QAEAnsatz_scaling.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f6538cfa",
   "metadata": {},
   "outputs": [],
   "source": [
    "import time\n",
    "import itertools\n",
    "import numpy as np\n",
    "\n",
    "import qiskit\n",
    "from qiskit import *\n",
    "from qiskit.quantum_info import Statevector\n",
    "from qiskit.algorithms.optimizers import COBYLA, L_BFGS_B, SPSA\n",
    "from qiskit.opflow.state_fns import StateFn, CircuitStateFn\n",
    "from qiskit.providers.aer import StatevectorSimulator, AerSimulator\n",
    "\n",
    "from qiskit.opflow import CircuitSampler\n",
    "\n",
    "from qiskit.ignis.mitigation.measurement import CompleteMeasFitter # you will need to pip install qiskit-ignis\n",
    "from qiskit.ignis.mitigation.measurement import complete_meas_cal\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.ticker import MaxNLocator\n",
    "from matplotlib.colors import BoundaryNorm\n",
    "cmap = plt.get_cmap(\"plasma\") #'viridis'\n",
    "\n",
    "from modules.utils import *\n",
    "\n",
    "from qae import *\n",
    "\n",
    "import datetime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ec3bfcd7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.17.4 1.20.1\n"
     ]
    }
   ],
   "source": [
    "print(qiskit.__version__, np.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1772efe-0e0e-4a47-bdd8-70c7b45e298c",
   "metadata": {},
   "source": [
    "# Plotting results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a37d62d5-4f62-4625-99fd-00d92a378192",
   "metadata": {},
   "outputs": [],
   "source": [
    "#plt.rc('text', usetex=True)\n",
    "plt.rc('font', family='serif',size=16)\n",
    "#plt.rc('font', family='serif')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "d5b31d33-f436-4d35-8d41-123d22fb9094",
   "metadata": {},
   "outputs": [],
   "source": [
    "temp = np.load(\"data/QAEAnsatz_scaling_losses.npz\", allow_pickle=True)\n",
    "losses0 = temp[\"losses\"]\n",
    "Ls = temp[\"Ls\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "217cf796-6a28-467d-bc84-61d18915d53a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# It took 51 hrs to obtain these results.\n",
    "# However, you can confirm the validity by just executing the circuit once for the optimized parameters (as demonstrated down below)\n",
    "temp2 = np.load(\"data/QAEAnsatz_scaling_MPS_script_L-32_tracked-losses_results.npz\",allow_pickle=True)\n",
    "losses32 = temp2[\"losses\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "5477bd42-34dd-4fba-bf5d-6fd3d92eb900",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3, 4, 8, 16, 32]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ls = list(Ls)\n",
    "Ls += [32]\n",
    "Ls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "723edddf-02a1-4b05-b04a-88c76829ccf3",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-38-2bc784230189>:18: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n",
      "  plt.tight_layout()\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6,5))\n",
    "for i in range(4):\n",
    "    ax.plot(np.array(losses0[i]),label=f\"L = {Ls[i]}\")\n",
    "ax.plot(losses32[1],label=f\"L = {Ls[-1]}\")\n",
    "ax.legend()\n",
    "\n",
    "left, bottom, width, height = [0.4,0.61, 0.25, 0.325]\n",
    "ax2 = fig.add_axes([left, bottom, width, height])\n",
    "for i in range(4):\n",
    "    ax2.plot(np.array(losses0[i]),label=f\"L = {Ls[i]}\")\n",
    "ax2.plot(losses32[1],label=f\"L = {Ls[-1]}\")\n",
    "ax2.set_yscale(\"log\")\n",
    "\n",
    "#ax.set_xlim(0,405)\n",
    "#ax.set_yscale(\"log\")\n",
    "ax.set_ylabel(\"cost\", fontsize=16)\n",
    "ax.set_xlabel(\"iteration\", fontsize=16)\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"plots/QAEAnsatz_Ising-scaling.pdf\")\n",
    "plt.savefig(\"plots/QAEAnsatz_Ising-scaling.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33c95c35-a8f8-411b-a987-b8522d39dd55",
   "metadata": {},
   "source": [
    "# Size scaling with exact diagonalization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1bf3dbbb",
   "metadata": {},
   "outputs": [],
   "source": [
