TFIM_time_indep_multi_qubit_.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multiple ancilla qubit simulation for time independent TFIM model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "References:\n",
    "- Zhiyan Ding, Chi-Fang Chen and Lin Lin:\n",
    "  [Single-ancilla ground state preparation via Lindbladians](https://arxiv.org/abs/2308.15676)\n",
    "\n",
    "- Zhiyan Ding and Xiantao Li and Lin Lin:\n",
    "  [Simulating Open Quantum Systems Using Hamiltonian Simulations](https://arxiv.org/abs/2311.15533)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TFIM damping model, time independent Hamiltonian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import qsimulations as qs\n",
    "import numpy as np\n",
    "from qutip import *\n",
    "import seaborn as sns\n",
    "\n",
    "# Activate Seaborn's default styling\n",
    "sns.set()\n",
    "sns.set_palette(\"coolwarm\") "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "g_values = [0.0, 0.5, 1, 5]\n",
    "\n",
    "exact_traces = []\n",
    "first_order_traces = []\n",
    "second_order_traces = []\n",
    "\n",
    "index = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantum object: dims=[[4], [4]], shape=(4, 4), type='oper', dtype=Dense, isherm=True\n",
      "Qobj data =\n",
      "[[-1.8  0.   0.   0. ]\n",
      " [ 0.   2.   0.   0. ]\n",
      " [ 0.   0.   2.   0. ]\n",
      " [ 0.   0.   0.  -2.2]]\n",
      "Eigenvalues:  [-2.2+0.j -1.8+0.j  2. +0.j  2. +0.j] \n",
      "\n",
      "\n",
      "Eigenvectors:  [[0.+0.j 0.+0.j 0.+0.j 1.+0.j]\n",
      " [1.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
      " [0.+0.j 1.+0.j 0.+0.j 0.+0.j]\n",
      " [0.+0.j 0.+0.j 1.+0.j 0.+0.j]] \n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "taylor_aprox_order = (\n",
    "    8  # Taylor approximation used for simulating exp(-i*sqrt*(dt)*H_tilde)\n",
    ")\n",
    "\n",
    "g = 1  # Couppling coefficient\n",
    "gamma = 1  # Damping parameter\n",
    "\n",
    "mu = 0.1\n",
    "\n",
    "systemSize = 2  # System Hamiltonian\n",
    "nrAncillas = 2  # Ancilla size\n",
    "J = systemSize  # Nr of jump operators is equal to the number of lattice elements\n",
    "systemSize_dim = np.power(2, systemSize)  # Hamiltonian system size\n",
    "\n",
    "\n",
    "T = 5  # Final time\n",
    "dt = 0.005  # Time step\n",
    "time_vec = np.arange(0, T, dt)  # Time vector to simulate on\n",
    "\n",
    "\n",
    "def H_operator(t=0):\n",
    "    H = np.zeros((systemSize_dim, systemSize_dim))\n",
    "    if systemSize > 1:\n",
    "        for i in np.arange(1, systemSize, 1):\n",
    "            H = H - qs.Pauli_array(qs.Z, i, systemSize) @ qs.Pauli_array(\n",
    "                qs.Z, i + 1, systemSize\n",
    "            )\n",
    "        H = H - qs.Pauli_array(qs.Z, systemSize, systemSize) @ qs.Pauli_array(\n",
    "            qs.Z, 1, systemSize\n",
    "        )\n",
    "    for i in np.arange(1, systemSize + 1, 1):\n",
    "        H = H - g_values[index] * qs.Pauli_array(qs.X, i, systemSize)\n",
    "    for i in np.arange(1, systemSize + 1, 1):\n",
    "        H = H + mu * qs.Pauli_array(qs.Z, i, systemSize)\n",
    "    return Qobj(H)\n",
    "\n",
    "\n",
    "print(H_operator())\n",
    "\n",
    "\n",
    "def V_damping(i, t=0):\n",
    "    if i == 0:\n",
    "        sum = 0\n",
    "        for j in np.arange(1, J + 1, 1):\n",
    "            sum = sum + V_damping(j).full().conj().T @ V_damping(j).full()\n",
    "        return Qobj(-1j * H_operator().full() - 0.5 * sum)\n",
    "\n",
    "    if i >= 1 and i <= systemSize_dim:\n",
    "        return Qobj(\n",
    "            0.5\n",
    "            * np.sqrt(gamma)\n",
    "            * (\n",
    "                qs.Pauli_array(qs.X, i, systemSize)\n",
