{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to create analytical signals for simulation and optimization\n",
    "**Use predefined signals from Boulder Opal**\n",
    "\n",
    "Boulder Opal contains analytical signals in the form of [piecewise-constant functions](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/graph/Pwc) (Pwcs), which can be used for simulation and optimization.\n",
    "The full list of Pwc analytical signals is available in the [reference documentation](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/graph/nodes#signals).\n",
    "\n",
    "All signals require a `duration`, defining the time interval for the signal between zero and `duration`. \n",
    "The signals also require a `segment_count`, which determines the number of segments in the Pwc.\n",
    "Many of the signal parameters can be passed as tensors and thus can be optimized to minimize a given cost function.\n",
    "\n",
    "In this notebook we show how to create signals for use in simulation and optimization.\n",
    "You can also define your own analytical Hamiltonians from the ground up, see [this user guide](https://docs.q-ctrl.com/boulder-opal/toolkit/design/represent-time-varying-signals/how-to-define-continuous-analytical-hamiltonians) for more information."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary workflow\n",
    "\n",
    "### 1. Create a node defining the signal\n",
    "Once a graph has been set up for the system, create a Pwc analytic signal using one of the signals from the [signal library](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/graph/nodes#signals).\n",
    "If one is running an optimization problem, define the optimizable signal parameters using `graph.optimization_variable` or `graph.optimizable_scalar`, before defining the signal.\n",
    "Then add the signal (multiplied by the appropriate operator) to the Hamiltonian.\n",
    "\n",
    "### 2. Execute the graph for the simulation/optimization\n",
    "With the graph object created, a simulation can be run using the `boulderopal.execute_graph` function. The outputs and the graph must be provided. The function returns the results of the simulation. \n",
    "\n",
    "Alternatively, an optimization can be run using the `boulderopal.run_optimization` function or the `boulderopal.run_stochastic_optimization` function. The cost, the outputs, and the graph must be provided. The function returns the results of the optimization. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Simulation with analytical signals \n",
    "\n",
    "In this example, we will simulate two interacting qubits (labeled 0 and 1), with one of the qubits (qubit 0) driven by an external signal. \n",
    "\n",
    "The Hamiltonian for the system is \n",
    "$$\n",
    "H(t) = \\frac{1}{2} \\left(\\Omega(t) \\sigma^{-}_{0} + \\Omega(t)^* \\sigma^{+}_{0} \\right) + \\sum_{i=x,y,z} \\delta_i \\sigma^{i}_{0} \\sigma^{i}_{1} ,\n",
    "$$\n",
    "where $\\Omega(t)$ is the external signal and $\\delta_i$ is the qubit coupling.\n",
    "\n",
    "The signal used for this example is the Gaussian signal, `graph.signals.gaussian_pulse_pwc`, defined as\n",
    "$$\\Omega(t) =\n",
    "           \\begin{cases}\n",
    "                A\n",
    "                \\exp \\left(- \\frac{(t-t_1)^2}{2\\sigma^2} \\right)\n",
    "                    &\\mathrm{if} \\quad t < t_1=t_0- t_\\mathrm{flat}/2 \\\\\n",
    "                A\n",
    "                    &\\mathrm{if} \\quad t_0-t_\\mathrm{flat}/2 \\le t < t_0+t_\\mathrm{flat}/2 \\\\\n",
    "                A\n",
    "                \\exp \\left(- \\frac{(t-t_2)^2}{2\\sigma^2} \\right)\n",
    "                    &\\mathrm{if} \\quad t > t_2=t_0+t_\\mathrm{flat}/2\n",
    "            \\end{cases}  ,\n",
    "$$\n",
    "where $A$ is the amplitude, \n",
    "$\\sigma$ is the width of the Gaussian, \n",
    "$t_0$ is the center of the signal, and\n",
    "$t_\\mathrm{flat}$ is the flat duration. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\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": [
    "# Create the data flow graph describing the system.\n",
    "graph = bo.Graph()\n",
    "\n",
    "# Define the duration of the pulse.\n",
    "duration = 4e-6  # s\n",
    "\n",
    "# Define the parameters of the pulse.\n",
    "# Use a minimal segmentation for a more efficient sampling.\n",