    "#IBMQ.load_account() # this then automatically loads your saved account\n",
    "#provider = IBMQ.get_provider(hub='ibm-q-research')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e1f4711d",
   "metadata": {},
   "outputs": [],
   "source": [
    "#device = provider.backend.ibmq_rome # 6 bogota ; 4 rome"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "afebca63",
   "metadata": {},
   "outputs": [],
   "source": [
    "### Real device execution:\n",
    "#backend = device \n",
    "\n",
    "### Simulation with noise profile from real device\n",
    "#backend = qiskit.providers.aer.AerSimulator.from_backend(device)\n",
    "\n",
    "### Simulation without noise\n",
    "backend = qiskit.providers.aer.AerSimulator()\n",
    "#backend = StatevectorSimulator()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a984702f",
   "metadata": {},
   "outputs": [],
   "source": [
    "### Preliminaries\n",
    "L = 5\n",
    "num_trash = 2\n",
    "anti = 1 # 1 for ferromagnetic Ising model, -1 for antiferromagnet\n",
    "\n",
    "filename = \"data/QAEAnsatz_scaling\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c811458e",
   "metadata": {},
   "outputs": [],
   "source": [
    "gz = 0\n",
    "gx = 0.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e5a16420",
   "metadata": {},
   "outputs": [],
   "source": [
    "ED_state, ED_E, ham = ising_groundstate(L, anti, np.float32(gx), np.float32(gz))\n",
    "Sen = ED_E\n",
    "Smag = ED_state.T.conj()@Mag(L,anti)@ED_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "747c613d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def prepare_circuit(thetas, L=6, num_trash=2, init_state=None, measurement=True,vqe=False):\n",
    "    # QAE ansatz\n",
    "    QAE_circ = QAEAnsatz(num_qubits = L, num_trash_qubits= num_trash, trash_qubits_idxs = list(range(num_trash)), measure_trash=measurement).assign_parameters(thetas)\n",
    "    # initialize state vector\n",
    "    initcirc = QuantumCircuit(QuantumRegister(L,\"q\"),ClassicalRegister(num_trash, 'c'))\n",
    "    initcirc.initialize(init_state, initcirc.qubits)\n",
    "    # compose circuits\n",
    "    fullcirc = initcirc.compose(QAE_circ)\n",
    "    return fullcirc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "2161ba41",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1591.6x1228.08 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circ = prepare_circuit(thetas = np.random.rand(2*L+2), L = L, init_state = ED_state)\n",
    "circ.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "id": "42fd59a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "### Execute circuit\n",
    "count = 0\n",
    "def run_circuit(thetas, L, num_trash, init_state, vqe=False, shots=100, meas_fitter = None):\n",
    "    #global count\n",
    "    #count += 1\n",
    "    #print(count, \"thetas: \", thetas)\n",
    "    circ = prepare_circuit(thetas, L, num_trash, init_state, vqe=vqe)\n",
    "    tcirc = qiskit.transpile(circ, backend)\n",
    "    # Execute the circuit \n",
    "    job_sim = backend.run(tcirc, shots=shots,seed_simulator=333, seed_transpiler=444) # , seed_simulator=123, seed_transpiler=234 fix seed to make it reproducible\n",
    "    result = job_sim.result()\n",
    "    # Results without mitigation\n",
    "    counts = result.get_counts()\n",
    "    if meas_fitter != None:\n",
    "        # Get the filter object\n",
    "        meas_filter = meas_fitter.filter\n",
    "\n",
    "        # Results with mitigation\n",
    "        mitigated_results = meas_filter.apply(result)\n",
    "        counts = mitigated_results.get_counts(0)\n",
    "    return counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b179e2a7",
   "metadata": {},
   "outputs": [],
   "source": [
    "res = run_circuit(thetas = np.random.rand(num_trash*L+num_trash), L = L, num_trash = num_trash, init_state = ED_state, shots=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "77c971be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'01': 182, '11': 284, '10': 188, '00': 346}"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "ce0f7986",
   "metadata": {},
   "outputs": [],
   "source": [
