{
 "cells": [
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to simulate quantum dynamics subject to noise\n",
    "**Simulate the dynamics of closed quantum systems in the presence of Non-Markovian noise**\n",
    "\n",
    "Boulder Opal enables you to simulate the dynamics of quantum systems that are affected by various noise processes. Such simulations can provide useful insights into the expected real-world performance of candidate control solutions. In this notebook we show how to use Boulder Opal to perform simulations of systems affected by different types of noise using graphs.\n",
    "\n",
    "**Note** This approach is preferable when a simulation becomes part of a larger computation where flexibility is prioritized. For instance, simulation of noisy quantum-system dynamics in the presence of multiple control signals, each distorted by a transmission line."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary workflow\n",
    "The simulation of quantum dynamics subject to Non-Markovian (colored) noise is used to provide insights into the time-domain evolution of a noise process characterized by a power spectral density with strong low-frequency content.  \n",
    "\n",
    "### 1. Create noise power spectrum\n",
    "An arbitrary frequency-domain representation of a noise power spectrum may simply be created using Python commands.\n",
    "\n",
    "### 2. Link sampled noise trajectories to a graph node\n",
    "A simulation graph can be built as explained in the [How to simulate quantum dynamics for noiseless systems using graphs](https://docs.q-ctrl.com/boulder-opal/toolkit/design/simulate-quantum-systems/how-to-simulate-closed-noiseless-systems) user guide. To include noise in the simulation you only need to add a term corresponding to the noise Hamiltonian to this graph.\n",
    "\n",
    "Given the power-spectral density defined in step 1, you can create random noise trajectories in the time domain with average characteristics reflected by the power spectrum. You can generate batches of noise trajectories using the `graph.random.colored_noise_stf_signal` graph operation. This node creates a batch of continuous noise trajectories from the power density of the pink noise. These trajectories can then be discretized with a user-defined number of equally spaced points between the start and the end of the operation evolution. \n",
    "\n",
    "From these batches of noise, you can create a batch of noise Hamiltonians where each Hamiltonian of the batch represents a different realization of the noise variable. The batch of noise Hamiltonians is then added to the (noise-free) system Hamiltonian to create a batch of total Hamiltonians. Boulder Opal automatically reconciles differing time segmentation while summing over Hamiltonian terms.\n",
    "\n",
    "Next create a unitary time-evolution operator from the total Hamiltonian via `graph.time_evolution_operators_pwc` and apply it to evolve the initial state into a final state.\n",
    "\n",
    "### 3. Execute the graph\n",
    "Once the overall graph is created it may be executed as usual via `boulderopal.execute_graph`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Non-Markovian-noise simulation of a single qubit subject to dephasing noise\n",
    "\n",
    "In this example we will show how to simulate the dynamics of a single qubit experiencing $1/f$ dephasing noise, driven by a $\\pi/2$ [CORPSE](https://docs.q-ctrl.com/open-controls/references/qctrl-open-controls/qctrlopencontrols/new_corpse_control) pulse. The Hamiltonian of the quantum system is:\n",
    "\n",
    "\\begin{align*}\n",
    "H(t) = & \\frac{\\Omega(t)}{2} \\sigma_- + \\frac{\\Omega^*(t)}{2} \\sigma_+ + \\frac{\\eta(t)}{2} \\sigma_z,\n",
    "\\end{align*}\n",
    "\n",
    "where $\\Omega(t)$ is a time-dependent Rabi rate, $\\eta(t)$ is a stochastic dephasing noise process, $\\sigma_\\pm = (\\sigma_x \\mp i \\sigma_y)/2$, and $\\sigma_k$ are the Pauli matrices.\n",
    "\n",
    "We assume that $\\eta(t)$ represents pink noise ($1/f$ noise), as defined below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\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": [
    {
