{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to represent quantum systems using graphs\n",
    "**Represent quantum systems for optimization, simulation, and other tasks using graphs**\n",
    "\n",
    "The typical purpose of graph objects in Boulder Opal is to represent quantum systems.\n",
    "The graph representation of such a system can be used to perform several tasks, including [robust control](https://docs.q-ctrl.com/boulder-opal/toolkit/design/design-error-robust-quantum-logic-gates/learn-to-design-robust-single-qubit-gates-using-computational-graphs) (for calculating optimized control pulses), [simulation](https://docs.q-ctrl.com/boulder-opal/toolkit/design/simulate-quantum-systems/learn-simulation-basics-through-the-dynamics-of-a-single-qubit) (to understand the dynamics of the system in the presence of specific controls and noises), and [system identification](https://docs.q-ctrl.com/boulder-opal/toolkit/design/characterize-hardware/how-to-perform-parameter-estimation-with-a-small-amount-of-data) (to estimate the values of unknown system parameters based on measurements of the system).\n",
    "\n",
    "Please refer to our topic [Understanding graphs in Boulder Opal](https://docs.q-ctrl.com/boulder-opal) for context on what graphs are used for and why.\n",
    "\n",
    "In what follows, we use graphs to define time-dependent Hamiltonians for simulation or optimization.\n",
    "For information on how to use graphs for optimization tasks, see the user guide on [calculating and optimizing with graphs](https://docs.q-ctrl.com/boulder-opal/toolkit/design/calculate-with-graphs/get-an-introduction-to-graphs-in-boulder-opal)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary workflow\n",
    "\n",
    "Here we outline the general procedure for representing your quantum systems and the computations performed on them in the form of graph objects.\n",
    "\n",
    "### 1. Create graph inputs\n",
    "For an optimization, these are optimizable variables that can be tuned by the optimizer to minimize a cost function.\n",
    "For a simulation, the inputs can be known values for control pulses, or  quantities derived from known values.\n",
    "\n",
    "### 2. Create signals\n",
    "*Signals* are scalar-valued functions of time, which may be non-linear, have enforced temporal structure such as time symmetry, or more generally can depend arbitrarily on the inputs.\n",
    "They only contain one numerical value in each period of time, which means their shape is zero-dimensional.\n",
    "Signals represent the time-dependent envelope of the Hamiltonian.\n",
    "You create piecewise-constant (PWC) signals using the `graph.pwc_signal` operation.\n",
    "\n",
    "### 3. Create Hamiltonian operators\n",
    "You create *operators* or PWC operator-valued (2D) functions of time by multiplying constant matrices (for example Pauli matrices) with signals.\n",
    "Usually these operators represent individual terms in your Hamiltonian.\n",
    "You can also create constant operators to represent static terms in your Hamiltonian.\n",
    "Finally, you sum the individual operators created into a single Hamiltonian operator.\n",
    "\n",
    "### 4. Add graph nodes representing computations on your quantum system\n",
    "Once you have defined the nodes that describe your quantum system, you can add extra nodes representing the computations that you want to perform on it.\n",
    "For example, Boulder Opal offers [time evolution operations](https://docs.q-ctrl.com/references/boulder-opal/toolkit/boulderopal/graph/nodes#time-evolution), among many others.\n",
    "\n",
    "Note that while this approach to constructing Hamiltonians is the most common, it is not a requirement.\n",
    "You can use graphs to perform a wide variety of other computations too.\n",