    "def count_ones(string):\n",
    "    return np.sum([int(_) for _ in string])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "bc2d26b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "count_ones(\"01010111\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "8e919acc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['01', '11', '10', '00']"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[_ for _ in res]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "d2d4078d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['01', '11', '10']"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[_ for _ in res if _ != \"0\" * num_trash]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "03f8cd10",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "938"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum([res[_]*count_ones(_) for _ in res if _ != \"0\" * num_trash]) # all measurement results except \"000\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "d69d0d57",
   "metadata": {},
   "outputs": [],
   "source": [
    "### Optimize circuit\n",
    "def cost_function_single(thetas, L, num_trash, init_state, shots=1000, vqe=True, param_encoding=False, x=0, meas_fitter=None):\n",
    "    \"\"\" Optimizes circuit \"\"\"\n",
    "    if param_encoding: thetas = feature_encoding(thetas, x) \n",
    "    out = run_circuit(thetas, L, num_trash, init_state, vqe=vqe, shots=shots, meas_fitter=meas_fitter)\n",
    "    cost = np.sum([out[_]*count_ones(_) for _ in out if _ != \"0\" * num_trash]) # all measurement results except \"000\"\n",
    "    return cost/shots\n",
    "\n",
    "def cost_function(thetas, L, num_trash, init_states, shots=1000, vqe=True, param_encoding=False, x=0, meas_fitter=None):\n",
    "    \"\"\" Optimizes circuit \"\"\"\n",
    "    cost = 0.\n",
    "    for init_state in init_states:\n",
    "        cost += cost_function_single(thetas, L, num_trash, init_state, shots, vqe, param_encoding, meas_fitter=meas_fitter)\n",
    "    return cost/len(init_states)\n",
    "\n",
    "def optimize(init_states, L=6, num_trash=2, thetas=None, shots=1000, max_iter=400, vqe=True, param_encoding=False, x=0, pick_optimizer = None,\n",
    "            meas_fitter=None):\n",
    "    if thetas is None:\n",
    "        n_params = (num_trash*L+num_trasg)*2 if param_encoding else (num_trash*L+num_trash)\n",
    "        thetas = np.random.uniform(0, 2*np.pi, n_params) # initial parameters without feature encoding\n",
    "        \n",
    "    #print(\"Initial cost: {:.3f}\".format(cost_function(thetas, L, num_trash, init_states, shots, vqe, param_encoding, x)))\n",
    "    \n",
    "    counts, values, accepted = [], [], []\n",
    "    def store_intermediate_result(eval_count, parameters, mean, std, ac):\n",
    "        # counts.append(eval_count)\n",
    "        values.append(mean)\n",
    "        accepted.append(ac)\n",
    "\n",
    "    # Initialize optimizer\n",
    "    if pick_optimizer == \"cobyla\":\n",
    "        optimizer = COBYLA(maxiter=max_iter, tol=0.0001)\n",
    "    if pick_optimizer == \"adam\" or pick_optimizer == \"ADAM\":\n",
    "        optimizer = qiskit.algorithms.optimizers.ADAM(maxiter=max_iter)\n",
    "    # optimizer = L_BFGS_B(maxfun=300, maxiter=max_iter)#, factr=10, iprint=- 1, epsilon=1e-08)\n",
    "    if pick_optimizer == \"spsa\" or pick_optimizer == None:\n",
    "        optimizer = SPSA(maxiter=max_iter,\n",
    "                         #blocking=True,\n",
    "                         callback=store_intermediate_result,\n",
    "                         #learning_rate=0.3,\n",
    "                         #perturbation=0.1\n",
    "                         ) # recommended from qiskit (first iteraction takes quite long)\n",
    "                           # to reduce time figure out optimal learning rate and perturbation in advance\n",
    "    start_time = time.time()\n",
    "    ret = optimizer.optimize(\n",
    "                            num_vars=len(thetas),\n",
    "                            objective_function=(lambda thetas: cost_function(thetas, L, num_trash, init_states, shots, vqe, param_encoding, x, meas_fitter=meas_fitter)),\n",
