{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to simulate open system dynamics\n",
    "**Calculating the dynamics of a quantum system described by a GKS–Lindblad master equation**\n",
    "\n",
    "Boulder Opal enables you to simulate not only the evolution of isolated quantum systems with and without noise, but also the evolution of systems that are interacting with their environment. \n",
    "You can express the dynamics of these open quantum systems in terms of a master equation, such as the one described by [Gorini, Kossakowski, and Sudarshan (GKS)](https://doi.org/10.1063/1.522979) and [Lindblad](https://doi.org/10.1007/BF01608499): \n",
    "\n",
    "$$ \\frac{\\mathrm{d} \\rho(t)}{\\mathrm{d} t} = - i \\left[ H_{\\rm s}(t), \\rho(t) \\right] + \\sum_i \\gamma_i \\left[ L_i \\rho(t) L_i^\\dagger - \\frac{1}{2} \\rho(t) L_i^\\dagger L_i - \\frac{1}{2} L_i^\\dagger L_i  \\rho(t) \\right]. $$\n",
    "\n",
    "This equation describes the evolution of a system that obeys a system Hamiltonian $H_{\\rm s}$ and also any number of extra Lindbladian terms consisting of a rate $\\gamma_i$ and a Lindblad operator $L_i$.\n",
    "\n",
    "The GKS–Lindblad equation can be solved either exactly or to a specified tolerance using the `graph.density_matrix_evolution_pwc` node.\n",
    "This node vectorizes the above equation, transforming the density matrix into a $D^2$-vector (where $D$ is the dimension of the Hilbert space) and evolves it in time using a $D^2\\times D^2$ matrix.\n",
    "Thus, solving the equation in this manner can be infeasible for large systems, especially if you are working with dense arrays.\n",
    "A separate [user guide](https://docs.q-ctrl.com/boulder-opal/toolkit/design/simulate-quantum-systems/how-to-simulate-large-open-system-dynamics) covers efficient approaches for large systems.\n",
    "Alternatively, a jump-based trajectory method can also be used.\n",
    "\n",
    "The dynamics can be approximated with the trajectory method, exposed via the `graph.jump_trajectory_evolution_pwc` node. \n",
    "Here, instead of evolving the density matrix, a set of pure states $\\{|\\psi_a(t)\\rangle\\}$  which are subject to stochastic jumps \n",
    "$$|\\psi_a(t)\\rangle \\rightarrow \\frac{L_i|\\psi_a(t)\\rangle}{\\sqrt{\\langle \\psi_a(t)|L_i^\\dagger L_i|\\psi_a(t)\\rangle}}$$\n",
    "are evolved.\n",
    "The density matrix can then be approximated as\n",
    "$$\\rho(t) \\approx \\frac{1}{N_\\text{traj}} \\sum_{a=1}^{N_\\text{traj}} |\\psi_a(t)\\rangle\\langle \\psi_a(t)| $$\n",
    "where $N_\\text{traj}$ is the number of trajectories.\n",
    "In the limit $N_\\text{traj} \\rightarrow \\infty$ we get the exact dynamics.\n",
    "Thus instead of solving for a $D^2\\times D^2$ generator, we are here simulating $N_\\text{traj}$ states evolving under a $D\\times D$ Hamiltonian. \n",
    "Hence for large systems this approach is much less memory intensive than the aforementioned method, allowing one to probe the dynamics of larger systems.\n",
    "\n",
    "The tools described in this notebook allow you to solve this GKS–Lindblad master equation to obtain the time evolution for the system that you want."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary workflow\n",
    "\n",
    "### 1. Define Lindblad terms in computational graph\n",
    "To describe the dynamics of an open system with Boulder Opal, you start by setting up a graph object as described in the [How to represent quantum systems using graphs](https://docs.q-ctrl.com/boulder-opal/toolkit/design/calculate-with-graphs/how-to-represent-quantum-systems-using-graphs) user guide. \n",
    "The difference is that besides setting up a graph with a piecewise-constant system `hamiltonian` $H_{\\rm s} (t)$ for the controls, you must also define the Lindblad terms that appear in the GKS–Lindblad master equation above.\n",