    "For example, Boulder Opal also provides specialized functions for working with trapped ions systems that take advantage of certain approximations to bypass Hamiltonian-level descriptions of the system (see the [How to design error-robust Mølmer–Sørensen gates for trapped ions](https://docs.q-ctrl.com/boulder-opal/toolkit/apply/trapped-ion-quantum-computing/learn-to-optimize-molmer-sorensen-gates-for-trapped-ions) user guide for details)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Optimize a pulse to steer a qubit to a target dynamics\n",
    "\n",
    "In this example, we will perform a simple optimization task for a quantum system using graphs. The system of interest is described by a Hamiltonian of the form\n",
    "$$\n",
    "H(t) = \\frac{\\omega_0}{2} \\sigma_z + \\alpha(t) \\sigma_x + \\beta(t) \\sigma_z,\n",
    "$$\n",
    "where $\\omega_0$ is the qubit frequency, $\\alpha(t)$ is a time-dependent control, which we can optimize, and $\\beta(t)$ is a dephasing noise process.\n",
    "The dephasing amplitude is slowly varying so that you can assume it is constant at each different realization.\n",
    "\n",
    "The goal of the optimization will be to remove the dephasing noise from the qubit by choosing an appropriate pulse $\\alpha(t)$. Thus, the target unitary at the total duration time $T$ of the experiment is given by\n",
    "$$\n",
    "U_\\mathrm{target}(T) = \\exp \\left(-i \\frac{\\omega_0}{2} T \\sigma_z \\right) = \\cos \\left( \\frac{\\omega_0}{2} T \\right) I - i \\sin \\left( \\frac{\\omega_0}{2} T \\right) \\sigma_z .\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\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": [],
   "source": [
    "# Define system parameters.\n",
    "\n",
    "# Qubit frequency.\n",
    "omega_0 = 2 * np.pi * 0.5e6  # rad/s\n",
    "\n",
    "# Pulse parameters.\n",
    "segment_count = 50\n",
    "duration = 10e-6  # s\n",
    "\n",
    "# Maximum value for |α(t)|.\n",
    "alpha_max = 2 * np.pi * 0.25e6  # rad/s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create an empty graph.\n",
    "graph = bo.Graph()\n",
    "\n",
    "# Real PWC signal representing α(t).\n",
    "alpha = graph.real_optimizable_pwc_signal(\n",
    "    segment_count=segment_count,\n",
    "    duration=duration,\n",
    "    minimum=-alpha_max,\n",
    "    maximum=alpha_max,\n",
    "    name=\"$\\\\alpha$\",\n",
    ")\n",
    "\n",
    "# System Hamiltonian without dephasing.\n",
    "hamiltonian = 0.5 * omega_0 * graph.pauli_matrix(\"Z\") + alpha * graph.pauli_matrix(\"X\")\n",
    "\n",
    "# Dephasing noise amplitude.\n",
    "beta = 2 * np.pi * 20e3  # rad/s\n",
    "\n",
    "# (Constant) dephasing noise term.\n",
    "dephasing = beta * graph.pauli_matrix(\"Z\")\n",
    "\n",
    "# Target operation.\n",
    "target_operator = np.cos(0.5 * omega_0 * duration) * graph.pauli_matrix(\n",
    "    \"I\"\n",
    ") - 1j * np.sin(0.5 * omega_0 * duration) * graph.pauli_matrix(\"Z\")\n",
    "\n",
    "# Target operation node.\n",
    "target = graph.target(operator=target_operator)\n",
    "\n",
    "# Robust infidelity.\n",
    "robust_infidelity = graph.infidelity_pwc(\n",
    "    hamiltonian=hamiltonian,\n",
    "    noise_operators=[dephasing],\n",
    "    target=target,\n",
    "    name=\"robust infidelity\",\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1829135\") is queued.\n",
      "Your task (action_id=\"1829135\") has started.\n",
      "Your task (action_id=\"1829135\") has completed.\n",
      "\n",
      "Optimized robust cost: 1.114e-11\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x180 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Run the optimization and plot the results.\n",
    "\n",
    "# Run the optimization.\n",
    "optimization_result = bo.run_optimization(\n",
    "    graph=graph, cost_node_name=\"robust infidelity\", output_node_names=\"$\\\\alpha$\"\n",
    ")\n",
    "\n",
    "# Print the optimized value of the cost function.\n",
    "print()\n",
