random_qubo_benchmarks.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import dimod\n",
    "import neal\n",
    "import numpy as np\n",
    "import pprint\n",
    "import time\n",
    "import os\n",
    "import pickle\n",
    "import dwave_token\n",
    "import dwave.inspector\n",
    "\n",
    "from dwave.system import DWaveSampler, DWaveCliqueSampler, LeapHybridCQMSampler\n",
    "from dwave.system import AutoEmbeddingComposite, FixedEmbeddingComposite, CutOffComposite\n",
    "\n",
    "# automatically generated embedding:\n",
    "sampler = AutoEmbeddingComposite(DWaveSampler(token=dwave_token.value))\n",
    "clique_sampler = DWaveCliqueSampler(token=dwave_token.value)\n",
    "hybrid_sampler = LeapHybridCQMSampler(token=dwave_token.value)\n",
    "simulated_sampler = neal.SimulatedAnnealingSampler()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 200\n",
    "scaling = 10\n",
    "\n",
    "# generate random upper triangle matrix\n",
    "Q = scaling*np.triu(-1+2*np.random.rand(n,n))\n",
    "for i in range(n): # do not allow small values\n",
    "    for j in range(i,n):\n",
    "        if abs(Q[i,j]) < 0.01:\n",
    "            Q[i,j] = np.sign(-1+2*np.random.rand() * (0.01 + 0.99*np.random.rand()))\n",
    "# print(Q)\n",
    "# convert into binary quadratic model\n",
    "bqm = dimod.BinaryQuadraticModel.from_qubo(Q)\n",
    "chain_strength = scaling # set chain strength close to largest QUBO entry"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "Ising = dimod.utilities.qubo_to_ising({(i,j):Q[i,j] for i in range(n) for j in range(i,n)})\n",
    "for i in range(n):\n",
    "    if abs(Ising[0][i]) < 0.01:\n",
    "        Ising[0][i] = np.sign(-1+2*np.random.rand() * (0.01 + 0.99*np.random.rand()))\n",
    "    for j in range(i+1,n):\n",
    "        if abs(Ising[1][i,j]) < 0.01:\n",
    "            Ising[1][i,j] = np.sign(-1+2*np.random.rand() * (0.01 + 0.99*np.random.rand()))\n",
    "bqm = dimod.BinaryQuadraticModel.from_ising(Ising[0],Ising[1]) # model creation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minimum: -1998.3383045847684\n",
      "100 variables encoded in 1267 physical qubits\n"
     ]
    }
   ],
   "source": [
    "# run calculation\n",
    "chain_strength = scaling # set chain strength close to largest QUBO entry\n",
    "sampleset = sampler.sample(\n",
    "    bqm,\n",
    "    num_reads=100,\n",
    "    chain_strength=chain_strength\n",
    ")\n",
    "print('minimum: ' + str(sampleset.lowest().first.energy))\n",
    "print(str(n) + ' variables encoded in ' + str(len([node for nodes in sampleset.info['embedding_context']['embedding'].values() for node in nodes])) + ' physical qubits')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minimum: -1655.0929967267894\n",
      "100 variables encoded in 982 physical qubits\n"
     ]
    }
   ],
   "source": [
    "#comparison when running the same problem on the Clique Sampler:\n",
    "sampleset2 = clique_sampler.sample(\n",
    "    bqm,\n",
    "    num_reads=1000,\n",
    "    chain_strength=chain_strength\n",
    ")\n",
    "print('minimum: ' + str(sampleset2.lowest().first.energy))\n",
    "print(str(n) + ' variables encoded in ' + str(len([node for nodes in sampleset2.info['embedding_context']['embedding'].values() for node in nodes])) + ' physical qubits')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minimum: -5097.6261461635395\n"
     ]
    }
   ],
   "source": [
    "#comparison when running the same problem on the Hybrid Sampler:\n",
    "cqm = dimod.ConstrainedQuadraticModel.from_bqm(bqm)\n",
    "sampleset3 = hybrid_sampler.sample_cqm(\n",
    "    cqm,\n",
    "    time_limit = 5,\n",
    "    )\n",
    "print('minimum: ' + str(sampleset3.lowest().first.energy))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minimum: -5097.626146163578\n"
     ]
    }
   ],
   "source": [
    "#comparison when running the same problem on simulated annealing:\n",
