example_exact_time_evolution.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "## import essential modules \n",
    "import qumcmc \n",
    "from qumcmc.basic_utils import *\n",
    "# from qumcmc.energy_models import IsingEnergyFunction\n",
    "from qumcmc.energy_models import IsingEnergyFunction, Exact_Sampling\n",
    "\n",
    "from qumcmc.classical_mcmc_routines import classical_mcmc\n",
    "#from qumcmc.quantum_mcmc_routines_qulacs import quantum_enhanced_mcmc     #for Qulacs Simulator backend (** Faster )\n",
    "from qumcmc.quantum_mcmc_routines_qulacs_exact import quantum_mcmc_exact\n",
    "#  from qumcmc.quantum_mcmc_routines_qiskit import quantum_enhanced_mcmc   #for qiskit Aer's Simulator backend \n",
    "\n",
    "from qumcmc.trajectory_processing import calculate_running_js_divergence, calculate_running_kl_divergence, calculate_runnning_magnetisation, get_trajectory_statistics\n",
    "from scipy.linalg import expm\n",
    "from qulacs.gate import DenseMatrix, SparseMatrix\n",
    "from qulacs import QuantumState\n",
    "from qumcmc.quantum_mcmc_routines_qulacs import quantum_enhanced_mcmc\n",
    "from qumcmc.quantum_mcmc_qulacs_2 import quantum_enhanced_mcmc_2\n",
    "from qumcmc.quantum_mcmc_routines_qulacs_exact import quantum_mcmc_exact\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define the model # seed 4\n",
    "seed_num=4\n",
    "np.random.seed(seed_num)#(610358)# should always be in the same cell!  ## best seed -> 610358\n",
    "n_spins = 10\n",
    "\n",
    "## construct problem Hamiltonian ##\n",
    "shape_of_J=(n_spins,n_spins)\n",
    "\n",
    "## defining J matrix (mutual 1-1 interaction)\n",
    "J =  np.round(np.random.choice([+1, 0, -1], size=(n_spins, n_spins)), decimals=2) \n",
    "J =  np.random.uniform(low= -2, high= 2, size= shape_of_J )\n",
    "J = 0.5 * (J + J.transpose() )\n",
    "J = np.round( J - np.diag(np.diag(J)) , decimals= 3)\n",
    "\n",
    "#evaluating J for BAS dataset\n",
    "#J=-1*wt#np.array([[0,0,0,4],[0,0,4,0],[0,4,0,0],[4,0,0,0]])\n",
    "# defining h\n",
    "#h = np.round(0.5 * np.random.randn(n_spins), decimals=2)\n",
    "h = np.round(np.random.uniform(low= -1, high = 1, size= (n_spins)), decimals=2)\n",
    "#h=np.zeros(np.shape(J)[0])\n",
    "# instantiate the model\n",
    "model = IsingEnergyFunction(J, h, name= 'my_model')\n",
    "#model=IsingEnergyFunction(J,h,name=f\"BAS data of gridsize {np.shape(J)[0]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set beta\n",