    "                            initial_point=thetas\n",
    "                            )\n",
    "    print(\"Time: {:.5f} sec\".format(time.time()-start_time))\n",
    "    print(ret)\n",
    "    return ret[0], values, accepted\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "fbae6044",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time: 9.77129 sec\n",
      "(array([-0.27620814, -0.07832044,  1.52004177, -0.21485598, -1.55547985,\n",
      "        3.17875132,  1.62009326,  4.51055365,  1.37937503,  4.38401314,\n",
      "       -2.03482615,  4.54135205]), 0.027, 360)\n"
     ]
    }
   ],
   "source": [
    "thetas_opt_mitigated, losses, accepted = optimize([ED_state], max_iter=120, L=5, meas_fitter=None) #, pick_optimizer=\"adam\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "72352aff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f2b35a0d160>]"
      ]
     },
     "execution_count": 24,
     "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": [
    "plt.plot(losses)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fa5ac38",
   "metadata": {},
   "source": [
    "# Scaling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "41a8c424",
   "metadata": {},
   "outputs": [],
   "source": [
    "Ls = [3,4,8,16] #note that L=16 may take up few hours, it is faster with MPS further below\n",
    "max_iter = [400] * len(Ls)\n",
    "num_trashs = np.log(Ls)/np.log(2)\n",
    "num_trashs = np.array(num_trashs, dtype=\"int\")\n",
    "gz = 0\n",
    "gx = 0.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "e8290a08",
   "metadata": {},
   "outputs": [],
   "source": [
    "losses = [None] * len(Ls); accepted = [None] * len(Ls); thetas_opt= [None] * len(Ls)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6e32783d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# may have to re-run some sizes when it gets stuck in local minima\n",
    "for j,(L,num_trash) in enumerate(zip(Ls,num_trashs)):\n",
    "    print(L,num_trash)\n",
    "    ED_state, ED_E, ham = ising_groundstate(L, anti, np.float32(gx), np.float32(gz))\n",
    "    thetas_opt[j], losses[j], accepted[j] = optimize([ED_state], max_iter=max_iter[j], L=L, num_trash=num_trash, meas_fitter=None) #, pick_optimizer=\"adam\")\n",
    "    plt.plot(losses[j])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "db52a4a1",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.savez(filename + \"_losses\", losses=losses, thetas_opt = thetas_opt, Ls=Ls, max_iter=max_iter, num_trashs=num_trashs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "5ff91c07",
   "metadata": {},
   "outputs": [],
   "source": [
    "temp = np.load(filename + \"_losses.npz\", allow_pickle=True)\n",
    "losses0 = temp[\"losses\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "ea34fb7d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'iterations')"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6,5))\n",
    "for i in range(4):\n",
    "    ax.plot(np.array(losses0[i]) + 1e-4,label=f\"L = {Ls[i]}\")\n",
    "ax.legend()\n",
    "ax.set_xlim(0,400)\n",
    "ax.set_yscale(\"log\")\n",
    "ax.set_yticks([1,1e-1,1e-2,1e-3,1e-4])\n",
    "ax.set_yticklabels([\"$10^{}$\".format(i) for i in range(4)] + [\"0.0\"])\n",
    "ax.set_ylabel(\"cost\", fontsize=16)\n",
    "ax.set_xlabel(\"iterations\", fontsize=16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "119c6d10",
   "metadata": {},
   "outputs": [],
   "source": [
    "min_losses = [np.min(l) for l in losses0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "5f64ce78",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.0, 0.0, 0.0, 0.0]"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min_losses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "70c3bd43",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f2b2de206a0>]"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6,5))\n",
    "ax.plot(Ls, min_losses,\"x--\")\n",
    "#ax.set_yscale(\"log\")\n",
    "#ax.set_xscale(\"log\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03da7080-c5d2-4da3-9d5d-f0024dcd7536",
   "metadata": {},
   "source": [