    "sampleset4 = simulated_sampler.sample(\n",
    "    bqm,\n",
    "    num_reads=1000,\n",
    "    chain_strength=chain_strength\n",
    ")\n",
    "print('minimum: ' + str(sampleset4.lowest().first.energy))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minimum: -4472.239493432756\n"
     ]
    }
   ],
   "source": [
    "# comparison when running with cutoff:\n",
    "cutoff = 2.1\n",
    "sampleset5 = CutOffComposite(sampler, cutoff).sample(\n",
    "    bqm,\n",
    "    num_reads=100,\n",
    "    chain_strength=chain_strength\n",
    ")\n",
    "print('minimum: ' + str(sampleset5.lowest().first.energy))\n",
    "#print(str(n) + ' variables encoded in ' + str(len([node for nodes in sampleset5.info['embedding_context']['embedding'].values() for node in nodes])) + ' physical qubits')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.35986959,  1.49402236, -1.87383377,  4.97455884, -2.91158476,\n",
       "       -8.36576968,  5.16145745, -7.69797602, -6.17214498, -8.98350261,\n",
       "       -6.74083093,  1.34696038, -9.5618722 , -8.30221462, -4.38269344,\n",
       "       -9.55596604, -8.76931816, -6.41333142,  4.29365209, -1.61229485,\n",
       "       -2.97888878, -2.33517716, -8.92780391, -4.76222707,  7.61217343,\n",
       "       -8.5297313 ,  3.96686705,  9.42041092,  6.9884969 ,  3.19704075,\n",
       "       -4.90323362, -2.17833186, -9.95593999, -8.6305805 , -8.57647533,\n",
       "        5.83738046, -5.70754126, -0.37254439, -2.64543821,  6.47134439,\n",
       "       -6.95310637, -4.73045034, -2.98902107,  6.49703702,  7.10978349,\n",
       "       -5.89225226, -5.74770741, -7.75831573, -1.90711442, -2.28116819,\n",
       "        6.17117915,  7.5293591 , -9.83379512, -5.40753776, -9.80979287,\n",
       "        6.96145782, -2.74471688,  3.63354148, -9.50148471, -2.86487486,\n",
       "        1.5543291 , -5.11621823, -7.73010301,  5.59994358, -7.69026335,\n",
       "        7.29949685,  0.06703156, -8.29419687,  6.56304288, -1.10103085,\n",
       "        6.14412307, -7.14334631, -8.06904942, -0.49485286, -4.88248267,\n",
       "        9.33949697,  7.85998955, -5.92309832,  6.80584983, -0.74271916,\n",
       "       -6.14115819, -7.15210655, -0.7492965 , -3.10609203,  6.41621723,\n",
       "       -1.74128136,  3.50917328,  1.67520273,  8.53899074,  4.69131392,\n",
       "       -9.3157587 , -4.75087089, -6.88356637,  6.08952049, -9.4020832 ,\n",
       "        7.42150601,  6.92826519,  8.457395  ,  0.50392724,  9.90748454,\n",
       "       -5.77198054,  3.79248832,  1.82634198, -5.80908524,  1.30106741,\n",
       "        0.91444371, -8.79169106,  4.17777749,  3.4550531 ,  6.3034768 ,\n",
       "       -2.02796433, -4.89034911,  5.56271563, -8.67999057,  8.31471492,\n",
       "        3.8161982 , -4.15056204,  2.5563803 , -5.49250685,  2.17085225,\n",
       "        3.83693983, -6.24764446, -5.87716175, -7.76957307, -8.98122465,\n",
       "       -7.39619358, -6.21120558, -5.65724009,  1.17394708,  8.95553403,\n",
       "        9.97699812,  0.27512418,  1.34612173, -6.78186534,  0.68089487,\n",
       "        4.59954091,  7.45324667, -5.5104736 , -4.74558355,  8.71186313,\n",
       "       -1.11111908,  7.04800061,  9.56823771,  8.16776861, -4.42588962,\n",
       "       -2.94253489,  7.97014065,  4.96844412, -6.41426117,  2.75060862,\n",
       "       -3.82214713,  9.07205289,  2.02486958,  4.08739423,  1.42663841,\n",
       "        9.22376441, -2.37189389,  4.55124739,  8.3051599 ,  8.01797668,\n",
       "        4.42251234,  6.55222737,  3.01488272, -5.83917445, -6.35002051,\n",
       "       -2.51264777, -5.61451303, -6.4418833 ,  6.37117998,  0.34868871,\n",
       "       -9.54982469, -7.34406819, -1.08245359,  8.76735705,  9.88298492,\n",
       "        7.7300167 , -7.01186464, -3.16876061, -7.49606731, -8.64129445,\n",