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",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define the non-Markovian noise power spectrum.\n",
    "def pink_spectrum(frequencies, frequency_cutoff):\n",
    "    return 1 / (frequencies + frequency_cutoff)\n",
    "\n",
    "\n",
    "frequency_step = 2 * 1e3\n",
    "frequencies = np.arange(0, 2 * 1e6, frequency_step)\n",
    "\n",
    "power_densities = 4e9 * pink_spectrum(\n",
    "    frequencies=frequencies, frequency_cutoff=0.05 * 1e6\n",
    ")\n",
    "\n",
    "fig = plt.figure(figsize=(10, 5))\n",
    "fig.suptitle(\"Dephasing noise spectral density\")\n",
    "plt.plot(frequencies / 1e6, power_densities * 1e6, color=\"#EB64B6\")\n",
    "plt.fill_between(frequencies / 1e6, 0, power_densities * 1e6, color=\"#F790DB\")\n",
    "plt.xlabel(\"Frequency (MHz)\")\n",
    "plt.ylabel(\"Power density (1/MHz)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Representing the quantum system and noise operator\n",
    "\n",
    "The drive Hamiltonian is defined as a $\\pi/2$ [CORPSE](https://docs.q-ctrl.com/open-controls/references/qctrl-open-controls/qctrlopencontrols/new_corpse_control) pulse, drawn directly from the [Q-CTRL Open Controls](https://github.com/qctrl/open-controls) library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define control parameters.\n",
    "omega_max = 2 * np.pi * 1e6  # Hz\n",
    "total_rotation = np.pi / 2\n",
    "\n",
    "# Import pulse from Q-CTRL Open Controls.\n",
    "pulse = oc.new_corpse_control(\n",
    "    rabi_rotation=total_rotation,\n",
    "    azimuthal_angle=0.0,\n",
    "    maximum_rabi_rate=omega_max,\n",
    "    name=\"CORPSE\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the simulation graph, we define batches of noise trajectories using the `graph.random.colored_noise_stf_signal` node. This node creates a batch of continuous noise trajectories from the power density, which we then discretize to $50$ equally spaced points in the system evolution using `graph.discretize_stf`. From these batches of noise, we will create a batch of noise Hamiltonians where each Hamiltonian of the batch represents a different realization of the noise variable.\n",
    "\n",
    "We will then create the full Hamiltonian by adding the noise and drive terms together. The noise Hamiltonians were sampled on $50$ time points whereas the CORPSE Hamiltonian contains only $3$ time segments. Boulder Opal automatically reconciles differing time segmentation while summing over Hamiltonian terms. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Number of simulations noise trajectories to average over.\n",
    "trajectory_count = 80\n",
    "\n",
    "# Define sample times for the output.\n",
    "sample_times = np.linspace(0, np.sum(pulse.durations), 100)\n",
    "\n",
    "graph = bo.Graph()\n",
    "\n",
    "# Define initial state.\n",
    "initial_state = graph.fock_state(2, 0)[:, None]\n",
    "\n",
    "# Signal for omega extracted from the imported pulse.\n",
    "omega_signal = graph.pwc(\n",
    "    values=pulse.rabi_rates * np.exp(1j * pulse.azimuthal_angles),\n",
    "    durations=pulse.durations,\n",
    "    name=\"omega\",\n",
    ")\n",
    "\n",
    "# System Hamiltonian.\n",
    "system_hamiltonian = graph.hermitian_part(omega_signal * graph.pauli_matrix(\"M\"))\n",
    "\n",
    "# Noise Hamiltonian. Generate random noise trajectories.\n",
    "noise_stf = graph.random.colored_noise_stf_signal(\n",
    "    power_spectral_density=power_densities,\n",
    "    frequency_step=frequency_step,\n",
    "    batch_shape=(trajectory_count,),\n",
    ")\n",
    "noise_pwc = graph.discretize_stf(\n",
    "    stf=noise_stf, duration=pulse.duration, segment_count=50\n",
    ")\n",
    "noise_hamiltonian = noise_pwc * graph.pauli_matrix(\"Z\")\n",
    "\n",
    "# Combine the system and the noise Hamiltonian to get the total Hamiltonian.\n",
    "# We can automatically combine a batched and a non-batched term.\n",
    "hamiltonian = system_hamiltonian + noise_hamiltonian\n",
    "\n",
    "# Compute the unitaries.\n",
    "unitaries = graph.time_evolution_operators_pwc(\n",
    "    hamiltonian=hamiltonian, sample_times=sample_times\n",