    "pulse = graph.signals.gaussian_pulse_pwc(\n",
    "    duration=duration,\n",
    "    segment_count=100,\n",
    "    amplitude=2 * np.pi * 1.0e6,  # rad/s\n",
    "    width=duration * 0.1,\n",
    "    flat_duration=duration * 0.2,\n",
    "    segmentation=\"MINIMAL\",\n",
    "    name=\"$\\\\Omega$\",\n",
    ")\n",
    "\n",
    "# Add the pulse terms to the Hamiltonian.\n",
    "hamiltonian = graph.hermitian_part(\n",
    "    pulse * graph.pauli_kronecker_product([(\"M\", 0)], subsystem_count=2)\n",
    ")\n",
    "\n",
    "# Add the qubit-qubit coupling terms to the Hamiltonian.\n",
    "couplings = {\"X\": 8.0e6, \"Y\": 8.0e6, \"Z\": 9.0e6}  # rad/s\n",
    "\n",
    "for i, coupling in couplings.items():\n",
    "    hamiltonian += coupling * graph.pauli_kronecker_product(\n",
    "        [(i, 0), (i, 1)], subsystem_count=2\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1829414\") has completed.\n"
     ]
    }
   ],
   "source": [
    "sample_times = np.linspace(0.0, duration, 100)\n",
    "\n",
    "# Compute the unitary using `time_evolution_operators_pwc`.\n",
    "unitaries = graph.time_evolution_operators_pwc(\n",
    "    hamiltonian=hamiltonian, sample_times=sample_times\n",
    ")\n",
    "\n",
    "# Define the initial state.\n",
    "initial_state = graph.fock_state(4, 0)[:, None]\n",
    "\n",
    "# Evolve the initial state with the unitary to get the final state.\n",
    "evolved_states = unitaries @ initial_state\n",
    "evolved_states.name = \"states\"\n",
    "\n",
    "# Run simulation.\n",
    "result = bo.execute_graph(graph=graph, output_node_names=[\"$\\\\Omega$\", \"states\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the evolution of the populations of the qubits using `plot_population_dynamics`.\n",
    "states = result[\"output\"].pop(\"states\")\n",
    "qubit_populations = np.abs(states[\"value\"].squeeze()) ** 2\n",
    "\n",
    "qv.plot_population_dynamics(\n",
    "    sample_times, {rf\"$|{k:02b}\\rangle$\": qubit_populations[:, k] for k in range(4)}\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x180 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# View the generated Gaussian pulse using the `plot_controls` function.\n",
    "qv.plot_controls(result[\"output\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Optimization with analytical signals \n",
    "\n",
    "In this example, we will implement an X gate in a noisy single-qubit system, by optimizing the parameters of two signals. \n",
    "\n",
    "The Hamiltonian for the system is \n",
    "$$\n",
    "H(t) = \\alpha(t) \\sigma_{z} + \\frac{1}{2}\\left(\\gamma(t)\\sigma_{-} + \\gamma^*(t)\\sigma_{+}\\right) + \\delta \\sigma_{z} + \\zeta(t) \\sigma_{z} , \n",
    "$$\n",
    "where $\\alpha(t)$ and $\\gamma(t)$ are signals with optimizable parameters, $\\delta$ is the qubit detuning, and $\\zeta(t)$ is a dephasing noise process.\n",
    "\n",
    "The $\\alpha(t)$ signal acting on $\\sigma_{z}$ is a hyperbolic tangent ramp, `graph.signals.tanh_ramp_pwc`, defined by\n",
    "$$\n",
    "\\alpha(t) = \\frac{a_+ + a_-}{2}\n",
    "                + \\frac{a_+ - a_-}{2} \\tanh\\left( \\frac{t - t_0}{t_\\mathrm{ramp}} \\right)  ,\n",
    "$$\n",
    "where $a_\\pm$ are the asymptotic values of the signal, $t_0$ is the center time, and $t_\\mathrm{ramp}$ is the characteristic duration of the ramp.\n",
    "\n",
    "The $\\gamma(t)$ signal acting on $\\sigma_{-}$ is a cosine pulse, `graph.signals.cosine_pulse_pwc`, defined by\n",
    "$$\n",
    "\\gamma(t) = \n",
    "\\frac{A}{2} \\left[1 + \\cos \\left(\\frac{2\\pi}{\\tau} t- \\pi \\right)\\right] = A \\sin^2 \\left(\\frac{\\pi}{\\tau}t\\right) ,\n",
    "$$\n",
    "where $A$ is the amplitude and $\\tau$ is the given duration of the signal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1829415\") has started.\n",
      "Your task (action_id=\"1829415\") has completed.\n",
      "Optimized cost: 1.711e-09\n"
     ]
    }
   ],
   "source": [
    "graph = bo.Graph()\n",
    "\n",
    "# Define the duration of the signals.\n",
    "duration = 3e-6  # s\n",
    "\n",
    "# Define the number of segments for Pwc signals.\n",
    "segment_count = 100\n",
    "\n",
    "# Define α tanh ramp acting on sigma_z.\n",
    "alpha_start_value = graph.optimizable_scalar(\n",
    "    lower_bound=-3e7, upper_bound=3e7, name=\"alpha_start_value\"\n",