       "       -1.75108301,  4.77821789, -1.74941058,  4.54979635, -6.00393056,\n",
       "       -6.93364421,  5.07231689,  5.31243464, -1.00827275,  5.54397724,\n",
       "       -5.20238471, -2.21043798, -6.53759811, -7.85793394,  7.38998731,\n",
       "       -0.99796827, -3.03027111,  2.08779382, -6.88694155, -7.45735722])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.diag(Q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<iframe src=http://127.0.0.1:18000/?problemId=342a3cc5-f4c5-4719-abc0-daab1b927011 width=\"100%\" height=640></iframe>"
      ],
      "text/plain": [
       "Serving Inspector on http://127.0.0.1:18000/?problemId=342a3cc5-f4c5-4719-abc0-daab1b927011"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'http://127.0.0.1:18000/?problemId=342a3cc5-f4c5-4719-abc0-daab1b927011'"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# print(sampleset)\n",
    "# pprint.pprint(sampleset.info)\n",
    "dwave.inspector.show(sampleset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "invalid combination of arguments provided: if data capture not enabled, problem/response/solver have to be specified; also, make sure a structured problem is being inspected",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[12], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mdwave\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43minspector\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshow\u001b[49m\u001b[43m(\u001b[49m\u001b[43msampleset5\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/.local/lib/python3.11/site-packages/dwave/inspector/__init__.py:190\u001b[0m, in \u001b[0;36mshow\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m    188\u001b[0m block \u001b[38;5;241m=\u001b[39m kwargs\u001b[38;5;241m.\u001b[39mpop(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mblock\u001b[39m\u001b[38;5;124m'\u001b[39m, Block\u001b[38;5;241m.\u001b[39mONCE)\n\u001b[1;32m    189\u001b[0m timeout \u001b[38;5;241m=\u001b[39m kwargs\u001b[38;5;241m.\u001b[39mpop(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mtimeout\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;28;01mNone\u001b[39;00m)\n\u001b[0;32m--> 190\u001b[0m data \u001b[38;5;241m=\u001b[39m \u001b[43mfrom_objects\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\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\u001b[1;32m    191\u001b[0m id_ \u001b[38;5;241m=\u001b[39m push_inspector_data(data)\n\u001b[1;32m    192\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m open_problem(id_, block\u001b[38;5;241m=\u001b[39mblock, timeout\u001b[38;5;241m=\u001b[39mtimeout)\n",
      "File \u001b[0;32m~/.local/lib/python3.11/site-packages/dwave/inspector/adapters.py:869\u001b[0m, in \u001b[0;36mfrom_objects\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m    864\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m bqm \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m \u001b[38;5;129;01mand\u001b[39;00m sampleset \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m \u001b[38;5;129;01mand\u001b[39;00m sampler \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m    865\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m from_bqm_sampleset(\n\u001b[1;32m    866\u001b[0m         bqm\u001b[38;5;241m=\u001b[39mbqm, sampleset\u001b[38;5;241m=\u001b[39msampleset, sampler\u001b[38;5;241m=\u001b[39msampler,\n\u001b[1;32m    867\u001b[0m         embedding_context\u001b[38;5;241m=\u001b[39membedding_context, warnings\u001b[38;5;241m=\u001b[39mwarnings)\n\u001b[0;32m--> 869\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\n\u001b[1;32m    870\u001b[0m     \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124minvalid combination of arguments provided: if data capture not \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m    871\u001b[0m     \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124menabled, problem/response/solver have to be specified; \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m    872\u001b[0m     \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124malso, make sure a structured problem is being inspected\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
