Investigating Itay Hen and AP Young's Quantum Annealer Approach to Graph Isomorphism Problem.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import defaultdict\n",
    "import numpy as np\n",
    "from itertools import combinations\n",
    "from dwave.system.samplers import DWaveSampler\n",
    "from dwave.system.composites import EmbeddingComposite\n",
    "from matplotlib import pyplot as plt\n",
    "import networkx as nx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_cl_graph(n):\n",
    "    G = nx.generators.classic.circular_ladder_graph(n)\n",
    "    adj = nx.to_numpy_matrix(G)\n",
    "    pos = nx.spring_layout(G)\n",
    "    default_axes = plt.axes(frameon=True)\n",
    "    nx.draw_networkx(G, node_size=600, alpha=.8, ax=default_axes, pos=pos)\n",
    "    plt.show()\n",
    "    return G, adj\n",
    "def gen_ml_graph(n):\n",
    "    G = nx.generators.classic.circulant_graph(2*n, [1,n])\n",
    "    adj = nx.to_numpy_matrix(G)\n",
    "    pos = nx.spring_layout(G)\n",
    "    default_axes = plt.axes(frameon=True)\n",
    "    nx.draw_networkx(G, node_size=600, alpha=.8, ax=default_axes, pos=pos)\n",
    "    plt.show()\n",
    "    return G, adj\n",
    "def maxcut_hamiltonian_eigenvalue(G):\n",
    "    # The Hamiltonian is H = sum(Pauli_Z(i) x Pauli_Z(j) - I)/2\n",
    "    # The eigenvalue is the negation of the edges in cut solution\n",
    "    # D-wave will minimize the energy of the Hamiltonian\n",
    "    # The QUBO should be -xi-xj+2xixj\n",
    "    # The corresponding Q matrix is as follows\n",
    "    Q = defaultdict(int)\n",
    "    for u, v in G.edges:\n",
    "        #should be -1 & -2, but use -0.5 & 1 so we are not overcounting twice xi_xj and xj_x_i\n",
    "        Q[(u,u)]+= -0.5 \n",
    "        Q[(v,v)]+= -0.5\n",
    "        Q[(u,v)]+= 1\n",
    "    return Q\n",
    "def hen_young_hamiltonian_eigenvalue(G):\n",
    "    # The Hamiltonian is H = sum(Pauli_Z(i) x Pauli_Z(j))\n",
    "    # D-wave will minimize the energy of the Hamiltonian\n",
    "    # The QUBO should be -2xi-2xj+4xixj+1-->1 cannot formulate, \n",
    "    # I will be using the matrix of the Hamiltoian directly\n",
    "    # The corresponding Q matrix is as follows\n",
    "    Q = defaultdict(int)\n",
    "    P_z = np.array([[1,0],[0,-1]])\n",
    "    H = np.zeros((2**len(G.nodes),2**len(G.nodes)))\n",
    "    I = np.identity(2)\n",
    "    for u, v in G.edges:\n",
    "        zu = P_z\n",
    "        zv = P_z\n",
    "        if u < v: #There will be no loop and edges are not directed\n",
    "            print(u,v)\n",
    "            for i in range(u):\n",
    "                #zu = np.kron(I, zu)\n",
    "                zu = (I[:, None, :, None]*zu[None, :, None, :]).reshape(2**(i+2),2**(i+2))\n",
    "                print(\"Zu\",zu.shape)\n",
    "            for j in range(v-u-1):\n",
    "                #zv = np.kron(I, zv)\n",
    "                zv = (I[:, None, :, None]*zv[None, :, None, :]).reshape(2**(j+2),2**(j+2))\n",
    "            #zu = np.kron(zu, zv)\n",
    "            zu = (zu[:, None, :, None]*zv[None, :, None, :]).reshape(2**(v+1),2**(v+1))\n",
    "            print(\"Zu\",zu.shape)\n",
    "            for k in range(v+1, len(G.nodes)):\n",
    "                #zu = np.kron(zu, I)\n",
    "                zu = (zu[:, None, :, None]*I[None, :, None, :]).reshape(2**(k+1),2**(k+1))\n",
    "                print(\"Zu\",zu.shape)\n",
    "            H += zu\n",
    "    for i in range(len(H)):\n",
    "        for j in range(len(H)):\n",
    "            Q[(i,j)]=H[i,j]\n",
    "    return Q\n",
    "\n",
    "def solve(Q, chainstrength=8, numruns=10):\n",
    "    # Run the QUBO on the solver from your config file\n",
    "    sampler = EmbeddingComposite(DWaveSampler(solver={'qpu': True}))\n",
    "    response = sampler.sample_qubo(Q, chain_strength=chainstrength, num_reads=numruns)\n",
    "    energies = iter(response.data())\n",
    "\n",
    "    return [e.energy for e in list(energies)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/victorli/anaconda3/lib/python3.7/site-packages/networkx/drawing/nx_pylab.py:579: MatplotlibDeprecationWarning: \n",
      "The iterable function was deprecated in Matplotlib 3.1 and will be removed in 3.3. Use np.iterable instead.\n",
      "  if not cb.iterable(width):\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cl, adj_cl = gen_cl_graph(8)\n",
    "Q_cl_maxcut = maxcut_hamiltonian_eigenvalue(cl)\n",
    "#Q_cl_hen_young = hen_young_hamiltonian_eigenvalue(cl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ml, adj_ml = gen_ml_graph(8)\n",
    "Q_ml_maxcut = maxcut_hamiltonian_eigenvalue(ml)\n",
    "#Q_ml_hen_young = hen_young_hamiltonian_eigenvalue(ml)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hen & Young hypothesized that Q2 along the adiabatic evolution will be a good differentiator for isomorphism\n",
    "I suppose that the expectation involved in Q2 is with respect to the sampled vector with the least energy at a certain point during evolution. Here let's just try to use $E[H] = min(\\lambda)$ when s=1 since they had the best result at s=1 anyways, we will switch to Q2 later"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "numruns = 30\n",
    "e_cl = solve(Q_cl_maxcut, numruns = numruns)[::-1] #revert because the first energy in the iter is the last\n",
    "e_ml = solve(Q_ml_maxcut, numruns = numruns)[::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x123f13f98>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(np.arange(0.0, 1.0, 1/numruns), e_cl,label=\"Circular Ladder\")\n",
    "ax.plot(np.arange(0.0, 1.0, 1/numruns), e_ml,label=\"Moebius Ladder\")\n",
    "ax.set_xlabel(\"s\")\n",
    "ax.set_ylabel(\"Energy\")\n",