    "beta = 1.0#1.100209\n",
    "\n",
    "## run exact sampling over all possible configurations \n",
    "exact_sampled_model = Exact_Sampling(model, beta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=============================================\n",
      "     MODEL : my_model |  beta : 1.0\n",
      "=============================================\n",
      "Num Most Probable States : 12\n",
      "Entropy : 2.839932901889561\n",
      "---------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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6q1PrKfpBuu5qo28S2X//U4Vq7AHuzczDuvRFxFWFahzyJPCqSfcyI+KRw1++IlXOgYrhdDfwucy8a8I+vL1QjVq9T55k+J8/wBci4hYmdyZY2Ce5m7nlAhARL2fyw71vrNM6NXoFPAi8ZsqDtyI9Kfq/Ap7KzB+sdltz1PoPdD+LOyesuzYzryhUZ/BzICK+zRLhVKqXS0S8FPhejk3q3q/bWOJBX60HvLV+/v32FtaZYOo+tRToWr6IeAfwlcz8swnr3pmZ/2UBuyXqhpPacEQEekR8ITO3NVSnSq+AGoY4ZrW6e06pXeUcqKXUg/EZNYo94J1Rp0oX2RrHbJpm7qFHxCunrQJOX4d1an3smxh4pL1ax6yvNam756uBD0REke6eldsz+JtTpQfjSyn5gHcpt9E9h1q1NXDMJhdv5Qo9Iv6abgS/ST1AzszMIg+RKtb5EdN7BZyfmc8rVOcKup4mO3mm58Ymugd8OzPzmgI1qhyzvtbg3T0rngNVPovQt2fag/GTMvPYAjWWfMCbmUUuLmt1ka1xzFa0Xw0F+r3AmzLzwQnrSj5AqlWnyse+o85Ie1WOWb+9B+geJH5/bPnxwN711J5an0Wo9GC81gPe/8v0LrL/KTNPLFRn8GO2Es3ccgGuYnqf2XeuwzqXA9Ouat5UsE6Nkfauos4xgzrdPa+iTntqjei3AzgBOCyc6MauL+FTwAuBST1mPl2oBtTrIruD4Y/ZsjVzha6ViYhzgN+l+xj7YSPt5fqcHWnNDZq0EhFxMXAl3S2Xw96cMvPGBe3amlWzi+xa1FSgx4KnbItK04+V7hUQFUePnFB7kGMWCxo0qXR7Fv3mFBGvzcz/VWhbVXsfxcBTEA7dmWBF+9RKoEc3zdlL6P60G324dxHwYGa+q8I+VBloqnSdiDqjR06pXbotp7PAQZOGOAcW9ebU1y41/k2tB7yn0N3yeA3dzzyAnwD+CNg+Pv7OKuoM3plgRfvVUKDXmrKtyvRjFXsFDD5yYK1j1te6h4EHTap4DpxOhTeniNg1bRVwVmauemySig94B5+CsN9mlakol6ulh6K1pjmrMv0Y9cak+B3g7PErl+hHDgRKjBxY65hBnUGTarXnRoafHhDgl4BfA8bHPT/0l1sJtR7w1piCEOpNRbksLQX6JdSZ5qzW9GO1egXUGDmw1jGDOoMm1WpPrRH9bgd+kJlfHl/RX1mXUGuwuRpTEEK9qSiXpZlbLodEhWnOWhIR7wXeQncvcHzkwJsz8zcXtW8rFWtw0KSViIrTA9ZQ4wFvTJ6C8FFgF4WnIFxkZ4Kp+9RaoE9ScQyHKtN1lW5PRGwBzmXg0SOn1G5qirPS7WnlzelIsshz+kgJ9HXZ+6R2naG7eU2pWbqXy/HAe+lCcCPdfdvHgM8D1wzVRW6kfrUp9WqICgPBlawREcfQXaG/kbHuy3RX6D+a8l+LWeQ50Mw99BljODy/YJ2lput6bsE6tdpzqJvXWXTPGyIiinbzqnXMejfT7furD91u62/DXdKve91qC1Q8B6q8OUWFgeBq1Oj9Pl2Hgvfz7O6EFwP/FfinJYpUPqfn1swVesUxHJ5i+nRd/zYzn1+oTq32DN7Nq9Yx62vty8yXLnfdMmvUOgdupXtz+uSEN6ezMnPVb079NgcfCK5Gjb7OxO7Ls9atoE61c3pZMrOJL7oT/x9OWffNgnX+FPiFKeseWYfteXAl69biMeu3dxvwHmDjyLKNwBXAF9dTe4B9K1m3gjp3AT87ZHtq1Oi3dTvdxchRI8uOorsyv6NgnWrn9HK+WrpCrzKGQ1SYrqvfVq327AQeZ3I3rxMz8y0FalQ5Zv32TgC288xtCoC/oOvlcG0WeD5Q8Ry4Dfgi3RX6dw5tn+4K/bWZWWQuzqgwPVyNGv22NgPX0t1CfIJnblEeuoX4zUJ1qp3Ty9FMoGtlanbz0vLUeHNqWUT8JEBmfm/R+1LLERHoUW9quCpTT9VqTw1DHLNY4CBttc6BWqLC9HCla8TkQbM+nxW6Lvf1F3YONBPosfS0YH+YmT9TqM5SU0/9WWZuKlSnVnsG7+ZV65j1tXYw8CBtlduz6BFEB++CV7JGVBo0q+Y5sBwtBXrNKegGn3qqYns+Q9fN65Mc3s3rBZm56m5etY5ZX2vwQdoqngM7qDCCaFQYCK5Gjb5OlUGzap7Ty9FMP3TgfrqBjCZOC1awzkMsMfVUwTq12vMLEwLwAHB7/8tRQq1jBnUGaavVnl+Z8uZ0E/AAUGpI6CcZfiC4GjWg3qBZNc/pubUU6FdRZ1qwHdSZeuoq6rTn8Yh4M/DfM/PHwKExKt7M4aMJrtQO6k3XdQnDD9K2gzrtqTWCaI2B4GoNNnc5dQbN2oFT0GmtqdXNq7ZoYJC2/jnK7wGT3pzekZl3LWrf1rK1OGhWLUdEoEe9qeGKTdc1o85Q07ZV7+Y1xDGLylOdjdUeoj0Le3OKCgPbla7RPy9ZyAxcff0qOTCx9hES6Ot60Kyh6yyym9cAbaky1dkS9YcYbGwhb059/fXWy2XwGbjm2AcH51qtWHpasI1T1q2kzlLTdf1kwTq12jPazevOfvEmuhleinTzqnXMeu+je9D75Ng+nADcQXcvd1UqngOT3pxeDXwgIkrOwzn4QHA1avRqzMBV+5yeWzOBTr1pwWpM1wX12vM2Jnfz+hBwH1Ci326tY3Zom0NPdVarPYO/OfXeyvSB4C5cRzWgzgxcUPecnltLgV5rWrAa03VBvfbU6OZV65hBnanOarWn1jyce4B7M/OwC4WIuGod1QD4BLCnH6NofAaujxesU/OcntsRcQ9d00XEOcDv0t1zPKybV61PJJYUFaY6qyEiLgaupLvlctibU2beWKjO4APB1agxUmthM3At2hER6OE0Z7O211w3r35UwtGeIQsZ/W61ar85RYVZq2rUqFVnrZ1nLd1yWco36K5sBhUVpuvqlW5Pjnwd+r7kp+qmKn3MIuJ04KPA8XT3UgPYFBFP0vVyuLtUrSn1i7YnM5+IiD/m2aFRNMzjmVmrXkP3ic6I8rNWDV5jrM5gM3D1dX6e7jMCxzPSm6bWeTZNM4Ee9aYFqzKVVsX2TO3mFRFFunnVOma9G+mGTLhjbB/OBG4AXrHaAhXPgdOp8+Z0E90nH/95Hj5r1U5g1bNWVapRs84NDHyerUQzt1yi3rRgtabSqtWe+4Ft07p5Zeaqu3nVOmZ9rQenDcAUEfsz88UFatQ6B+5hemh8LDOLhMaMYzZ13VqrsYbqFDnPVqKZK3TgbuBzkz4OHRFvL1jna8BvZ+a9E+oUmUGmV6s9Nbp51TpmAF+IiFvouvSN9nK4CCj1gLdWe44bD3OAzLw9Io4rWOeuiPgIk2et+uo6qlGzTo3zbNlaukKvNS1Yram0arXnvcBb6P4cHe/mdXNm/maBGlWO2cg2tzFhBqbM3F1o+7XOgQ8DL2JyaHwzM4sMNhUVZq2qUaNmnb7WoOfZivaplUDXykXEy5l8YjbfzWutW4uhobXriAj0KDglVDwzw8+b6D6QA4Vn+JljH9bVNGc1j1l0Y5+8l2fm4Uzgsb7WNSXGQFkL50BJUWfWqsFr1KwzYx+cgm61ot7UcIPP8NPXWfgUV1Fo7tJax6yvdStdF7VPZj8qYXSjFV4CnJWZrytQo9Y5MPibU1+nxqxVtY7ZEfP7ObF4Q4Fea1qwiVOczVq3gjq12jP43KW1jlm/vX2Z+dLlrltmjVrnwOBvTv02B29PxWPW1O/ncrXUy6XWlFA1ZviBeu3Zw/S5S59fqEatYwbwrYh4D10IfqevtZEuBEsdt1rt2ZyZ144u6IP9moh4a8E6NdpT65i19vu5PJnZxBfwDuAVU9a9s2CdzXQfXniMbl7HB/p/3wScug7bcy9w2pR1j6ynY9bXOoFuBqY/Bx7vv+7vl52wntpDN4bLe4CNI8s2AlcAXyxYZ/D2VDxmTf1+LvermVsuADF5ooZdmXl/4TqTeoV8foA6g7cnIs4Hvp6Zh40QFxFvzMzPFapT5ZjN2IdiMz3VaE9047hs7+v8VL/4O3Rd8K7JgkMAVGpPrd+bZn4/l2vaJMTrTv9n9k66Wwd39l8BfCYithescwXdpLZJNyb1oQ9+lK5TpT2Z+dlJYd47oUSNWsdsDu8vsZFa7cnMJzLzisx8WWa+oP96eWZeQdeLo4ga7an4e9PU7+ey96uVK/SIeIDJEzUcC9yX5T7y21SdGftQZCqtmm2JpWd6eklmPqdAjWZ+Nv22Bm9Pa783a+EcmKSlh6I1Jmpors6MACw11V2tYwZ1Znpq6WcDddrT1O9NxTrL0lKgXw58KSImTtRgnalqBODl1GkL1Jnp6XLa+dlAnfbUqNFinWVp5pYL/E33pMEnamipTkR8HLghM78yYd2nM/OfFarT1CQaLf1s+u3VaE8zvzc16yxrn1oKdEk6kjXTy0WSjnQGuiQ1wkCXpEYY6JLUCANdkhrx/wFbkDMDlSBQvAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## get the distribution from model\n",
