt.plot(nqs, [np.mean([nq*np.log(1-0.99)/np.log(1-problems[nq][case][\"results\"][\"probability\"]) for case in problems[nq].keys() if problems[nq][case][\"results\"][\"probability\"] > 0]) for nq in nqs])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b0deb462",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x312d79090>"
      ]
     },
     "execution_count": 20,
     "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\"][\"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
}