    "print(f\"Optimized robust cost: {optimization_result['cost']:.3e}\")\n",
    "\n",
    "# Plot the optimized control pulse.\n",
    "qv.plot_controls(controls=optimization_result[\"output\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Noisy qubit evolution\n",
    "\n",
    "In this example, we will represent the following single qubit Hamiltonian as a graph\n",
    "$$\n",
    "H(t) = \\frac{\\Omega}{2} \\sigma_x + \\delta \\sigma_z + \\beta(t) \\sigma_z,\n",
    "$$\n",
    "where $\\Omega$ is the qubit Rabi frequency, $\\delta$ is a detuning, and $\\beta(t)$ is a random dephasing noise process induced by a classical bath.\n",
    "We will model $\\beta(t)$ as a Wiener process, which physically corresponds to Brownian noise, for example, through instrument errors.\n",
    "The goal will be to simulate the qubit's noisy time evolution by using a graph.\n",
    "For this purpose, we will add a node to the graph that computes random values corresponding to the Wiener process $\\beta(t)$.\n",
    "This is done by using the operations `graph.random.normal`, which produces random samples from a normal distribution, and `graph.cumulative_sum`, which adds to each element of a list the sum of all previous elements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define system parameters.\n",
    "\n",
    "# Simulation parameters.\n",
    "segment_count = 200\n",
    "duration = 30e-8  # s\n",
    "sample_times = np.linspace(0.0, duration, segment_count)\n",
    "\n",
    "# Physical system parameters.\n",
    "Omega = 2 * np.pi * 10e6  # rad/s\n",
    "delta = 2 * np.pi * 2e4  # rad/s\n",
    "average_noise_strength = 2 * np.pi * 1.5e6  # rad/s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create an empty graph.\n",
    "graph = bo.Graph()\n",
    "\n",
    "# Add respective nodes to the graph.\n",
    "\n",
    "# Create the Hamiltonian corresponding to the noiseless evolution.\n",
    "noiseless_hamiltonian = graph.constant_pwc(\n",
    "    constant=0.5 * Omega * graph.pauli_matrix(\"X\") + delta * graph.pauli_matrix(\"Z\"),\n",
    "    duration=duration,\n",
    ")\n",
    "\n",
    "# Wiener process which models the dephasing noise.\n",
    "\n",
    "# Compute random samples from a normal distribution.\n",
    "samples = graph.random.normal(\n",
    "    shape=(segment_count,),\n",
    "    mean=0.0,\n",
    "    standard_deviation=average_noise_strength,\n",
    "    seed=0,\n",
    "    name=\"samples\",\n",
    ")\n",
    "\n",
    "# Build a Wiener process from the randomly chosen samples.\n",
    "beta_values = graph.cumulative_sum(samples, name=\"beta values\")\n",
    "\n",
    "# Create a piecewise-constant signal from beta_vales.\n",
    "beta_signal = graph.pwc_signal(\n",
    "    values=beta_values, duration=duration, name=\"beta signal\"\n",
    ")\n",
    "\n",
    "# Create a node corresponding to the dephasing Hamiltonian.\n",
    "dephasing = beta_signal * graph.pauli_matrix(\"Z\")\n",
    "\n",
    "# Define the total Hamiltonian.\n",
    "noisy_hamiltonian = noiseless_hamiltonian + dephasing\n",
    "\n",
    "# Unitary time evolution generated by the total noisy Hamiltonian.\n",
    "noisy_unitaries = graph.time_evolution_operators_pwc(\n",
    "    hamiltonian=noisy_hamiltonian, sample_times=sample_times, name=\"noisy unitaries\"\n",
    ")\n",
    "\n",
    "# Initial state of the qubit, |0⟩.\n",
    "initial_state = graph.fock_state(2, 0)[:, None]\n",
    "\n",
    "# Evolved states, |ψ(t)⟩ = U(t) |0⟩.\n",
    "evolved_noisy_states = noisy_unitaries @ initial_state\n",
    "evolved_noisy_states.name = \"noisy states\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1829136\") has started.\n",
      "Your task (action_id=\"1829136\") has completed.\n",
      "\n",
      "Final noisy unitary:\n",
      "[[-0.694-0.053j -0.333+0.637j]\n",
      " [ 0.333+0.637j -0.694+0.053j]]\n",
      "\n",
      "Final noisy state:\n",
