Markovian.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "21694f88-303b-4935-b340-038add5f261e",
   "metadata": {},
   "source": [
    "# Trapped-ion quantum simulation of excitation transport"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a23780c8-2c2c-4a71-b168-7ab415177a2e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from qutip import *\n",
    "from scipy import constants\n",
    "import math as m\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bbb43826-6e1d-4c5f-9fb0-8514a125dc3e",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qutip.superoperator import liouvillian_ref"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d050d50d-5f59-42e5-8a62-18108dd2ef31",
   "metadata": {},
   "source": [
    "$$ \\frac{d}{dt}\\rho = - \\frac{i}{\\hbar} [H, \\rho] + \\mathcal{L}_{diss}(\\rho) + \\mathcal{L}_{deph}(\\rho)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4c0afa2-93c7-4b90-9e00-44d8a7adbecb",
   "metadata": {},
   "source": [
    "Where the Hamiltonian is:\n",
    "$$ H = H_j + H_{w_{i}}$$\n",
    "With:\n",
    "$$ H_J = \\hbar \\sum_{i<j} J_{ij} \\sigma_i^+ \\sigma_j^- + H.c$$ ($J_{ij}$ Coupling strengths)\n",
    "$$ H_{w_i} = \\hbar \\sum_{i} \\omega_i \\sigma_i^+ \\sigma_i^-$$ ($\\hbar \\omega_i$ on-site excitation energy)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44574272-1ea7-423d-9a0e-a21fe7fb991e",
   "metadata": {},
   "source": [
    "And the Lindblanian operators:\n",
    "$$ \\mathcal{L}_{diss}(\\rho) = \\frac{\\Gamma}{2} [- \\{ \\sigma_{i_{sink}}^+ \\sigma_{i_{sink}}^-,\\rho \\} + 2 \\sigma_{i_{sink}}^- \\rho \n",
    "\\sigma_{i_{sink}}^+]$$ \n",
    "$$ \\mathcal{L}_{deph}(\\rho) = \\sum_i \\frac{\\gamma_i}{2} [- \\{ \\sigma_i^+ \\sigma_i^-,\\rho \\} + 2\\sigma_i^+\\sigma_i^- \\rho \\sigma_i ^+ \\sigma_i^-] $$ "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fc7c65e-1e4f-40b0-a710-d98bdad1ae92",
   "metadata": {},
   "source": [
    "Liouvillian Dissipator\n",
    "$$D[a,b]\\rho = a \\rho b^\\dagger -\\frac{1}{2}a^\\dagger b\\rho - \\frac{1}{2}\\rho a^\\dagger b$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b1fffff-0f41-4f51-9659-37254d2c6d94",
   "metadata": {},
   "source": [
    "J_ij\n",
    "\n",
    "power-law approximation for equidistant ions\n",
    "$$ |J_{ij}| \\propto |i-j|^{-\\alpha}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "816691b2-cb94-4710-8e95-c4af8591fd11",
   "metadata": {},
   "source": [
    "# Dephasing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0103d8eb-6500-440f-abd9-6a4e53852af8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def lindblad_dephasing(c):\n",
    "    cdc = c.dag()*c\n",
    "    return spre(cdc) * spost(cdc) - 0.5 * spre(cdc) - 0.5 * spost(cdc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "f7cab53d-b125-4b1b-9ed5-3eb9b048540e",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 10           # Número de qubits\n",
    "b = 0.1        # Multiplicador J\n",
    "alpha = 1       # Hoppping range\n",
    "i= 6            # i-1 site\n",
    "\n",
    "h = constants.hbar\n",
    "\n",
    "### Estado inicial\n",
    "# Todos los spins en estado |0>\n",
    "psi_list = []\n",
    "\n",
    "for n in range(N):\n",
    "    psi_list.append(basis(2,0))\n",
    "    \n",
    "# Spin 3 en estado |1>\n",
    "psi_list[2] = basis(2,1)\n",
    "psi0 = tensor(psi_list)\n",
    "\n",
    "\n",
    "# Tiempo de evolución\n",
    "tlist = np.linspace(0, 3, 300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "7f56a5a2-c162-4551-af5c-031f3c51365c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Construimos los operadores\n",
    "si = qeye(2)\n",
    "sm = sigmam()\n",
    "sp = sigmap()\n",
    "\n",
    "sm_list = []\n",
    "sp_list = []\n",
    "\n",
    "for n in range(N):\n",
    "    op_list = []\n",
    "    for m in range(N):\n",
    "        op_list.append(si)\n",
    "\n",
    "    op_list[n] = sm\n",
    "    sm_list.append(tensor(op_list))\n",
    "\n",
    "    op_list[n] = sp\n",
    "    sp_list.append(tensor(op_list))\n",
    "    \n",
    "# Coupling strengths with the aproximation\n",
    "J = np.zeros((N,N))\n",
    "\n",
    "for i in range(N):\n",
    "    for j in range(N):\n",