    "                + 1j * qs.Pauli_array(qs.Y, i, systemSize)\n",
    "            )\n",
    "        )\n",
    "    return 0\n",
    "\n",
    "\n",
    "def H_operator_derivative(t):\n",
    "    return Qobj(0)\n",
    "\n",
    "\n",
    "def V_operator_derivative(i, t):\n",
    "    return Qobj(0)\n",
    "\n",
    "\n",
    "QSystem = qs.qsimulations(systemSize, systemSize, nrAncillas)\n",
    "QSystem.H_op = H_operator\n",
    "QSystem.H_op_derivative = H_operator_derivative\n",
    "QSystem.V_op = V_damping\n",
    "QSystem.V_op_derivative = V_operator_derivative\n",
    "QSystem._update_module_varibles()\n",
    "QSystem._prep_energy_states()\n",
    "\n",
    "\n",
    "starting_state = QSystem.rho_highest_en\n",
    "mesurement_op = QSystem.rho_ground"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Extra math\n",
    "Simulating extra jump operator free TFIM time independent model and evaluating results both from Qutip and numerical Taylor approximation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-2.2+0.j -1.8+0.j  2. +0.j  2. +0.j]\n",
      "[[0.+0.j 0.+0.j 0.+0.j 1.+0.j]\n",
      " [1.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
      " [0.+0.j 1.+0.j 0.+0.j 0.+0.j]\n",
      " [0.+0.j 0.+0.j 1.+0.j 0.+0.j]]\n",
      "Calculated:  (1+0j)\n",
      "[[0.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
      " [0.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
      " [0.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
      " [0.+0.j 0.+0.j 0.+0.j 1.+0.j]]\n",
      "Quantum object: dims=[[4], [4]], shape=(4, 4), type='oper', dtype=Dense, isherm=True\n",
      "Qobj data =\n",
      "[[0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 1. 0.]\n",
      " [0. 0. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "import scipy.linalg as la\n",
    "import scipy, numpy, math\n",
    "\n",
    "# All ground state energy vectors:\n",
    "eigenValues, eigenVectors = la.eig(H_operator(0).full())\n",
    "idx = eigenValues.argsort()\n",
    "eigenValues = eigenValues[idx]\n",
    "eigenVectors = eigenVectors[idx]\n",
    "\n",
    "print(eigenValues)\n",
    "print(eigenVectors)\n",
    "print(\"Calculated: \", np.array(eigenVectors[0]).conj().T  @ np.array(eigenVectors[0]))\n",
    "\n",
    "\n",
    "print(np.einsum('i,j->ij', eigenVectors[0], eigenVectors[0]))\n",
    "\n",
    "print(starting_state)\n",
    "# Time evolution of time independent hamiltonian, without damping operators\n",
    "\n",
    "def single_taylor(matrix, order, time_step):\n",
    "    sum_tmp = np.zeros(np.power(2,systemSize))  \n",
    "    for i in np.arange(0, order, 1):\n",
    "        # tmp = np.power(matrix, i)\n",
    "        tmp = np.linalg.matrix_power(matrix, i)\n",
    "        tmp = tmp / math.factorial(i)\n",
    "        tmp = np.power(-1j*time_step, i)*tmp\n",
    "        sum_tmp = sum_tmp + tmp\n",
    "    return sum_tmp\n",
    "\n",
    "results_Taylor = []\n",
    "time_evolution = starting_state.full()\n",
    "\n",
    "N = (int)(T/dt)\n",
    "matrix = H_operator(0).full()\n",
    "order = 5\n",
    "\n",
    "for n in np.arange(0, N, 1):\n",
    "    time_evolution = single_taylor(matrix, order, dt) @ time_evolution @ np.conj(single_taylor(matrix, order, dt)).T\n",
    "    results_Taylor.append(time_evolution)\n",
    "\n",
    "\n",
    "result_taylor_overlap = []\n",
    "for i in results_Taylor:\n",
    "        result_taylor_overlap.append(np.trace(i @ mesurement_op.full()))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exact simulation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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",
    "from qutip import mesolve\n",
    "import numpy as np\n",
    "\n",
    "rho = starting_state\n",