      "[[-0.694-0.053j]\n",
      " [ 0.333+0.637j]]\n"
     ]
    },
    {
     "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-8540fb0f631f42548567e61deb247113\"\n",
       "        ></div>\n",
       "        <input\n",
       "            class=\"qctrlvisualizer-progress-bar\"\n",
       "            style=\"margin:0.5rem 0\"\n",
       "            id=\"qctrlvisualizer-progress-bar-8540fb0f631f42548567e61deb247113\"\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-8540fb0f631f42548567e61deb247113\"\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, -0.0008329636868957673, -0.0027470981665911457, -0.01494250245053959, -0.03164016741512497, -0.06650391978383108, -0.08327330350767431, -0.110755247177769, -0.09470643220132129, -0.06979187339294632, -0.041255318112986085, -0.038397117817510804, -0.017541608887204185, -0.02670690619191457, -0.022845708439565002, -0.03607882196534992, -0.008385228821397153, 0.05154604617500491, 0.1027172749114558, 0.15203966834567337, 0.22969872845069098, 0.3163855750342746, 0.37664897508882184, 0.42947839423184075, 0.4880639900550442, 0.5545522237747488, 0.6003996431875871, 0.635243561817656, 0.6559291980390922, 0.6552373452251171, 0.6190193338646774, 0.5350662128211712, 0.4006615663899645, 0.21613615081809623, 0.009778926408976762, -0.1998299988622152, -0.40336267277360227, -0.5909763436597267, -0.7789275922012209, -0.9103551385297354, -0.9870444804084134, -0.9776167728041074, -0.8929353051302586, -0.7241262171979449, -0.4588754236608348, -0.14394172289824622, 0.15282053052838412, 0.4200609100118088, 0.6377969447667646, 0.7620175793233965, 0.7798293512830707, 0.6800922130613741, 0.4549593530909477, 0.12073752102830393, -0.27527893218876204, -0.6300910294242368, -0.8796042457729815, -0.9747723301190333, -0.9071079105442807, -0.7240072007544247, -0.44657967117551745, -0.1322330976280095, 0.1733728417657141, 0.42981202364306514, 0.60093937105558, 0.7076879290493439, 0.7202903764729688, 0.614629270293929, 0.39705514361568384, 0.1186237658885117, -0.19490301364071067, -0.5330331236960921, -0.8197944043161806, -0.954762143875454, -0.9119517884932348, -0.722562631686531, -0.45844389345043374, -0.14304715450928707, 0.1826458857714568, 0.46334208589554754, 0.6460837643974539, 0.7207221960845149, 0.6481161884465023, 0.4288176266163667, 0.09938544786778597, -0.2848909240399342, -0.6329755894174116, -0.8599366254339287, -0.9405715215191979, -0.8658600285707706, -0.6612779349559191, -0.36761996147326753, -0.037976888246601365, 0.25001396459115344, 0.4788833011575353, 0.6279259606941674, 0.6728074278036105, 0.6031170837176733, 0.4305976662687375, 0.16989352820566217, -0.15744760195593344, -0.4916694624007407, -0.7755677544645851, -0.9202930828622158, -0.8991021931298868, -0.7477101843626449, -0.5060060487925726, -0.21660894133901004, 0.07965545667471349, 0.3453426902627994, 0.5266592811607039, 0.6206084857233457, 0.6307139554624998, 0.5667075183878663, 0.4329754283471083, 0.2557973689035966, 0.0664081733604916, -0.1333141375686887, -0.32892471455756883, -0.5131692919529574, -0.6842843233223378, -0.8241507884385992, -0.9273618425762332, -0.9826894696028848, -0.9870693774818444, -0.938239112623926, -0.8311208554917178, -0.6802874211721871, -0.47312609380430876, -0.2184805345031869, 0.044375067412693564, 0.30059767619585065, 0.516256166821706, 0.6469355829095927, 0.7078960905944383, 0.7029447659465375, 0.6387448701633814, 0.5305331732725033, 0.3923437796423668, 0.25906873649298784, 0.13411113662458152, 0.01452627591529565, -0.10615126630357019, -0.24598773456536788, -0.39769786309627436, -0.5597436600546095, -0.7097621526492661, -0.8448788751176161, -0.9240492343819712, -0.9586528418717877, -0.9702551672826218, -0.9679425542735259, -0.9471768267077942, -0.8963301048262914, -0.8077144281786859, -0.6842868647197855, -0.5237073186937116, -0.35895744409954183, -0.17861928362308005, -0.01119758824282989, 0.1726273172858041, 0.36406107630159057, 