    "The `lindblad_terms` must be a tuple or list of tuples each containing a rate $\\gamma_i$ and a Lindblad operator $L_i$.\n",
    "\n",
    "### 2. Calculate density matrix evolution\n",
    "Pass the piecewise constant `hamiltonian` and `lindblad_terms` to either `graph.density_matrix_evolution_pwc` or `graph.jump_trajectory_evolution_pwc` to calculate the evolved density matrices.\n",
    "For the `graph.density_matrix_evolution_pwc` node an `initial_density_matrix` must be passed, while for the `graph.jump_trajectory_evolution_pwc` node an `initial_state_vector` must be passed. \n",
    "A `max_time_step` (which affects how accurately the jump processes are sampled) must also be passed to the `graph.jump_trajectory_evolution_pwc` node.\n",
    "\n",
    "To obtain the density matrix $\\rho(t)$ for a range of times, pass a value for the `sample_times`.\n",
    "If omitted only the evolved density matrix at the final time of the system Hamiltonian is returned"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Simulating a single-qubit open system\n",
    "\n",
    "For this example, consider a single-qubit system whose evolution you can control through a complex Rabi rate $\\Omega(t)$ and a detuning $\\Delta(t)$, so that the system Hamiltonian is:\n",
    "\n",
    "$$ H_{\\rm s}(t) = \\frac{1}{2} \\left( \\Omega(t) \\sigma_- + \\Omega^* (t) \\sigma_+ \\right) + \\Delta(t) \\sigma_z, $$\n",
    "\n",
    "where $\\sigma_x$, $\\sigma_y$, and $\\sigma_z$ are the Pauli matrices and $\\sigma_\\pm = (\\sigma_x \\mp i \\sigma_y)/2$.\n",
    "Suppose this system is also subject to $T_2$ noise, which you can represent by the Lindblad operator $L= \\sigma_z$ with associated rate $\\gamma = 1/(2T_2)$. \n",
    "\n",
    "The master equation integration tool from Boulder Opal allows you to obtain the solution of a GKS–Lindblad equation:\n",
    "\n",
    "$$ \n",
    "\\frac{\\mathrm{d} \\rho(t)}{\\mathrm{d} t} = - i \\left[ H_{\\rm s} (t), \\rho(t) \\right] + \\gamma  \\left[ \\sigma_z \\rho(t) \\sigma_z - \\rho(t) \\right].\\\\\n",
    "$$\n",
    "\n",
    "By using the tools from Boulder Opal to solve this master equation, you can obtain the evolution of the system in terms of $\\rho(t)$.\n",
    "\n",
    "The first step is to set up the Python object that represents the pulse, which you can define by yourself or by importing one of the predefined pulses in the [Q-CTRL Open Controls](https://docs.q-ctrl.com/open-controls/references/qctrl-open-controls) package.\n",
    "In particular, this example illustrates the case where the target operation is an $X_{\\pi}$ rotation applied to a system initially at the state $\\left|0\\right\\rangle$, which corresponds to the initial density matrix $\\rho(0) = \\left| 0 \\right\\rangle \\left\\langle 0 \\right|$.\n",
    "Such an operation should flip the qubit from the state $\\left|0\\right\\rangle$ to the state $\\left|1\\right\\rangle$, however this will be disrupted by the presence of $T_2$ noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import qctrlopencontrols as oc\n",
    "import qctrlvisualizer as qv\n",
    "import boulderopal as bo\n",
    "\n",
    "plt.style.use(qv.get_qctrl_style())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1829143\") has started.\n",
      "Your task (action_id=\"1829143\") has completed.\n"
     ]
    }
   ],
   "source": [
    "# Define control parameters.\n",
    "omega_max = 2 * np.pi * 1e6  # Hz\n",
    "total_rotation = np.pi\n",
    "\n",
    "# Obtain predefined pulse from Q-CTRL Open Controls.\n",
    "predefined_pulse = oc.new_primitive_control(\n",
    "    rabi_rotation=total_rotation, azimuthal_angle=0.0, maximum_rabi_rate=omega_max\n",
    ")\n",
    "\n",
    "# Define time parameters of the simulation.\n",
    "duration = sum(predefined_pulse.durations)\n",
    "sample_times = np.linspace(0, duration, 100)\n",
    "\n",
    "# Create simulation graph.\n",