    "exact_trace = []\n",
    "for t in time_vec:\n",
    "    sum = Qobj(np.zeros((QSystem._systemSizeDim, QSystem._systemSizeDim)))\n",
    "    for j in np.arange(1, J + 1, 1):\n",
    "        sum = (\n",
    "            sum\n",
    "            + QSystem.V_op(j) @ rho @ QSystem.V_op(j).conj().trans()\n",
    "            - 0.5\n",
    "            * (\n",
    "                QSystem.V_op(j).conj().trans() @ QSystem.V_op(j) @ rho\n",
    "                + rho @ QSystem.V_op(j).conj().trans() @ QSystem.V_op(j)\n",
    "            )\n",
    "        )\n",
    "    delta_rho = -1j * (QSystem.H_op() @ rho - rho @ QSystem.H_op()) + sum\n",
    "    rho = rho + dt * delta_rho\n",
    "    exact_trace.append((rho @ mesurement_op).tr())\n",
    "\n",
    "V1 = V_damping(1)\n",
    "V2 = V_damping(2)\n",
    "results2 = mesolve(\n",
    "    QSystem.H_op(), Qobj(starting_state), time_vec, [V1, V2], [mesurement_op]\n",
    ")\n",
    "\n",
    "# results2 = mesolve(\n",
    "#     QSystem.H_op(), Qobj(starting_state), time_vec, c_ops=None, e_ops=[mesurement_op]\n",
    "# )\n",
    "\n",
    "\n",
    "# Add Taylor simulation for only the Hamiltonian system\n",
    "\n",
    "plt.figure()\n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"Tr(q * q_ground)\")\n",
    "plt.plot(time_vec, exact_trace, label=\"Exact simulation\")\n",
    "plt.plot(time_vec, results2.expect[0], label=\"Qutip simulation\")\n",
    "# plt.plot(time_vec, result_taylor_overlap, label=\"Taylor aprox simulation\")\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.savefig(\"tfim_time_indep/exact_sim_gamma_\"+str(g_values[index])+\".png\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "exact_traces.append(exact_trace)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# plt.figure()\n",
    "# plt.xlabel(\"Time\")\n",
    "# plt.ylabel(\"Tr(q * q_ground)\")\n",
    "# # plt.plot(time_vec, exact_trace, label=\"Exact simulation\")\n",
    "# plt.plot(time_vec, results2.expect[0], label=\"Qutip simulation\")\n",
    "# plt.plot(time_vec, results_Taylor, label=\"Taylor aprox simulation\")\n",
    "# plt.legend(loc=\"upper left\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### First order approximation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "\n",
    "ancilla = 2  # Ancillary system size\n",
    "QSystem.set_nr_of_ancillas(ancilla)\n",
    "ancilla_dim = np.power(2, ancilla)\n",
    "total_systemSize = systemSize + ancilla  # Total system size\n",
    "total_systemSize_dim = np.power(2, total_systemSize)\n",
    "taylor_aproximation_order = 10\n",
    "\n",
    "# First order scheme\n",
    "psi_ancilla = 1\n",
    "for i in range(ancilla):\n",
    "    psi_ancilla = np.kron(psi_ancilla, qs.ket_0)\n",
    "rho_ancilla = Qobj(psi_ancilla.conj().T @ psi_ancilla)\n",
    "\n",
    "rho = starting_state\n",
    "first_order_trace = []\n",
    "for t in time_vec:\n",
    "    # Extended system, zero initialized ancilla + hamiltonian system\n",
    "    system = Qobj(\n",
    "        tensor(rho_ancilla, rho),\n",
    "        dims=[[ancilla_dim, systemSize_dim], [ancilla_dim, systemSize_dim]],\n",
    "    )\n",
    "    # First element of taylor approximation, I\n",
    "    approximation = Qobj(\n",
    "        qeye(ancilla_dim * systemSize_dim),\n",
    "        dims=[[ancilla_dim, systemSize_dim], [ancilla_dim, systemSize_dim]],\n",
    "    )\n",
    "\n",
    "    approximation = qs.Taylor_approximtion(\n",
    "        QSystem.H_tilde_first_order(dt),\n",
    "        taylor_aproximation_order,\n",
    "        np.sqrt(dt),\n",
    "        approximation,\n",
    "    )\n",
    "    evolved_system = approximation @ system @ approximation.conj().trans()\n",
    "\n",
    "    rho = evolved_system.ptrace(1)\n",