0.5560782860171116, 0.7055519883652545, 0.7885123373709682, 0.8045436859076901, 0.7641025376288256, 0.6670829252448368, 0.5178322764969636, 0.3101428603063354, 0.07861315565527793, -0.17002693051197254, -0.4285948935952568, -0.6497918073965393, -0.8356661445492555, -0.9656165800189304, -0.9962583165932812, -0.9150427146908551, -0.7257708907281916, -0.43871957547919976, -0.08488501100505075, 0.26278373161310475, 0.5471558882198214, 0.7279829401577113, 0.8454415085122847, 0.8798659716819937, 0.8554085867765033, 0.764296632532128, 0.5927945303448848, 0.3743419958061983, 0.11248836780446209, -0.18747999564528545, -0.4927671903033962, -0.7474746756306074, -0.9160363686725379, -0.9857209177890455, -0.9813758104132028, -0.9057404082087295, -0.7596398441657148, -0.5287863590275979], \"y\": [0.0, -0.0945749134280453, -0.1882842861105095, -0.279888822336116, -0.3682472655979059, -0.45035228495375257, -0.5299993142772331, -0.6027399881092285, -0.6773479896748363, -0.7461898944589438, -0.8075073424987126, -0.8596743793094264, -0.9046621856130181, -0.940656488320847, -0.968537317064446, -0.987235898171894, -0.998101109277579, -0.9981046752548333, -0.986479870534392, -0.9635425164273184, -0.9226972429883382, -0.8628092138718304, -0.7965221764433258, -0.720161430177605, -0.6254231360233568, -0.5037684095732893, -0.37890865916942523, -0.24119179304948754, -0.0890323496509011, 0.09643619095526462, 0.28676515742383146, 0.4807420041176119, 0.6549847867805122, 0.7914539689241649, 0.8702166429380086, 0.8905098753408074, 0.8551298605482238, 0.7675599155933746, 0.5997913568314486, 0.39098374885871234, 0.11559016077870488, -0.17651335666186552, -0.4268354927744843, -0.6615856284242781, -0.8474390202372405, -0.9248907149591619, -0.8856394632971419, -0.7461072158712295, -0.5104771688491788, -0.21356088034768345, 0.10846748629188424, 0.4342376490880765, 0.7112805070858175, 0.8799887510334811, 0.8854900003906823, 0.7174116665901553, 0.40906717138750026, 0.01849476888882995, -0.3466581291923251, -0.6280139408984466, -0.8213388960295411, -0.8896987723481237, -0.8366043869570772, -0.6816985244922091, -0.46915915815651615, -0.194904406776191, 0.12284340344964756, 0.43806569181226224, 0.6931329863973723, 0.8408819045759871, 0.8736135516493022, 0.7623723295460452, 0.48348710834073494, 0.10400249348343371, -0.292469617841643, -0.6065629019606833, -0.7942373537803555, -0.8663987321653541, -0.8089189954208793, -0.6257151653796453, -0.3568210586880346, -0.016099439102612023, 0.3485752128537987, 0.64836918862416, 0.823726986353446, 0.8306493254608291, 0.6588052883176128, 0.36413675295761716, 0.009034570194035085, -0.3513692761136179, -0.6322957713797298, -0.801056330483006, -0.8336429069218123, -0.7384217242080621, -0.5454331707967603, -0.2773347994459343, 0.02954186341624393, 0.3400803343685026, 0.5974763119696918, 0.7732798932761163, 0.8308171368185586, 0.7405182092945655, 0.48960986109907273, 0.1303042847072295, -0.22756460264920972, -0.522193050253647, -0.7232305507330745, -0.8109016149372631, -0.7806196139491716, -0.6383332140132356, -0.4212875953221054, -0.16543560421116674, 0.10190280102254451, 0.3458917444255662, 0.5621917301056039, 0.7217356973980421, 0.8191371721663603, 0.8616353650175286, 0.8515808691708553, 0.7923368186915714, 0.6814047032757979, 0.5290653500308111, 0.3378998839022979, 0.1226549824352188, -0.08285299134781277, -0.30919198872728454, -0.5207683410742266, -0.6880323263906925, -0.8191524549557352, -0.8875155904666371, -0.8707900751784254, -0.766237537781687, -0.577813539674443, -0.35252552995131303, -0.10716519443327774, 0.14514357589341811, 0.37596159398762913, 0.5714178681240815, 0.7263834271919225, 0.8322968918194451, 0.9032430919621985, 0.9473773901935465, 0.9676439654364926, 0.9594900346078405, 0.9162479229250858, 0.8279348628359822, 0.6962221854408964, 0.5089072695114373, 0.3232945079595079, 0.17151229898989012, 