    "# 32 Qubits result from cluster re-evaluated\n",
    "To confirm we are not bullshitting w/o having to re-run the script for 50+ hours (without loss tracking during optimization 24 hrs), you can re-evaluate with the optimized parameters. For this result with 32 qubits we need to use MPS."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "63604d29",
   "metadata": {},
   "outputs": [],
   "source": [
    "def DMRG_Ising(L, J, g, chi_max=30, bc_MPS='finite'):\n",
    "    print(\"finite DMRG, transverse field Ising model\")\n",
    "    print(\"L={L:d}, g={g:.2f}\".format(L=L, g=g))\n",
    "    model_params = dict(L=L, J=J, g=g, bc_MPS=bc_MPS, conserve=None)\n",
    "    M = TFIChain(model_params)\n",
    "    product_state = [\"up\"] * M.lat.N_sites\n",
    "    psi = MPS.from_product_state(M.lat.mps_sites(), product_state, bc=M.lat.bc_MPS)\n",
    "    dmrg_params = {\n",
    "        'mixer': None,  # setting this to True helps to escape local minima\n",
    "        'max_E_err': 1.e-10,\n",
    "        'trunc_params': {\n",
    "            'chi_max': chi_max,\n",
    "            'svd_min': 1.e-10\n",
    "        },\n",
    "        'combine': True\n",
    "    }\n",
    "    info = dmrg.run(psi, M, dmrg_params)  # the main work...\n",
    "    E = info['E']\n",
    "    print(\"E = {E:.13f}\".format(E=E))\n",
    "    print(\"final bond dimensions: \", psi.chi)\n",
    "    mag_x = np.sum(psi.expectation_value(\"Sigmax\"))\n",
    "    mag_z = np.sum(psi.expectation_value(\"Sigmaz\"))\n",
    "    print(\"magnetization in X = {mag_x:.5f}\".format(mag_x=mag_x))\n",
    "    print(\"magnetization in Z = {mag_z:.5f}\".format(mag_z=mag_z))\n",
    "    #if L < 20:  # compare to exact result\n",
    "    #    from tfi_exact import finite_gs_energy\n",
    "    #    E_exact = finite_gs_energy(L, 1., g)\n",
    "    #    print(\"Exact diagonalization: E = {E:.13f}\".format(E=E_exact))\n",
    "    #    print(\"relative error: \", abs((E - E_exact) / E_exact))\n",
    "    return E, psi #, M\n",
    "\n",
    "### Preliminaries\n",
    "qiskit_chi = 100\n",
    "L = 8\n",
    "num_trash = int(np.log(L)/np.log(2))\n",
    "anti = 1 # 1 for ferromagnetic Ising model, -1 for antiferromagnet\n",
    "g = 0.05\n",
    "J=anti\n",
    "filename = \"data/QAEAnsatz_scaling_MPS_script_L-32_tracked-losses\"\n",
    "\n",
    "backend = qiskit.providers.aer.AerSimulator(method=\"matrix_product_state\",\n",
    "                                            precision=\"single\",\n",
    "                                            matrix_product_state_max_bond_dimension = qiskit_chi,\n",
    "                                            matrix_product_state_truncation_threshold = 1e-10,\n",
    "                                            #mps_sample_measure_algorithm = \"mps_apply_measure\", #alt: \"mps_probabilities\" \n",
    "                                           )\n",
    "\n",
    "from qiskit.utils import algorithm_globals\n",
    "algorithm_globals.random_seed = 333\n",
    "\n",
    "def qiskit_state(psi0):\n",
    "    # G is only the local tensor (not multiplied by any singular values) - see https://tenpy.readthedocs.io/en/latest/reference/tenpy.networks.mps.html\n",
    "    A_list = [psi0.get_B(i, form=\"G\").to_ndarray().transpose([1,0,2]) for i in range(L)]\n",
    "    for i,A in enumerate(A_list):\n",
    "        A_list[i] = (A[0], A[1])\n",
    "    S_list = [psi0.get_SR(i) for i in range(L-1)] # skip trivial last bond; hast to be of size L-1\n",
    "    return (A_list, S_list)\n",
    "\n",
    "def prepare_circuit(thetas, L=6, num_trash=2, init_state=None, measurement=True,vqe=False):\n",
    "    # QAE ansatz\n",
    "    QAE_circ = QAEAnsatz(num_qubits = L, num_trash_qubits= num_trash, trash_qubits_idxs = list(range(L//2-1,L//2-1+num_trash)), measure_trash=measurement).assign_parameters(thetas)\n",
    "    # initialize state vector\n",
    "    initcirc = QuantumCircuit(QuantumRegister(L,\"q\"),ClassicalRegister(num_trash, 'c'))\n",
    "    if init_state != None:\n",
    "        initcirc.set_matrix_product_state(qiskit_state(init_state))\n",
    "    # compose circuits\n",