    "    first_order_trace.append((rho @ mesurement_op).tr())\n",
    "\n",
    "plt.figure()\n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"Tr(q * q_ground)\")\n",
    "plt.plot(time_vec, first_order_trace, label=\"First order simulation\")\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.savefig(\"tfim_time_indep/first_order_gamma_\"+str(g_values[index])+\".png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "first_order_traces.append(first_order_trace)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Second order approximation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "\n",
    "ancilla = 5  # Ancillary system size\n",
    "QSystem.set_nr_of_ancillas(ancilla)\n",
    "ancilla_dim = np.power(2, ancilla)\n",
    "total_systemSize = systemSize + ancilla  # Total system size\n",
    "total_systemSize_dim = np.power(2, total_systemSize)\n",
    "taylor_aproximation_order = 10\n",
    "\n",
    "# First order scheme\n",
    "psi_ancilla = 1\n",
    "for i in range(ancilla):\n",
    "    psi_ancilla = np.kron(psi_ancilla, qs.ket_0)\n",
    "rho_ancilla = Qobj(psi_ancilla.conj().T @ psi_ancilla)\n",
    "\n",
    "rho = starting_state\n",
    "second_order_trace = []\n",
    "for t in time_vec:\n",
    "    # print(t)\n",
    "    # Extended system, zero initialized ancilla + hamiltonian system\n",
    "    system = Qobj(\n",
    "        tensor(rho_ancilla, rho),\n",
    "        dims=[[ancilla_dim, systemSize_dim], [ancilla_dim, systemSize_dim]],\n",
    "    )\n",
    "    # First element of taylor approximation, I\n",
    "    approximation = Qobj(\n",
    "        qeye(ancilla_dim * systemSize_dim),\n",
    "        dims=[[ancilla_dim, systemSize_dim], [ancilla_dim, systemSize_dim]],\n",
    "    )\n",
    "\n",
    "    approximation = qs.Taylor_approximtion(\n",
    "        QSystem.H_tilde_second_order(dt),\n",
    "        taylor_aproximation_order,\n",
    "        np.sqrt(dt),\n",
    "        approximation,\n",
    "    )\n",
    "    evolved_system = approximation @ system @ approximation.conj().trans()\n",
    "\n",
    "    rho = evolved_system.ptrace(1)\n",
    "    second_order_trace.append((rho @ mesurement_op).tr())\n",
    "\n",
    "plt.figure()\n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"Tr(q * q_ground)\")\n",
    "plt.plot(time_vec, second_order_trace, label=\"Second order simulation\")\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.savefig(\"tfim_time_indep/second_order_gamma_\"+str(g_values[index])+\".png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "second_order_traces.append(second_order_trace)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n"
     ]
    },
    {
     "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",
    "\n",
    "total_nr_of_points = 100\n",
    "plot_density = (int)(np.size(time_vec) / total_nr_of_points)\n",
    "print(plot_density)\n",
    "\n",
    "plt.figure()\n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"Tr(q * q_ground)\")\n",
    "# plt.plot(time_vec, exact_trace, label=\"Exact simulation\")\n",
    "plt.plot(\n",
    "    time_vec,\n",
    "    exact_trace,\n",
    "    label=\"Qutip simulation\",\n",
    "    color=\"green\",\n",
    "    marker=\"o\",\n",
    "    linestyle=\"dashed\",\n",
    "    markevery=plot_density,\n",
    ")\n",
    "plt.plot(\n",
    "    time_vec,\n",
    "    first_order_trace,\n",
    "    label=\"First order approximation\",\n",
    "    color=\"red\",\n",
    "    marker=\"x\",\n",
    "    linestyle=\"dashed\",\n",
    "    markevery=plot_density,\n",
    ")\n",
    "plt.plot(\n",
    "    time_vec,\n",
    "    second_order_trace,\n",
    "    label=\"Second order approximation\",\n",
    "    color=\"blue\",\n",
    "    marker=\"+\",\n",
    "    linestyle=\"dashed\",\n",