    "bpd = exact_sampled_model.boltzmann_pd\n",
    "\n",
    "## exact sampling summary\n",
    "exact_sampled_model.sampling_summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "steps = 5000\n",
    "cl_chain =classical_mcmc(\n",
    "    n_hops=steps,\n",
    "    model=model,\n",
    "    temperature=1/beta,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "### H_mix\n",
    "from qumcmc.quantum_mcmc_routines_qulacs_exact import create_X_mixer_hamiltonian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "type_mixer_hamiltonian: <class 'qulacs_core.Observable'>\n",
      "list_individual_terms:\n",
      "['X 0 ', 'X 1 ', 'X 2 ', 'X 3 ', 'X 4 ', 'X 5 ', 'X 6 ', 'X 7 ', 'X 8 ', 'X 9 ']\n"
     ]
    }
   ],
   "source": [
    "H_mixer=create_X_mixer_hamiltonian(num_spins=n_spins,\n",
    "                                    weight_individual_pauli=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# aa=H_mixer.get_matrix()\n",
    "# print(type(aa))\n",
    "# aa.toarray()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Run quantum mcmc: exact time evolution\n",
    "steps=100\n",
    "qamcmc_chain_1=quantum_mcmc_exact(n_hops=steps,\n",
    "                                model=model,\n",
    "                                H_mix=H_mixer,\n",
    "                                temperature=1/beta,\n",
    "                                verbose= True)\n",
    "# took ~10 minutes for num_spins=7 and 5K iterations.\n",
    "# using just scipy.linalg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "cl_statistic = get_trajectory_statistics(cl_chain, exact_sampled_model, verbose= False)\n",
    "qumcm1_statistic = get_trajectory_statistics(qamcmc_chain_1, exact_sampled_model, verbose= False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# acceptance prob\n",
    "plt.figure(figsize=(10,10))\n",
    "\n",
    "plt.hist(np.log10(cl_statistic['acceptance_prob']),label= 'classical uniform' ,alpha= 0.8, bins= 20)\n",
    "plt.hist(np.log10(qumcm1_statistic['acceptance_prob']),label= 'quantum-exact, default gamma range (0.2,0.6)' , alpha= 0.8, bins= 20)\n",
    "\n",
    "# plt.xscale(\"log\")\n",
    "\n",
    "plt.xlabel(\"Acceptance Probabilities | scale: log10\")\n",