    ")\n",
    "alpha_end_value = graph.optimizable_scalar(\n",
    "    lower_bound=-3e7, upper_bound=3e7, name=\"alpha_end_value\"\n",
    ")\n",
    "alpha_ramp_duration = graph.optimizable_scalar(\n",
    "    lower_bound=0.1e-6, upper_bound=duration, name=\"alpha_ramp_duration\"\n",
    ")\n",
    "alpha_center_time = graph.optimizable_scalar(\n",
    "    lower_bound=0.0, upper_bound=duration, name=\"alpha_center_time\"\n",
    ")\n",
    "alpha_ramp = graph.signals.tanh_ramp_pwc(\n",
    "    duration=duration,\n",
    "    segment_count=segment_count,\n",
    "    start_value=alpha_start_value,\n",
    "    end_value=alpha_end_value,\n",
    "    ramp_duration=alpha_ramp_duration,\n",
    "    center_time=alpha_center_time,\n",
    "    name=r\"$\\alpha$\",\n",
    ")\n",
    "\n",
    "# Define γ cosine pulse acting on sigma_-.\n",
    "gamma_amplitude = graph.optimizable_scalar(\n",
    "    lower_bound=-2.0 * np.pi * 1e6,  # rad/s\n",
    "    upper_bound=2.0 * np.pi * 1e6,  # rad/s\n",
    "    name=\"gamma_amplitude\",\n",
    ")\n",
    "gamma_pulse = graph.signals.cosine_pulse_pwc(\n",
    "    duration=duration,\n",
    "    segment_count=segment_count,\n",
    "    amplitude=gamma_amplitude,\n",
    "    flat_duration=duration * 0.2,\n",
    "    name=r\"$\\gamma$\",\n",
    ")\n",
    "\n",
    "# Create pulse Hamiltonian.\n",
    "hamiltonian = alpha_ramp * graph.pauli_matrix(\"Z\")\n",
    "hamiltonian += graph.hermitian_part(gamma_pulse * graph.pauli_matrix(\"M\"))\n",
    "\n",
    "# Add detuning term.\n",
    "delta = 2 * np.pi * 0.25e6  # rad/s\n",
    "hamiltonian += delta * graph.pauli_matrix(\"Z\")\n",
    "\n",
    "# Define target gate.\n",
    "target = graph.target(operator=graph.pauli_matrix(\"X\"))\n",
    "\n",
    "# Add dephasing noise term.\n",
    "zeta = 2 * np.pi * 20e3  # rad/s\n",
    "dephasing = zeta * graph.pauli_matrix(\"Z\")\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",
    ")\n",
    "\n",
    "# Compute the unitary using `time_evolution_operators_pwc`.\n",
    "unitary = graph.time_evolution_operators_pwc(\n",
    "    hamiltonian=hamiltonian, sample_times=np.array([duration]), name=\"unitary\"\n",
    ")\n",
    "\n",
    "result = bo.run_optimization(\n",
    "    graph=graph,\n",
    "    cost_node_name=\"robust_infidelity\",\n",
    "    output_node_names=[\n",
    "        \"alpha_start_value\",\n",
    "        \"alpha_end_value\",\n",
    "        \"alpha_ramp_duration\",\n",
    "        \"alpha_center_time\",\n",
    "        \"gamma_amplitude\",\n",
    "        \"unitary\",\n",
    "        r\"$\\alpha$\",\n",
    "        r\"$\\gamma$\",\n",
    "    ],\n",
    "    optimization_count=8,\n",
    "    seed=1,\n",
    ")\n",
    "\n",
    "print(f\"Optimized cost: {result['cost']:.3e}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 1.e-05+4.e-05j, -0.e+00-1.e+00j],\n",
       "        [ 0.e+00-1.e+00j,  1.e-05-4.e-05j]]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Check that the unitary operator associated with the evolution of the system Hamiltonian\n",
    "# does indeed correspond to an X gate.\n",
    "result[\"output\"].pop(\"unitary\")[\"value\"].round(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Alpha signal\n",
      "\tstart_value: \t2.726e+06 rad/s\n",
      "\tend_value: \t-5.867e+06 rad/s\n",
      "\tramp_duration: \t1.451e-06 s\n",
      "\tcenter_time: \t1.500e-06 s\n",
      "Gamma signal\n",
      "\tamplitude: \t4.031e+06 rad/s\n"
     ]
    }
   ],
   "source": [
    "# Print out the converged signal parameters.\n",
    "print(\"Alpha signal\")\n",
    "for param in [\"start_value\", \"end_value\"]:\n",
    "    print(f\"\\t{param}: \\t{result['output'].pop(f'alpha_{param}')['value']:.3e} rad/s\")\n",
    "\n",
    "for param in [\"ramp_duration\", \"center_time\"]:\n",
    "    print(f\"\\t{param}: \\t{result['output'].pop(f'alpha_{param}')['value']:.3e} s\")\n",
    "\n",
    "print(\"Gamma signal\")\n",
    "for param in [\"amplitude\"]:\n",
    "    print(f\"\\t{param}: \\t{result['output'].pop(f'gamma_{param}')['value']:.3e} rad/s\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# View the optimized signals using the `plot_controls` function.\n",
    "qv.plot_controls(result[\"output\"])"
   ]
  }
 ],
 "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
}