    "    fullcirc = initcirc.compose(QAE_circ)\n",
    "    return fullcirc\n",
    "\n",
    "### Execute circuit\n",
    "count = 0\n",
    "def run_circuit(thetas, L, num_trash, init_state, vqe=False, shots=100, meas_fitter = None):\n",
    "    #global count\n",
    "    #count += 1\n",
    "    #print(count, \"thetas: \", thetas)\n",
    "    #print(L, num_trash)\n",
    "    circ = prepare_circuit(thetas, L, num_trash, init_state, vqe=vqe)\n",
    "    #circ.draw(\"mpl\")\n",
    "    #tcirc = qiskit.transpile(circ, backend)\n",
    "    # Execute the circuit \n",
    "    job_sim = backend.run(circ, shots=shots, seed_simulator=333, seed_transpiler=444) #fix seed to make it reproducible\n",
    "    result = job_sim.result()\n",
    "    # Results without mitigation\n",
    "    counts = result.get_counts()\n",
    "    if meas_fitter != None:\n",
    "        # Get the filter object\n",
    "        meas_filter = meas_fitter.filter\n",
    "\n",
    "        # Results with mitigation\n",
    "        mitigated_results = meas_filter.apply(result)\n",
    "        counts = mitigated_results.get_counts(0)\n",
    "    return counts\n",
    "\n",
    "def count_ones(string):\n",
    "    return np.sum([int(_) for _ in string])\n",
    "\n",
    "### Optimize circuit\n",
    "def cost_function_single(thetas, L, num_trash, init_state, shots=1000, vqe=True, param_encoding=False, x=0, meas_fitter=None):\n",
    "    \"\"\" Optimizes circuit \"\"\"\n",
    "    if param_encoding: thetas = feature_encoding(thetas, x) \n",
    "    out = run_circuit(thetas, L, num_trash, init_state, vqe=vqe, shots=shots, meas_fitter=meas_fitter)\n",
    "    cost = np.sum([out[_]*count_ones(_) for _ in out if _ != \"0\" * num_trash]) # all measurement results except \"000\"\n",
    "    return cost/shots\n",
    "\n",
    "def cost_function(thetas, L, num_trash, init_states, shots=1000, vqe=True, param_encoding=False, x=0, meas_fitter=None):\n",
    "    \"\"\" Optimizes circuit \"\"\"\n",
    "    cost = 0.\n",
    "    for init_state in init_states:\n",
    "        cost += cost_function_single(thetas, L, num_trash, init_state, shots, vqe, param_encoding, meas_fitter=meas_fitter)\n",
    "    return cost/len(init_states)\n",
    "\n",
    "def optimize(init_states, L=6, num_trash=2, thetas=None, shots=1000, max_iter=400, vqe=True, param_encoding=False, x=0, pick_optimizer = None,\n",
    "            meas_fitter=None):\n",
    "    if thetas is None:\n",
    "        n_params = (num_trash*L+num_trasg)*2 if param_encoding else (num_trash*L+num_trash)\n",
    "        thetas = np.random.uniform(0, 2*np.pi, n_params) # initial parameters without feature encoding\n",
    "        \n",
    "    #print(\"Initial cost: {:.3f}\".format(cost_function(thetas, L, num_trash, init_states, shots, vqe, param_encoding, x)))\n",
    "    \n",
    "    counts, values, accepted = [], [], []\n",
    "    def store_intermediate_result(eval_count, parameters, mean, std, ac):\n",
    "        # counts.append(eval_count)\n",
    "        values.append(mean)\n",
    "        accepted.append(ac)\n",
    "\n",
    "    # Initialize optimizer\n",
    "    if pick_optimizer == \"cobyla\":\n",
    "        optimizer = COBYLA(maxiter=max_iter, tol=0.0001)\n",
    "    if pick_optimizer == \"adam\" or pick_optimizer == \"ADAM\":\n",
    "        optimizer = qiskit.algorithms.optimizers.ADAM(maxiter=max_iter)\n",
    "    # optimizer = L_BFGS_B(maxfun=300, maxiter=max_iter)#, factr=10, iprint=- 1, epsilon=1e-08)\n",
    "    if pick_optimizer == \"spsa\" or pick_optimizer == None:\n",
    "        optimizer = SPSA(maxiter=max_iter,\n",
    "                         #blocking=True,\n",
    "                         callback=store_intermediate_result,\n",
    "                         #learning_rate=0.3,\n",
    "                         #perturbation=0.1\n",
    "                         ) # recommended from qiskit (first iteraction takes quite long)\n",
    "                           # to reduce time figure out optimal learning rate and perturbation in advance\n",
    "    start_time = time.time()\n",
    "    ret = optimizer.optimize(\n",