0.04813166637786398, -0.08701910553046804, -0.23287356517940178, -0.4002668111456523, -0.5715493372271094, -0.7244635822768613, -0.8518588081416058, -0.9302047800737677, -0.9696609513526834, -0.9658455774507053, -0.9212317396585161, -0.8252524399338695, -0.661815369008931, -0.44021375056476864, -0.1889289824446838, 0.05210452426723755, 0.2918898008861224, 0.5165738254472156, 0.7091938365315221, 0.860741225559789, 0.9449656158967101, 0.958977177151004, 0.8928229273134697, 0.7577549136219142, 0.5492314649221058, 0.2566636546101023, -0.07031505311675079, -0.40240452283927897, -0.6875014417746137, -0.8930267748753095, -0.9781357241847028, -0.9230429301487434, -0.7550817326127827, -0.5396786054452435, -0.2688384297377885, -0.01688987481380355, 0.22848475768758814, 0.47953371020809776, 0.7130864637499419, 0.8779660694125079, 0.9711689579932581, 0.9752507389207995, 0.8696791555265847, 0.6628089491237908, 0.3897708394945293, 0.11927272048181403, -0.15213458380973122, -0.41410299170090636, -0.6491379524905653, -0.8481541167591069], \"z\": [1.0, 0.995517399105397, 0.9821107274923339, 0.9599161258942476, 0.9291893516316311, 0.8903707363173623, 0.8438994512313563, 0.7902137571294751, 0.7295412206196147, 0.6620647519809955, 0.5884130271654993, 0.5093973134030678, 0.4257682725139672, 0.33830771812294214, 0.24781755196011712, 0.15512446604688707, 0.0610234675881719, -0.0336164001370417, -0.12769740195171958, -0.220158484474832, -0.3096260517622201, -0.39428470470982224, -0.47295662803108474, -0.5448998287507456, -0.6088016446579826, -0.6623361839900371, -0.7042361084655149, -0.7336839483965816, -0.7495532855477582, -0.7492423389640941, -0.7311503325509886, -0.6946878963780767, -0.6406756108234759, -0.5717392582145562, -0.4925721946598245, -0.40872990283955457, -0.3256554556762642, -0.24819092894156092, -0.1830905087051214, -0.13559214535103392, -0.11127492272044787, -0.11449227245560128, -0.1431013730189173, -0.1947965036366186, -0.26698399303972714, -0.3519345760101108, -0.43850727074904416, -0.5165973812408808, -0.5767392108482929, -0.6113272112275374, -0.6165233063680161, -0.5906879428664081, -0.53580969315123, -0.4593933489619542, -0.374338040681321, -0.29716291033614317, -0.24281766844935415, -0.22243391818260516, -0.2387119186234138, -0.28532799248049534, -0.35492113935598196, -0.4369788351556066, -0.5196488790156879, -0.592071571718322, -0.6471178846494652, -0.6791097608612888, -0.682708775239736, -0.6559949007080785, -0.6015927826164447, -0.5280587322666833, -0.44588359203772837, -0.36696610222925047, -0.30688328517565, -0.2785906135740781, -0.2877593753530196, -0.3316393964161621, -0.39876838191862046, -0.47842527994355943, -0.5588296155878343, -0.6275305914868988, -0.6747255008214644, -0.6930370294087506, -0.6770825114101805, -0.6290729992186637, -0.5582081911842581, -0.47839195176252325, -0.40659254209397794, -0.35764986422869793, -0.33947546221853164, -0.35612644204949584, -0.40362550741468867, -0.4724027088401509, -0.5509966058861653, -0.6262797894927035, -0.6878760353923308, -0.7271825059107302, -0.7392275991859374, -0.721522799018656, -0.6764670771286896, -0.6108800174573804, -0.5338100203321005, -0.45814181368409984, -0.39846811936380655, -0.3688921726235404, -0.37393796000159507, -0.4101754483964033, -0.46999515856196017, -0.5436167192279437, -0.6199096922454196, -0.6879455895415045, -0.7383405471698214, -0.76646993959808, -0.7692956034767324, -0.7477977599197037, -0.7046082152860034, -0.6431681655394491, -0.5697405090795644, -0.4897058693495981, -0.4081893622027044, -0.32993884818590036, -0.25969712206516876, -0.20215175812450753, -0.16069748408872475, -0.13884221841873423, -0.13722035513123326, -0.1552664859187366, -0.19503450592531713, -0.2526272796756679, -0.3242544601104064, -0.4056874815937511, -0.4896483415298094, -0.5679093878075385, -0.6321479918400998, -0.6761657358207335, -0.6981394889441593, -0.6962772424869718, -0.6713105620249602, -0.6261119484932074, -0.5642991009002958, -0.49006660122848583, -0.4076347873475125, -0.31978909902952923, -0.22890405155110272, -0.1373641435443268, -0.04823021277318562, 