    ")\n",
    "\n",
    "# Use the unitaries to evolve the initial state.\n",
    "final_states = unitaries @ initial_state\n",
    "\n",
    "# Calculate the density matrix from simulated states, ρ = |ψ⟩⟨ψ|.\n",
    "density_matrices = graph.outer_product(final_states[..., 0], final_states[..., 0])\n",
    "\n",
    "# Calculate the average density matrices.\n",
    "average_density_matrices = graph.sum(density_matrices, axis=0) / trajectory_count\n",
    "average_density_matrices.name = \"average_density_matrices\"\n",
    "\n",
    "# Calculate the sigma_x expectation.\n",
    "sigma_x_expectations = graph.real(\n",
    "    graph.expectation_value(final_states[..., 0], graph.pauli_matrix(\"X\")),\n",
    "    name=\"sigma_x_expectations\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Running the simulation\n",
    "\n",
    "In the following cell we execute the simulation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1829176\") has started.\n",
      "Your task (action_id=\"1829176\") has completed.\n"
     ]
    }
   ],
   "source": [
    "# Run simulation.\n",
    "simulation_result = bo.execute_graph(\n",
    "    graph=graph, output_node_names=[\"average_density_matrices\", \"sigma_x_expectations\"]\n",
    ")\n",
    "\n",
    "average_density_matrices = simulation_result[\"output\"][\"average_density_matrices\"][\n",
    "    \"value\"\n",
    "]\n",
    "sigma_x_expectations = simulation_result[\"output\"][\"sigma_x_expectations\"][\"value\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Extracting the average density matrices\n",
    "\n",
    "Here we visualize the average evolution of observables."
   ]
  },
  {
   "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": [
    "# Plot average sigma_x expectation.\n",
    "fig = plt.figure(figsize=(10, 5))\n",
    "plt.suptitle(r\"Average $\\sigma_x$ expectation\")\n",
    "plt.plot(sample_times * 1e6, np.average(sigma_x_expectations, axis=0))\n",
    "plt.axhline(y=0.0, c=\"k\", lw=0.5)\n",
    "plt.xlabel(\"Time (µs)\")\n",
    "plt.ylabel(r\"$\\overline{\\langle\\sigma_x\\rangle}$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing the state evolution in the Bloch sphere\n",
    "\n",
    "Here we visualize the trajectory represented by this evolution in an interactive Bloch sphere using the Q-CTRL Visualizer Python package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div\n",
       "        class=\"qctrlvisualizer\"\n",
       "        style=\"display:flex;flex-direction:column;align-items:center;\"\n",
       "    >\n",
       "        <div\n",
       "            class=\"qctrlvisualizer-wrapper\"\n",
       "            style=\"width:300px;height:300px;margin:0.5rem 0\"\n",
       "            id=\"qctrlvisualizer-wrapper-3032ef8dab194119809ec764f3051f9e\"\n",
       "        ></div>\n",
       "        <input\n",
       "            class=\"qctrlvisualizer-progress-bar\"\n",
       "            style=\"margin:0.5rem 0\"\n",
       "            id=\"qctrlvisualizer-progress-bar-3032ef8dab194119809ec764f3051f9e\"\n",
       "            type=\"range\"\n",
       "            min=\"0\"\n",
       "            max=\"1\"\n",
       "            step=\"0.01\"\n",
       "            value=\"0\"\n",
       "        >\n",
       "        <button\n",
       "            class=\"qctrlvisualizer-button qctrlvisualizer-button-play\"\n",
       "            style=\"margin:0.5rem 0\"\n",
       "            id=\"qctrlvisualizer-button-3032ef8dab194119809ec764f3051f9e\"\n",
       "        >Play</button>\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": "\n    function visualizerLoader() {\n      if ((typeof Visualizer) == \"function\") {\n        console.log(\"Using preloaded Q-CTRL Visualizer JavaScript package.\");\n        displayBlochSphere();\n        return;\n      }\n\n      try {\n        console.log(\"Attempting to load https://cdn.jsdelivr.net/npm/@qctrl/visualizer@3.1.14/umd/visualizer.min.js with require.js.\");\n        requirejs([\"https://cdn.jsdelivr.net/npm/@qctrl/visualizer@3.1.14/umd/visualizer.min.js\"], displayBlochSphere, displayErrorMessage);\n      } catch(error) {\n        var existing_script = document.getElementById(\"qctrlvisualizer-script\");\n\n        if (existing_script !