    "        if i != j:\n",
    "            J[i,j]=(abs(i-j))**(alpha)\n",
    "\n",
    "J_max = J.max()\n",
    "\n",
    "# construct the hamiltonian\n",
    "H_j = 0\n",
    "\n",
    "w = 0.1\n",
    "\n",
    "for i in range(N):\n",
    "    for j in range(N):\n",
    "        if (i<j):\n",
    "            H_j += J[i,j] * sp_list[i] * sm_list[j]\n",
    "            H_j += (J[i,j] * sp_list[i] * sm_list[j]).dag()\n",
    "\n",
    "for i in range(N):\n",
    "    H_j += w * (sp_list[i] * sm_list[i])\n",
    "            \n",
    "L0 = superoperator.liouvillian(H_j)\n",
    "\n",
    "#L_deph = 0\n",
    "\n",
    "#for i in range(N):\n",
    "#    L_deph += 0.0*lindblad_dephasing(sm_list[i])\n",
    "\n",
    "L_diss = lindblad_dissipator(sm_list[6])\n",
    "    \n",
    "L = L0  + L_diss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "4f0fe4c1-66eb-40fc-ab30-a47a3a2678e9",
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[37], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m result \u001b[38;5;241m=\u001b[39m \u001b[43mmesolve\u001b[49m\u001b[43m(\u001b[49m\u001b[43mL\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mpsi0\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mtlist\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m[\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m[\u001b[49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/qutip/mesolve.py:244\u001b[0m, in \u001b[0;36mmesolve\u001b[0;34m(H, rho0, tlist, c_ops, e_ops, args, options, progress_bar, _safe_mode)\u001b[0m\n\u001b[1;32m    241\u001b[0m     v \u001b[38;5;241m=\u001b[39m rho0\u001b[38;5;241m.\u001b[39mfull()\u001b[38;5;241m.\u001b[39mravel(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mF\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m    242\u001b[0m     func(\u001b[38;5;241m0.\u001b[39m, v, \u001b[38;5;241m*\u001b[39mode_args) \u001b[38;5;241m+\u001b[39m v\n\u001b[0;32m--> 244\u001b[0m res \u001b[38;5;241m=\u001b[39m \u001b[43m_generic_ode_solve\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfunc\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mode_args\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mrho0\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mtlist\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43me_ops\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43moptions\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    245\u001b[0m \u001b[43m                         \u001b[49m\u001b[43mprogress_bar\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdims\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mrho0\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdims\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    246\u001b[0m res\u001b[38;5;241m.\u001b[39mnum_collapse \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mlen\u001b[39m(c_ops)\n\u001b[1;32m    248\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m e_ops_dict:\n",
      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/qutip/mesolve.py:526\u001b[0m, in \u001b[0;36m_generic_ode_solve\u001b[0;34m(func, ode_args, rho0, tlist, e_ops, opt, progress_bar, dims)\u001b[0m\n\u001b[1;32m    521\u001b[0m         output\u001b[38;5;241m.\u001b[39mexpect[m][t_idx] \u001b[38;5;241m=\u001b[39m expect_rho_vec(e_ops_data[m], r\u001b[38;5;241m.\u001b[39my,\n\u001b[1;32m    522\u001b[0m                                                  e_ops[m]\u001b[38;5;241m.\u001b[39misherm\n\u001b[1;32m    523\u001b[0m                                                  \u001b[38;5;129;01mand\u001b[39;00m rho0\u001b[38;5;241m.\u001b[39misherm)\n\u001b[1;32m    525\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m t_idx \u001b[38;5;241m<\u001b[39m n_tsteps \u001b[38;5;241m-\u001b[39m \u001b[38;5;241m1\u001b[39m:\n\u001b[0;32m--> 526\u001b[0m         \u001b[43mr\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mintegrate\u001b[49m\u001b[43m(\u001b[49m\u001b[43mr\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mt\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m+\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mdt\u001b[49m\u001b[43m[\u001b[49m\u001b[43mt_idx\u001b[49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    528\u001b[0m progress_bar\u001b[38;5;241m.\u001b[39mfinished()\n\u001b[1;32m    530\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m opt\u001b[38;5;241m.\u001b[39mstore_final_state:\n",