0.03479795869668706, 0.1072956437447749, 0.16490323653108702, 0.20399429786475942, 0.22708645945183836, 0.2372514553234274, 0.2356159733531314, 0.22051295106730678, 0.19073233359187663, 0.14466774909168045, 0.08309034075369981, 0.008198496095561336, -0.07660692170726063, -0.16689155442924863, -0.25887629195521494, -0.3486142440757032, -0.4317614423560123, -0.5027696860033077, -0.5553451589125059, -0.5852812429987911, -0.5916033941898692, -0.575280502127328, -0.5367977772957351, -0.4784285063033904, -0.4036532532048484, -0.31758456595195417, -0.22683389650620878, -0.1384689049841053, -0.05981720423260417, 0.0026254130573989953, 0.04133266014609127, 0.05025096938298845, 0.02770253218937002, -0.02446184231523324, -0.10014146717107147, -0.18985531327924415, -0.28095633024001126, -0.3612090960383957, -0.42283311325395156, -0.46146999293627755, -0.47492168196965906, -0.4648342340808003, -0.4311589941936965, -0.3743024712846615, -0.29840182830572126, -0.21018378181722353, -0.1172060043994832, -0.028959672012577653, 0.044338541387221264, 0.09463648318155538, 0.11886248517511044, 0.11728847831259781, 0.09029410391746989, 0.03958820269045604, -0.031930874258816966]}]}};\n    const themeSettings = {\"highlightColor\": \"#EB6467\", \"pathColor\": \"#EB6467\"};\n    const labels = {\"xAxis\": true, \"yAxis\": true, \"zAxis\": true, \"theta\": true, \"phi\": true, \"northPole\": true, \"southPole\": true, \"nonErrorState\": false};\n\n    const wrapper = document.getElementById(\"qctrlvisualizer-wrapper-8540fb0f631f42548567e61deb247113\");\n    const progressBar = document.getElementById(\"qctrlvisualizer-progress-bar-8540fb0f631f42548567e61deb247113\");\n    const button = document.getElementById(\"qctrlvisualizer-button-8540fb0f631f42548567e61deb247113\");\n\n    function updateButton () {\n      button.classList.remove(...[\n        \"qctrlvisualizer-button-play\",\n        \"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-8540fb0f631f42548567e61deb247113\");\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"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Run the simulation and plot the results.\n",
    "\n",
    "# Calculate the graph to obtain the unitaries.\n",
    "result = bo.execute_graph(\n",
    "    graph=graph, output_node_names=[\"noisy unitaries\", \"noisy states\", \"beta values\"]\n",
    ")\n",
    "\n",
    "# Retrieve the results.\n",
    "noisy_unitaries = result[\"output\"][\"noisy unitaries\"][\"value\"]\n",
    "noisy_states = result[\"output\"][\"noisy states\"][\"value\"]\n",
    "\n",
    "# Print the final unitary and final state of the time evolution.\n",
    "print()\n",
    "print(f\"Final noisy unitary:\\n{np.round(noisy_unitaries[-1], 3)}\")\n",
    "print()\n",
    "print(f\"Final noisy state:\\n{np.round(noisy_states[-1], 3)}\")\n",
    "\n",
    "# Calculate qubit populations |⟨ψ|k⟩|².\n",
    "noisy_qubit_populations = np.abs(noisy_states.squeeze()) ** 2\n",
    "\n",
    "# Plot noisy populations.\n",
    "qv.plot_population_dynamics(\n",
    "    sample_times, {rf\"$|{k}\\rangle$\": noisy_qubit_populations[:, k] for k in [0, 1]}\n",
    ")\n",
    "\n",
    "# Visualize noisy qubit dynamics on the Bloch sphere.\n",
    "qv.display_bloch_sphere(noisy_states.squeeze())\n",
    "\n",
    "# Retrieve noise values.\n",
    "beta_values = result[\"output\"][\"beta values\"][\"value\"]\n",
    "\n",
    "# Create plot with the noise process.\n",
    "plt.figure()\n",
    "plt.plot(sample_times / 1e-9, beta_values)\n",
    "plt.xlabel(r\"$Time$ (ns)\")\n",
    "plt.ylabel(r\"$\\beta(t)$ (rad/s)\")\n",
    "\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"
  },
  "vscode": {
   "interpreter": {
    "hash": "8205af0cf92e71743549f83038e4bd76188c96d301281c9bd6c9e5bac04fb32a"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}