    "                            num_vars=len(thetas),\n",
    "                            objective_function=(lambda thetas: cost_function(thetas, L, num_trash, init_states, shots, vqe, param_encoding, x, meas_fitter=meas_fitter)),\n",
    "                            initial_point=thetas\n",
    "                            )\n",
    "    print(\"Time: {:.5f} sec\".format(time.time()-start_time))\n",
    "    print(ret)\n",
    "    return ret[0], values, accepted"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e261e8be-2b19-4b32-8c0f-b9734ff47fcd",
   "metadata": {},
   "source": [
    "This was the initial test without loss tracking to see if it works, here we achieve 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "ef1825ce",
   "metadata": {},
   "outputs": [],
   "source": [
    "temp2 = np.load(\"data/QAEAnsatz_scaling/QAEAnsatz_scaling_MPS_script_L-32_results.npz\",allow_pickle=True) # 500 iterations, gx = 0.3, chi=100 (but resulting bond dimension of state much smaller)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "60c62a04",
   "metadata": {},
   "outputs": [],
   "source": [
    "psi0 = temp2[\"psi0\"].item()\n",
    "thetas_opt = temp2[\"thetas_opt\"][0]\n",
    "L = psi0.L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "6046d359",
   "metadata": {},
   "outputs": [],
   "source": [
    "loss_final = cost_function_single(thetas_opt, L, int(np.log(L)/np.log(2)), psi0, shots=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "62f7552f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Result for L = 32: loss_opt = 0.0 with optimal parameters [ 4.83855054 -0.20582669  6.83525964  6.21561499  1.94371101  1.81630798\n",
      " -2.44834111  2.88498123  7.81926284  3.11987048  4.37616758  4.97561373\n",
      "  1.44112904  2.13434186  1.40920099  6.83006267  5.5905621   0.16458605\n",
      "  0.30815472  2.17978814  4.40622637  4.91121821  6.02030696  5.30211198\n",
      "  0.39306616  5.9249213  -0.98698015  0.90086792  2.15806054  2.99258229\n",
      "  1.94737421 -1.18349407 -1.88232239  8.32568445  6.20363456  3.11065863\n",
      "  4.82745289 -0.56261306 -1.25618723  3.60737977  5.72683799  3.52368627\n",
      " -0.68207825 -1.53779217  5.16929927 -1.29041715  4.31125081  5.19327236\n",
      "  2.3255499   3.29342905 -1.13838463  0.26985152  3.88154487  4.611061\n",
      "  5.61231369  3.64121651  6.20467819  7.34565202  0.74564719  2.02414372\n",
      "  7.75811751 -0.72283332  6.32894993  4.41188814  4.81020359  1.73088927\n",
      "  6.73079369  2.70860382  6.45612467  4.99078111  0.01792506 -0.04260768\n",
      "  4.02136698  6.97120237  1.72843076  4.83951581  8.15791455  0.28411242\n",
      "  0.55151084  3.95474238  6.82441122  6.11058857  4.12570681  0.99257909\n",
      "  7.81131038  5.66715993  4.80552113  5.01486403  2.28363229  4.17750759\n",
      "  2.66896688  2.20078254 -3.10746585  0.622526    2.84952119  2.02397458\n",
      "  5.76422371  1.67002055  1.3340512   5.57414309  0.59709442  6.75636791\n",
      "  0.62397586  5.89700951 -2.10132152  1.84097282  1.20711461  6.08285888\n",
      "  1.43439855  6.61472343  6.06046084  6.86819379  6.76676515  1.49957308\n",
      "  3.41683826  6.14897173  2.73602773  4.37721692  5.69060697  5.95108916\n",
      "  5.14306621  8.91678877  4.41975862  2.11178225  4.56151988  0.87067002\n",
      "  3.43657591  1.60372516  3.01992952  3.26913158  0.25566528  0.7232415\n",
      "  3.8104705   6.85750047  3.35945098 -2.18694803  6.74639897  2.747931\n",
      "  5.08056715  3.44148168  3.03664689  3.0650314   8.54641797  6.2357912\n",
      "  3.42252243  0.01407374  5.939186    6.64328193  4.14246188  3.08970372\n",
      "  3.99310199 -1.64907449  2.33069966  0.9779311   1.35055799  2.62746173\n",
      "  5.37032242  6.63468681  1.20963115  4.05963486  6.25675268  3.13221622\n",
      "  6.28737346  6.23392077  6.28978125]\n"
     ]
    }
   ],
   "source": [
    "print(f\"Result for L = {L}: loss_opt = {loss_final} with optimal parameters {thetas_opt}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c75f2185-a69e-4222-978e-cfa631d208fe",
   "metadata": {},