      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/scipy/integrate/_ode.py:431\u001b[0m, in \u001b[0;36mode.integrate\u001b[0;34m(self, t, step, relax)\u001b[0m\n\u001b[1;32m    428\u001b[0m     mth \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_integrator\u001b[38;5;241m.\u001b[39mrun\n\u001b[1;32m    430\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m--> 431\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_y, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mt \u001b[38;5;241m=\u001b[39m \u001b[43mmth\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mf\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mjac\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;129;43;01mor\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43;01mlambda\u001b[39;49;00m\u001b[43m:\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mNone\u001b[39;49;00m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    432\u001b[0m \u001b[43m                          \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_y\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mt\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mt\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    433\u001b[0m \u001b[43m                          \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mf_params\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mjac_params\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    434\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mSystemError\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m e:\n\u001b[1;32m    435\u001b[0m     \u001b[38;5;66;03m# f2py issue with tuple returns, see ticket 1187.\u001b[39;00m\n\u001b[1;32m    436\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\n\u001b[1;32m    437\u001b[0m         \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mFunction to integrate must not return a tuple.\u001b[39m\u001b[38;5;124m'\u001b[39m\n\u001b[1;32m    438\u001b[0m     ) \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01me\u001b[39;00m\n",
      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/scipy/integrate/_ode.py:1007\u001b[0m, in \u001b[0;36mvode.run\u001b[0;34m(self, f, jac, y0, t0, t1, f_params, jac_params)\u001b[0m\n\u001b[1;32m   1003\u001b[0m     jac \u001b[38;5;241m=\u001b[39m _vode_banded_jac_wrapper(jac, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mml, jac_params)\n\u001b[1;32m   1005\u001b[0m args \u001b[38;5;241m=\u001b[39m ((f, jac, y0, t0, t1) \u001b[38;5;241m+\u001b[39m \u001b[38;5;28mtuple\u001b[39m(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcall_args) \u001b[38;5;241m+\u001b[39m\n\u001b[1;32m   1006\u001b[0m         (f_params, jac_params))\n\u001b[0;32m-> 1007\u001b[0m y1, t, istate \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrunner\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   1008\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mistate \u001b[38;5;241m=\u001b[39m istate\n\u001b[1;32m   1009\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m istate \u001b[38;5;241m<\u001b[39m \u001b[38;5;241m0\u001b[39m:\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "result = mesolve(L, psi0, tlist, [], [])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "385650d4-b3b5-4a95-aa64-2df21e1f01fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "states = [s * s.dag() for s in result.states]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9f8c0b71-d433-4a31-9d4c-57750889243a",
   "metadata": {},
   "outputs": [],
   "source": [
    "sm_sp = []\n",
    "\n",
    "for i in range(N):\n",
    "    sm_sp.append(sm_list[i]*sp_list[i])\n",
    "\n",
    "exp_sz = np.array(expect(states, sm_sp ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bd68fedb-d2cf-4f53-bf58-b67bb6cba295",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(figsize=(10,6))\n",
    "\n",
    "ax.plot(list(tlist),exp_sz , label=list(range(1,11,1)))\n",
    "ax.plot(list(tlist), exp_sz[:,0] + exp_sz[:,1] + exp_sz[:,2]\n",