    "ax.set_title(\"Energy vs. s\")\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "no embedding found",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-16-47eb756a968b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mnumruns\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m50\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0me_cl\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msolve\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mQ_cl_hen_young\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnumruns\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnumruns\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;31m#revert because the first energy in the iter is the last\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0me_ml\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msolve\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mQ_ml_hen_young\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnumruns\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnumruns\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-2-6e8f7be557c9>\u001b[0m in \u001b[0;36msolve\u001b[0;34m(Q, chainstrength, numruns)\u001b[0m\n\u001b[1;32m     66\u001b[0m     \u001b[0;31m# Run the QUBO on the solver from your config file\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     67\u001b[0m     \u001b[0msampler\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mEmbeddingComposite\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mDWaveSampler\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msolver\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0;34m'qpu'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 68\u001b[0;31m     \u001b[0mresponse\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msampler\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msample_qubo\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mQ\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchain_strength\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mchainstrength\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnum_reads\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnumruns\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     69\u001b[0m     \u001b[0menergies\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0miter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresponse\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     70\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/dimod/core/sampler.py\u001b[0m in \u001b[0;36msample_qubo\u001b[0;34m(self, Q, **parameters)\u001b[0m\n\u001b[1;32m    239\u001b[0m         \"\"\"\n\u001b[1;32m    240\u001b[0m         \u001b[0mbqm\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mBinaryQuadraticModel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfrom_qubo\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mQ\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 241\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msample\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbqm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mparameters\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/dwave/system/composites/embedding.py\u001b[0m in \u001b[0;36msample\u001b[0;34m(self, bqm, chain_strength, chain_break_method, chain_break_fraction, embedding_parameters, return_embedding, warnings, **parameters)\u001b[0m\n\u001b[1;32m    240\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    241\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mbqm\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0membedding\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 242\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"no embedding found\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    243\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    244\u001b[0m         bqm_embedded = embed_bqm(bqm, embedding, target_adjacency,\n",
      "\u001b[0;31mValueError\u001b[0m: no embedding found"
     ]
    }
   ],
   "source": [
    "numruns = 50\n",
    "e_cl = solve(Q_cl_hen_young, numruns = numruns)[::-1] #revert because the first energy in the iter is the last\n",
    "e_ml = solve(Q_ml_hen_young, numruns = numruns)[::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  1.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0. -1. -0.  0.  0. -0. -0.]\n",
      " [ 0.  0. -0. -1.  0.  0. -0. -0.]\n",
      " [ 0.  0.  0.  0.  1.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  1.  0.  0.]\n",
      " [ 0.  0. -0. -0.  0.  0. -1. -0.]\n",
      " [ 0.  0. -0. -0.  0.  0. -0. -1.]]\n"
     ]
    },
    {
     "ename": "ValueError",
     "evalue": "cannot reshape array of size 32 into shape (8,8)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-21-5405c7bd78a9>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mres\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0mtest\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mI\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mZ\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0mtest\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mtest\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mI\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      8\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtest\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: cannot reshape array of size 32 into shape (8,8)"
     ]
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(np.arange(0.0, 1.0, 1/numruns), e_cl,label=\"Circular Ladder\")\n",
    "ax.plot(np.arange(0.0, 1.0, 1/numruns), e_ml,label=\"Moebius Ladder\")\n",
    "ax.set_xlabel(\"s\")\n",
    "ax.set_ylabel(\"Energy\")\n",
    "ax.set_title(\"Energy vs. s\")\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  0.  0.  0.]\n",
      " [ 0. -1.  0. -0.]\n",
      " [ 0.  0.  1.  0.]\n",
      " [ 0. -0.  0. -1.]]\n"
     ]
    }
   ],
   "source": [
    "a = np.identity(2)\n",
    "b = np.array([[1,0],[0,-1]])\n",
    "ab = np.kron(a,b)\n",
    "abb = (a[:, None, :, None]*b[None, :, None, :]).reshape(4,4)\n",
    "print(abb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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