    "    markevery=plot_density,\n",
    ")\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.savefig(\"tfim_time_indep/combined_gamma_\"+str(g_values[index])+\".png\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n"
     ]
    },
    {
     "ename": "IndexError",
     "evalue": "list index out of range",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[13], line 11\u001b[0m\n\u001b[1;32m      6\u001b[0m plt\u001b[38;5;241m.\u001b[39mylabel(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mTr(q * q_ground)\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m      8\u001b[0m \u001b[38;5;66;03m# plt.plot(time_vec, exact_trace, label=\"Exact simulation\")\u001b[39;00m\n\u001b[1;32m      9\u001b[0m plt\u001b[38;5;241m.\u001b[39mplot(\n\u001b[1;32m     10\u001b[0m     time_vec,\n\u001b[0;32m---> 11\u001b[0m     \u001b[43mexact_traces\u001b[49m\u001b[43m[\u001b[49m\u001b[43mi\u001b[49m\u001b[43m]\u001b[49m,\n\u001b[1;32m     12\u001b[0m     label\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mg=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;241m+\u001b[39m\u001b[38;5;28mstr\u001b[39m(g_values[i]),\n\u001b[1;32m     13\u001b[0m     \u001b[38;5;66;03m# color=\"green\",\u001b[39;00m\n\u001b[1;32m     14\u001b[0m     marker\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mo\u001b[39m\u001b[38;5;124m\"\u001b[39m,\n\u001b[1;32m     15\u001b[0m     linestyle\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mdashed\u001b[39m\u001b[38;5;124m\"\u001b[39m,\n\u001b[1;32m     16\u001b[0m     markevery\u001b[38;5;241m=\u001b[39mplot_density,\n\u001b[1;32m     17\u001b[0m )\n\u001b[1;32m     18\u001b[0m plt\u001b[38;5;241m.\u001b[39mlegend(loc\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mupper left\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m     19\u001b[0m plt\u001b[38;5;241m.\u001b[39msavefig(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mtfim_time_indep/exact_simulation.png\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
      "\u001b[0;31mIndexError\u001b[0m: list index out of range"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "\n",
    "for i in range(len(g_values)):\n",
    "    print(i)\n",
    "    plt.xlabel(\"Time\")\n",
    "    plt.ylabel(\"Tr(q * q_ground)\")\n",
    "\n",
    "    # plt.plot(time_vec, exact_trace, label=\"Exact simulation\")\n",
    "    plt.plot(\n",
    "        time_vec,\n",
    "        exact_traces[i],\n",
    "        label=\"g=\"+str(g_values[i]),\n",
    "        # color=\"green\",\n",
    "        marker=\"o\",\n",
    "        linestyle=\"dashed\",\n",
    "        markevery=plot_density,\n",
    "    )\n",
    "    plt.legend(loc=\"upper left\")\n",
    "    plt.savefig(\"tfim_time_indep/exact_simulation.png\")\n",
    "\n",
    "    # plt.plot(\n",
    "    #     time_vec,\n",
    "    #     first_order_traces[i],\n",
    "    #     label=\"g=\"+str(g_values[i]),\n",
    "    #     # color=\"red\",\n",
    "    #     marker=\"o\",\n",
    "    #     linestyle=\"dashed\",\n",
    "    #     markevery=plot_density,\n",
    "    # )\n",
    "    # plt.legend(loc=\"upper left\")\n",
    "    # plt.savefig(\"tfim_time_indep/first_order.png\")\n",
    "\n",
    "    # plt.plot(\n",
    "    #     time_vec,\n",
    "    #     second_order_traces[i],\n",
    "    #     label=\"g=\"+str(g_values[i]),\n",
    "    #     marker=\"o\",\n",
    "    #     linestyle=\"dashed\",\n",
    "    #     markevery=plot_density,\n",
    "    # )\n",
    "    # plt.legend(loc=\"upper left\")\n",
    "    # plt.savefig(\"tfim_time_indep/second_order.png\")\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "quspin_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": "3.9.19"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}