    "                        + exp_sz[:,3] + exp_sz[:,4] + exp_sz[:,5] +\n",
    "        exp_sz[:,6] + exp_sz[:,7] + exp_sz[:,8] + exp_sz[:,9] , label=\"Sum\")\n",
    "\n",
    "\n",
    "ax.legend(loc=0)\n",
    "ax.set_xlabel(r'Time')\n",
    "ax.set_ylabel(r'Absortion Probability')\n",
    "ax.set_title(r'\\gamma = 0.1 J_max')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4dafb488-3a1f-4306-8c01-a2d9302f10e0",
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   "source": []
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   "id": "69f8cef0-d286-4230-b168-e3c6142a7f55",
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   "id": "a2b19b8d-a215-43c0-a601-9121f0e38833",
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   "execution_count": null,
   "id": "67ddb3ae-049b-4405-9d3a-195949cb1822",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3b0cb16c-990d-4a8f-846b-26fd1e99e34f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "eda1b507-ee6e-4a8c-a469-9b2837542b10",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "eb2c3b2d-a164-4254-a8fe-daf535cc3727",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "00fc7944-2740-4c96-9d86-fff3dd03ede4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '\\\\gamma = 0.1 J_max')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10,6))\n",
    "\n",
    "ax.plot(list(tlist),exp_sz[:] , label=\"7\")\n",
    "\n",
    "ax.legend(loc=0)\n",
    "ax.set_xlabel(r'Time')\n",
    "ax.set_ylabel(r'Absortion Probability')\n",
    "ax.set_title(r'\\gamma = 0.1 J_max')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "3edd8baa-05df-4e62-ae47-bf44abccf85f",
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "x and y must have same first dimension, but have shapes (300,) and (10,)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[22], line 3\u001b[0m\n\u001b[1;32m      1\u001b[0m fig, ax \u001b[38;5;241m=\u001b[39m plt\u001b[38;5;241m.\u001b[39msubplots(figsize\u001b[38;5;241m=\u001b[39m(\u001b[38;5;241m10\u001b[39m,\u001b[38;5;241m6\u001b[39m))\n\u001b[0;32m----> 3\u001b[0m \u001b[43max\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mplot\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mlist\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mtlist\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43mexp_sz\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m6\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m \u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mlabel\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;124;43mr\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43m0.8\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      5\u001b[0m ax\u001b[38;5;241m.\u001b[39mlegend(loc\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m)\n\u001b[1;32m      6\u001b[0m ax\u001b[38;5;241m.\u001b[39mset_xlabel(\u001b[38;5;124mr\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mTime\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/matplotlib/axes/_axes.py:1662\u001b[0m, in \u001b[0;36mAxes.plot\u001b[0;34m(self, scalex, scaley, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1419\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m   1420\u001b[0m \u001b[38;5;124;03mPlot y versus x as lines and/or markers.\u001b[39;00m\n\u001b[1;32m   1421\u001b[0m \n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   1659\u001b[0m \u001b[38;5;124;03m(``'green'``) or hex strings (``'#008000'``).\u001b[39;00m\n\u001b[1;32m   1660\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m   1661\u001b[0m kwargs \u001b[38;5;241m=\u001b[39m cbook\u001b[38;5;241m.\u001b[39mnormalize_kwargs(kwargs, mlines\u001b[38;5;241m.\u001b[39mLine2D)\n\u001b[0;32m-> 1662\u001b[0m lines \u001b[38;5;241m=\u001b[39m [\u001b[38;5;241m*\u001b[39m\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_get_lines(\u001b[38;5;241m*\u001b[39margs, data\u001b[38;5;241m=\u001b[39mdata, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)]\n\u001b[1;32m   1663\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m line \u001b[38;5;129;01min\u001b[39;00m lines:\n\u001b[1;32m   1664\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39madd_line(line)\n",