   "source": [
    "This was the second attempt with loss tracking (run 1 got stuck in a local minima), where we achieve 0.03. From the looks of it, it seems it has not fully converged and would probably reach 0.0 as above if continued further"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "71fc9113-6a7b-4856-b06a-4485c4d96989",
   "metadata": {},
   "outputs": [],
   "source": [
    "temp2 = np.load(\"data/QAEAnsatz_scaling_MPS_script_L-32_tracked-losses_results.npz\",allow_pickle=True) # 500 iterations, gx = 0.3, chi=100 (but resulting bond dimension of state much smaller)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "03b725c4-0e69-4a72-bf93-94a2a239fa94",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/kkottmann/TeNPy/tenpy/tools/optimization.py:308: UserWarning: Couldn't load compiled cython code. Code will run a bit slower.\n",
      "  warnings.warn(\"Couldn't load compiled cython code. Code will run a bit slower.\")\n"
     ]
    }
   ],
   "source": [
    "psi0 = temp2[\"psis\"][1]\n",
    "thetas_opt = temp2[\"thetas_opt\"][1]\n",
    "L = psi0.L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "289c5af0-cd25-4e77-a8f1-c63e086606da",
   "metadata": {},
   "outputs": [],
   "source": [
    "loss_final = cost_function_single(thetas_opt, L, int(np.log(L)/np.log(2)), psi0, shots=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "88f49e9d-69ba-432d-942e-10e8e2849e84",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Result for L = 32: loss_opt = 0.03 with optimal parameters [ 6.21676459 -1.55776429  2.84439856  3.301513    2.07886255  5.67643171\n",
      "  3.50247431  5.84086743  1.64367106  1.11376773  2.53941036  1.69663221\n",
      "  1.47292149  3.00041416 -1.16119221  4.26513816  2.20638967  2.18709795\n",
      "  4.12388773  0.3708488   3.12146944  2.37876178  3.29402502  5.55660998\n",
      "  1.17407458  3.00632402  2.29374058  0.18987393  0.23470515  1.12183805\n",
      "  6.20631059  0.74957526  3.65378116  1.54123766  2.57887947  1.24851182\n",
      "  4.8197619   4.90642999  6.46265771  4.38958421  3.01961285  0.18158946\n",
      "  3.45754455  6.79818957  5.58190116  3.60408904  3.8778992   7.02948568\n",
      "  3.25533895  4.73484338  4.70245539  2.40527401  6.14016219  4.15921922\n",
      "  5.96725584  2.47082308  7.15496531  3.11336783  4.78194967  3.22412708\n",
      "  1.90111938  2.65975529  2.50538548  5.43719036  4.8352712   6.31349783\n",
      "  1.91406539  2.44427131  5.21442657  6.23449834  3.84184492  4.60104775\n",
      "  4.95927497  0.63817309  0.55927357  1.6898246  -1.26323238  3.75827478\n",
      "  3.39696315  0.27528789  6.67242997  5.57873101  3.12263418  2.18775497\n",
      "  1.51200795  5.0990656   2.55651606  3.60602251  4.89790339 -0.56289668\n",
      "  6.03780649  5.23268395 -1.13260171  5.19570497  0.52307912  5.33399435\n",
      "  3.221016    0.60966215  2.08249318  3.028516    4.16944335  4.6299577\n",
      "  2.65046733  3.12874913  1.94748554  4.7402047   1.01697884  1.03568539\n",
      "  1.34897453  6.00145324  3.92723983  3.64141039  2.59067584  3.74430252\n",
      "  2.42579564 -0.82554629  1.58136045  3.98603453  3.65294353  2.29124145\n",
      "  2.728404   -0.64355659  3.50729978  3.76108911  3.13484029  1.59802265\n",
      "  6.67223178  4.08567301  4.92119484  2.4980634   4.3396069   3.42900238\n",
      "  0.64092188  3.1790072   3.01457786  0.20479666  3.17128938  0.43525393\n",
      "  1.85507612  6.07415499  4.82743258  6.28769573  5.90286419 -0.1065667\n",
      "  3.36314059  1.28779767  6.52279034  6.16996361 -1.06319648  6.3756311\n",
      "  2.22871603  0.60358035  3.9005143  -0.22609031  4.93264903  2.09753002\n",
      "  5.45997332 -0.07832536  2.50426008  4.00224283  6.28864469 -0.02017658\n",
      "  3.13163934  4.7569349   6.29258209]\n"
     ]
    }
   ],
   "source": [
    "print(f\"Result for L = {L}: loss_opt = {loss_final} with optimal parameters {thetas_opt}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "49774d0a-0d80-4e03-b226-ddcbc79dfd58",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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