    "graph = bo.Graph()\n",
    "\n",
    "initial_state = graph.fock_state(2, 0)\n",
    "initial_density_matrix = graph.outer_product(initial_state, initial_state)\n",
    "\n",
    "# Define the controls using the predefined pulse.\n",
    "omega = graph.pwc(\n",
    "    values=predefined_pulse.rabi_rates * np.exp(1j * predefined_pulse.azimuthal_angles),\n",
    "    durations=predefined_pulse.durations,\n",
    ")\n",
    "delta = graph.pwc(\n",
    "    values=predefined_pulse.detunings, durations=predefined_pulse.durations\n",
    ")\n",
    "\n",
    "# Define terms of the Hamiltonian.\n",
    "sigma_x_term = graph.hermitian_part(omega * graph.pauli_matrix(\"M\"))\n",
    "sigma_z_term = delta * graph.pauli_matrix(\"Z\")\n",
    "hamiltonian = sigma_x_term + sigma_z_term\n",
    "\n",
    "# Calculate vector state evolution for a closed system.\n",
    "graph.matmul(\n",
    "    graph.time_evolution_operators_pwc(hamiltonian, sample_times),\n",
    "    initial_state[:, None],\n",
    "    name=\"closed_system_states\",\n",
    ")\n",
    "\n",
    "# Define Lindblad term of the master equation.\n",
    "lindblad_operator = graph.pauli_matrix(\"Z\")\n",
    "T2 = 1e-6  # s\n",
    "\n",
    "# Calculate density matrix evolution according to the master equation.\n",
    "graph.density_matrix_evolution_pwc(\n",
    "    initial_density_matrix=initial_density_matrix,\n",
    "    hamiltonian=hamiltonian,\n",
    "    lindblad_terms=[(1 / (2 * T2), lindblad_operator)],\n",
    "    sample_times=sample_times,\n",
    "    name=\"density_matrices\",\n",
    ")\n",
    "\n",
    "# Run simulation.\n",
    "results = bo.execute_graph(\n",
    "    graph=graph, output_node_names=[\"closed_system_states\", \"density_matrices\"]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "closed_system_populations = (\n",
    "    np.abs(results[\"output\"][\"closed_system_states\"][\"value\"][:, :, 0]) ** 2\n",
    ")\n",
    "open_system_populations = np.real_if_close(\n",
    "    np.diagonal(results[\"output\"][\"density_matrices\"][\"value\"], axis1=-1, axis2=-2)\n",
    ")\n",
    "\n",
    "qv.plot_population_dynamics(\n",
    "    sample_times,\n",
    "    {\n",
    "        r\"$|{0}\\rangle$ (closed system)\": closed_system_populations[:, 0],\n",
    "        r\"$|{1}\\rangle$ (closed system)\": closed_system_populations[:, 1],\n",
    "        r\"$|{0}\\rangle$ (open system)\": open_system_populations[:, 0],\n",
    "        r\"$|{1}\\rangle$ (open system)\": open_system_populations[:, 1],\n",
    "    },\n",
    ")\n",
    "plt.suptitle(\n",
    "    f\"Dynamics comparison between closed and open system ($T_2$ = {T2*1e6} μs)\"\n",
    ")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Simulating the decoherence of a cat-state with the trajectory method\n",
    "\n",
    "For this example, we consider a system initially in an even cat-state\n",
    "$$|\\psi(0)\\rangle = N_+(|\\alpha\\rangle + |-\\alpha\\rangle) ,$$\n",
    "where $N_+$ is a normalization factor and $|\\alpha\\rangle$ is a coherent state. \n",
    "The system has Hamiltonian\n",
    "$$ H_{\\rm s} = \\omega a^\\dagger a , $$\n",
    "where $a$ ($a^\\dagger$) is \n",
    "the annihilation (creation) operator, and is subject to dissipation via Lindblad operator $L=a$ with an associated rate of $\\gamma$.\n",
    "Thus the master equation is\n",
    "$$ \\frac{\\mathrm{d} \\rho(t)}{\\mathrm{d} t} = - i \\omega \\left[ a^\\dagger a, \\rho(t) \\right] + \\gamma [ a \\rho(t) a^\\dagger - \\frac{1}{2} \\rho(t) a^\\dagger a - \\frac{1}{2} a^\\dagger a  \\rho(t)]. $$\n",
    "\n",
    "Again we use the tools from Boulder Opal to solve this master equation, although this time we use the trajectory method.\n",
    "We obtain the evolution of the system in terms of $\\rho(t)$ and find that the number operator mean decays approximately as\n",