      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/matplotlib/axes/_base.py:311\u001b[0m, in \u001b[0;36m_process_plot_var_args.__call__\u001b[0;34m(self, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m    309\u001b[0m     this \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m args[\u001b[38;5;241m0\u001b[39m],\n\u001b[1;32m    310\u001b[0m     args \u001b[38;5;241m=\u001b[39m args[\u001b[38;5;241m1\u001b[39m:]\n\u001b[0;32m--> 311\u001b[0m \u001b[38;5;28;01myield from\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_plot_args\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m    312\u001b[0m \u001b[43m    \u001b[49m\u001b[43mthis\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mambiguous_fmt_datakey\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mambiguous_fmt_datakey\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/matplotlib/axes/_base.py:504\u001b[0m, in \u001b[0;36m_process_plot_var_args._plot_args\u001b[0;34m(self, tup, kwargs, return_kwargs, ambiguous_fmt_datakey)\u001b[0m\n\u001b[1;32m    501\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39maxes\u001b[38;5;241m.\u001b[39myaxis\u001b[38;5;241m.\u001b[39mupdate_units(y)\n\u001b[1;32m    503\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m x\u001b[38;5;241m.\u001b[39mshape[\u001b[38;5;241m0\u001b[39m] \u001b[38;5;241m!=\u001b[39m y\u001b[38;5;241m.\u001b[39mshape[\u001b[38;5;241m0\u001b[39m]:\n\u001b[0;32m--> 504\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mx and y must have same first dimension, but \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m    505\u001b[0m                      \u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mhave shapes \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mx\u001b[38;5;241m.\u001b[39mshape\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m and \u001b[39m\u001b[38;5;132;01m{\u001b[39;00my\u001b[38;5;241m.\u001b[39mshape\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m    506\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m x\u001b[38;5;241m.\u001b[39mndim \u001b[38;5;241m>\u001b[39m \u001b[38;5;241m2\u001b[39m \u001b[38;5;129;01mor\u001b[39;00m y\u001b[38;5;241m.\u001b[39mndim \u001b[38;5;241m>\u001b[39m \u001b[38;5;241m2\u001b[39m:\n\u001b[1;32m    507\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mx and y can be no greater than 2D, but have \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m    508\u001b[0m                      \u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mshapes \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mx\u001b[38;5;241m.\u001b[39mshape\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m and \u001b[39m\u001b[38;5;132;01m{\u001b[39;00my\u001b[38;5;241m.\u001b[39mshape\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m)\n",
      "\u001b[0;31mValueError\u001b[0m: x and y must have same first dimension, but have shapes (300,) and (10,)"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10,6))\n",
    "\n",
    "ax.plot(list(tlist),expect(states, sm_sp) , label=r'0.8')\n",
    "\n",
    "ax.legend(loc=0)\n",
    "ax.set_xlabel(r'Time')\n",
    "ax.set_ylabel(r'Absortion Probability')\n",
    "ax.set_title(r'\\gamma = 0.1 J_max');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fe54713b-c5a4-400e-8e1f-23078b634836",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a9aa581e-1637-457d-9cae-4fa0711af406",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "679a36e7-d10a-4b55-bcf2-091f57e35360",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.44225520e-05, 9.76769925e-05, 9.79959376e-01, 9.76747096e-05,\n",
       "       2.44229560e-05, 1.08575306e-05, 1.05789367e-04, 3.91052715e-06,\n",
       "       2.71453211e-06, 1.99401812e-06])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "\n",
    "exp_sz[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3c5aa9cf-8095-4c51-aae0-25ca7d6bd778",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0ac0e4fb-250c-4823-8ed2-603c2022d63e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dc576ccb-6b61-45bf-92cf-ff8712c9086d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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