    "# plt.ylabel(\"Hamming Distance\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# energy-difference\n",
    "plt.figure(figsize=(10,10))\n",
    "\n",
    "plt.hist(cl_statistic['energy'],label= 'classical uniform' ,alpha= 0.8, bins= 20)\n",
    "plt.hist(qumcm1_statistic['energy'],label= 'quantum-exact,gamma range (0.2,0.6)' , alpha= 0.8, bins= 20)\n",
    "# plt.xscale(\"log\")\n",
    "\n",
    "plt.xlabel(\"Energy-Difference Statistics\")\n",
    "# plt.ylabel(\"Hamming Distance\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# hamming distance\n",
    "plt.figure(figsize=(10,10))\n",
    "\n",
    "plt.hist(cl_statistic['hamming'],label= 'classical uniform' ,alpha= 0.8, bins= 20)\n",
    "plt.hist(qumcm1_statistic['hamming'],label= 'quantum-exact,gamma range (0.2,0.6)' , alpha= 0.8, bins= 20)\n",
    "# plt.xscale(\"log\")\n",
    "\n",
    "plt.xlabel(\"Hamming-Distance Statistics\")\n",
    "# plt.ylabel(\"Hamming Distance\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 5000/5000 [00:02<00:00, 1780.76it/s]\n",
      "100%|██████████| 5000/5000 [00:02<00:00, 1812.13it/s]\n"
     ]
    }
   ],
   "source": [
    "# magnetisation\n",
    "magnetization_model = exact_sampled_model.get_observable_expectation(magnetization_of_state)\n",
    "magnetization_c = calculate_runnning_magnetisation(cl_chain)\n",
    "magnetization_q1 = calculate_runnning_magnetisation(qamcmc_chain_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,8))\n",
    "plt.plot(magnetization_c, label= 'classical-uniform')\n",
    "plt.plot(magnetization_q1, label= 'quantum-exact, gammarange=(0.2,0.6)')\n",
    "plt.axhline(magnetization_model, label= 'actual value')\n",
    "plt.xlabel(\"iterations\")\n",
    "plt.ylabel(\"magnetisation\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# KL divergence\n",
    "kldiv_c = calculate_running_kl_divergence(exact_sampled_model.boltzmann_pd, cl_chain)\n",
    "kldiv_q1 = calculate_running_kl_divergence(exact_sampled_model.boltzmann_pd, qamcmc_chain_1)\n",
    "\n",
    "plt.figure(figsize=(10,8))\n",
    "plt.plot(kldiv_c, label= 'classical-uniform')\n",
    "plt.plot(kldiv_q1, label= 'quantum-exact, old gmma range (0.2,0.6)')\n",
    "plt.xlabel(\"iterations \")\n",
    "plt.ylabel(\"KL divergence\")\n",
    "plt.yscale('log')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "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": "3.8.8"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}