    "$$ \\mathrm{Tr}[\\rho(t) a^\\dagger a] \\approx |\\alpha|^2 e^{-\\gamma t} .$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1829144\") has started.\n",
      "Your task (action_id=\"1829144\") has completed.\n"
     ]
    }
   ],
   "source": [
    "dimension = 15  # The dimension of the Hilbert space.\n",
    "\n",
    "duration = 300 * 1e-9  # s\n",
    "sample_times = np.linspace(0.0, duration, 10)\n",
    "\n",
    "graph = bo.Graph()\n",
    "\n",
    "# Create the initial cat-state.\n",
    "alpha = 2.4\n",
    "initial_state = graph.coherent_state(alpha, dimension) + graph.coherent_state(\n",
    "    -alpha, dimension\n",
    ")\n",
    "# Normalize the state.\n",
    "initial_state = initial_state / graph.sqrt(\n",
    "    graph.inner_product(initial_state, initial_state)\n",
    ")\n",
    "\n",
    "# Create the system Hamiltonian.\n",
    "omega = 2 * np.pi * 1e6  # Hz\n",
    "hamiltonian = graph.constant_pwc_operator(\n",
    "    duration, omega * graph.number_operator(dimension)\n",
    ")\n",
    "\n",
    "# Define Lindblad term of the master equation.\n",
    "lindblad_operator = graph.annihilation_operator(dimension)\n",
    "gamma = 5e6  # Hz\n",
    "\n",
    "evolved_density_matrices = graph.jump_trajectory_evolution_pwc(\n",
    "    initial_state_vector=initial_state,\n",
    "    hamiltonian=hamiltonian,\n",
    "    lindblad_terms=[(gamma, lindblad_operator)],\n",
    "    sample_times=sample_times,\n",
    "    max_time_step=duration * 1e-3,\n",
    "    trajectory_count=50,\n",
    ")\n",
    "\n",
    "# Return the initial density matrix.\n",
    "initial_density_matrix = evolved_density_matrices[0]\n",
    "initial_density_matrix.name = \"initial_density_matrix\"\n",
    "\n",
    "# Return the final density matrix.\n",
    "final_density_matrix = evolved_density_matrices[-1]\n",
    "final_density_matrix.name = \"final_density_matrix\"\n",
    "\n",
    "# Compute the expectation values of the number operator.\n",
    "graph.density_matrix_expectation_value(\n",
    "    evolved_density_matrices, graph.number_operator(dimension), name=\"number_operator\"\n",
    ")\n",
    "\n",
    "results = bo.execute_graph(\n",
    "    graph, [\"number_operator\", \"initial_density_matrix\", \"final_density_matrix\"]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(\n",
    "    sample_times * 1e9,\n",
    "    results[\"output\"][\"number_operator\"][\"value\"].real,\n",
    "    \"o\",\n",
    "    label=\"Simulation\",\n",
    ")\n",
    "\n",
    "fine_times = np.linspace(0.0, sample_times[-1], 100)\n",
    "plt.plot(\n",
    "    fine_times * 1e9,\n",
    "    np.conj(alpha) * alpha * np.exp(-gamma * fine_times),\n",
    "    label=\"Theory\",\n",
    ")\n",
    "\n",
    "plt.ylabel(\"Number operator mean\")\n",
    "plt.xlabel(\"Time (ns)\")\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "populations = {\n",
    "    \"Initial\": np.diag(results[\"output\"][\"initial_density_matrix\"][\"value\"]).real,\n",
    "    \"Final\": np.diag(results[\"output\"][\"final_density_matrix\"][\"value\"]).real,\n",
    "}\n",
    "\n",
    "qv.plot_population_distributions(populations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Summary\n",
    "\n",
    "The open-system tools from Boulder Opal allow you to use the graph framework to calculate more general types of system evolution.\n",
    "While the tools described in [this user guide](https://docs.q-ctrl.com/boulder-opal/toolkit/design/simulate-quantum-systems/how-to-simulate-quantum-dynamics-subject-to-noise) show how you can obtain the evolution of a system that follows the Schrödinger equation, the open system tools allow you to solve a more general master equation.\n",
    "You can also use these tools in optimization graphs, if you have a cost function that represents what you want to optimize."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