      "\u001b[0;31mValueError\u001b[0m: invalid combination of arguments provided: if data capture not enabled, problem/response/solver have to be specified; also, make sure a structured problem is being inspected"
     ]
    }
   ],
   "source": [
    "dwave.inspector.show(sampleset5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# save embedding:\n",
    "file_name = str(n) + '_QUBO'\n",
    "embedding_folder = 'Embeddings'\n",
    "embedding_file_name = file_name + '_embedding.pkl'\n",
    "with open(os.path.join(embedding_folder,embedding_file_name), 'wb') as f:\n",
    "    pickle.dump(sampleset.to_serializable()['info']['embedding_context']['embedding'], f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fixed embedding:\n",
    "embedding = sampleset.info['embedding_context']['embedding']\n",
    "fixed_sampler = FixedEmbeddingComposite(child_sampler=DWaveSampler(token=dwave_token.value), embedding=embedding)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minimum: -1966.401191811369\n",
      "Old embedding:\n",
      "minimum: -1972.745190286486\n",
      "Time for fixed embedding calculation:3.4141244888305664\n"
     ]
    }
   ],
   "source": [
    "#compare embeddings on new QUBO:\n",
    "P = scaling*np.triu(-1+2*np.random.rand(n,n))\n",
    "bqm2 = dimod.BinaryQuadraticModel.from_qubo(P)\n",
    "samplesetP = sampler.sample(\n",
    "    bqm2,\n",
    "    num_reads=1000,\n",
    "    chain_strength=chain_strength\n",
    ")\n",
    "print('minimum: ' + str(samplesetP.lowest().first.energy))\n",
    "if samplesetP.info['embedding_context']['embedding'] != embedding:\n",
    "    print('Old embedding:')\n",
    "    time_stamp = time.time()\n",
    "    samplesetP2 = fixed_sampler.sample(\n",
    "        bqm2,\n",
    "        num_reads=1000,\n",
    "        chain_strength=chain_strength\n",
    "    )\n",
    "    print('minimum: ' + str(samplesetP2.lowest().first.energy))\n",
    "    print('Time for fixed embedding calculation:' + str(time.time()-time_stamp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<iframe src=http://127.0.0.1:18000/?problemId=b04e2571-0219-42af-a5d6-6ae5582db524 width=\"100%\" height=640></iframe>"
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      "text/plain": [
       "Serving Inspector on http://127.0.0.1:18000/?problemId=b04e2571-0219-42af-a5d6-6ae5582db524"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'http://127.0.0.1:18000/?problemId=b04e2571-0219-42af-a5d6-6ae5582db524'"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dwave.inspector.show(samplesetP)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<iframe src=http://127.0.0.1:18000/?problemId=0c536058-335a-47ff-a55d-17ba0e66cdb3 width=\"100%\" height=640></iframe>"
      ],
      "text/plain": [
       "Serving Inspector on http://127.0.0.1:18000/?problemId=0c536058-335a-47ff-a55d-17ba0e66cdb3"
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     "data": {
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       "'http://127.0.0.1:18000/?problemId=0c536058-335a-47ff-a55d-17ba0e66cdb3'"
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     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dwave.inspector.show(samplesetP2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "# plot how many physical qubits where used per variables with random dense qubo (with all to all connection)\n",
    "plt.plot(\n",
    "    [5,10,15,20,25,30,35,40,50,60,70,80,90,100,110,120,130,140,150,160,170],\n",
    "    [6,16,35,56,91,123,168,204,336,451,636,820,1076,1328,1599,1867,2028,2791,3292,3635,3668]\n",
    ")\n",
    "plt.show()"
   ]
  }
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