== null) {\n          console.log(\n            \"Script tag for the Q-CTRL Visualizer JavaScript package already exists.\"\n            + \" Delaying execution of function until script is loaded.\"\n          );\n          existing_script.addEventListener(\"load\", displayBlochSphere);\n          existing_script.addEventListener(\"error\", displayErrorMessage);\n          return;\n        }\n\n        console.log(\"Attempting to load https://cdn.jsdelivr.net/npm/@qctrl/visualizer@3.1.14/umd/visualizer.min.js with script tag.\");\n        var script = document.createElement(\"script\");\n        script.onload = displayBlochSphere;\n        script.onerror = displayErrorMessage;\n        script.id = \"qctrlvisualizer-script\";\n        script.src = \"https://cdn.jsdelivr.net/npm/@qctrl/visualizer@3.1.14/umd/visualizer.min.js\";\n        document.head.appendChild(script);\n      }\n    }\n\n    function displayBlochSphere() { \n    let isPlaying = false;\n    let progress = 0;\n\n    const visualizationData = {\"data\": {\"qubits\": [{\"name\": \"qubit1\", \"x\": [0.0, -1.5549618654276858e-05, -6.221101373843748e-05, -0.00015547590757108504, -0.00028470347047448633, -0.0004690147971849895, -0.0006889461185354659, -0.0009560114460059805, -0.0012515707146682996, 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\"qctrlvisualizer-button-pause\",\n        \"qctrlvisualizer-button-replay\"\n      ]);\n      if (isPlaying) {\n        button.classList.add(\"qctrlvisualizer-button-pause\");\n        button.innerHTML = \"Pause\";\n        return;\n      }\n      if (progress>=1) {\n        button.classList.add(\"qctrlvisualizer-button-replay\");\n        button.innerHTML = \"Replay\";\n        return;\n      }\n      button.classList.add(\"qctrlvisualizer-button-play\");\n      button.innerHTML = \"Play\";\n    }\n\n    button.onclick = () => {\n      isPlaying = !isPlaying;\n      if (progress >= 1) progress = 0;\n      updateButton();\n      visualizer.update({ isPlaying, progress });\n    };\n\n    progressBar.oninput = ({ target }) => {\n      progress = +target.value;\n      visualizer.update({ progress });\n      updateButton();\n    };\n\n    const onUpdate = ({ target, data }) => {\n      progress = data.progress;\n      progressBar.value = progress;\n      if (progress >= 1) {\n        isPlaying = false;\n        target.update({ isPlaying });\n        updateButton();\n      }\n    };\n\n    const visualizer = new Visualizer({\n      visualizationData,\n      wrapper,\n      onUpdate,\n      labels,\n    }).init();\n\n    visualizer.update({ themeSettings });\n     }\n\n    function displayErrorMessage() {\n      console.log(\"Failed to load https://cdn.jsdelivr.net/npm/@qctrl/visualizer@3.1.14/umd/visualizer.min.js.\");\n      const wrapper = document.getElementById(\"qctrlvisualizer-wrapper-3032ef8dab194119809ec764f3051f9e\");\n      wrapper.innerHTML = \"Could not load JavaScript at https://cdn.jsdelivr.net/npm/@qctrl/visualizer@3.1.14/umd/visualizer.min.js.\";\n    }\n\n    visualizerLoader();\n    ",
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qv.display_bloch_sphere_from_density_matrices(density_matrices=average_density_matrices)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Extracting the individual time evolution trajectories\n",
    "\n",
    "Here we show how to extract the individual random trajectories for the system state under the dephasing noise process employed in the time-domain simulation. For clarity, we only plot the first 10 trajectories."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot individual sigma_x expectations.\n",
    "fig = plt.figure(figsize=(10, 5))\n",
    "fig.suptitle(r\"$\\sigma_x$ expectations\")\n",
    "plt.plot(sample_times * 1e6, sigma_x_expectations[0:10].T)\n",
    "plt.axhline(y=0, c=\"k\", lw=0.5)\n",
    "plt.xlabel(\"Time (µs)\")\n",
    "plt.ylabel(r\"$\\langle\\sigma_x\\rangle$\")\n",
    "plt.show()"
   ]
  }
 ],
 "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"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": false,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
