{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to create dephasing and amplitude robust single-qubit gates\n",
    "\n",
    "**Incorporate robustness into the design of optimal pulses**\n",
    "\n",
    "Boulder Opal exposes a highly-flexible optimization engine for general-purpose gradient-based optimization. It can be directly applied to model-based control optimization for arbitrary-dimensional quantum systems. Boulder Opal's optimization engine also allows the user to design pulses that are robust against certain types of noise. In this notebook, we demonstrate how to produce single qubit gates that are simultaneously robust to dephasing and amplitude noises.\n",
    "\n",
    "\n",
    "## Summary workflow\n",
    "### 1. Define robustness condition in computational graph\n",
    "The flexible Boulder Opal optimization engine expresses all optimization problems as [data flow graphs](https://docs.q-ctrl.com/boulder-opal/toolkit/design/calculate-with-graphs/get-an-introduction-to-graphs-in-boulder-opal), which describe how optimization variables (variables that can be tuned by the optimizer) are transformed into the cost function (the objective that the optimizer attempts to minimize). \n",
    "\n",
    "For an optimal control problem, the cost is typically given by the gate infidelity using, for example, the `graph.infidelity_pwc` graph operation. To enforce robustness, we use the same function and just add a list with noise operators to the parameter `noise_operators`: \n",
    "```python\n",
    "cost = graph.infidelity_pwc(\n",
    "    hamiltonian=hamiltonian,\n",
    "    target=target_operator,\n",
    "    noise_operators=noise_list,\n",
    "    name=\"robust_cost\"\n",
    ")\n",
    "```\n",
    "\n",
    "You would typically choose this list to be made of the operators characterizing the dominant noise in your system dynamics, such as the dephasing and control noise operators demonstrated in this guide. The addition of this parameter in `graph.infidelity_pwc` ensures that the optimization cost will take into account both the infidelity with respect to the defined `target` operation and the robustness term.\n",
    "\n",
    "### 2. Execute graph-based optimization\n",
    "\n",
    "With the graph object created, an optimization can be run using the `boulderopal.run_optimization` function. The function returns the results of the optimization. Note that this example code block uses naming that should be replaced with the naming used in your graph.\n",
    "```python\n",
    "optimization_result = bo.run_optimization(\n",
    "    graph=graph, cost_node_name=\"robust_cost\", output_node_names=[\"alpha\", \"gamma\"]\n",
    ")\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Single qubit gate robust to amplitude and dephasing noises\n",
    "\n",
    "We present a detailed example of robust optimization in a single-qubit system. Specifically, we consider a single-qubit system represented by the following Hamiltonian:\n",
    "$$\n",
    "H(t) = \\frac{(1+\\beta_{\\gamma}(t))}{2}\\left(\\gamma(t)\\sigma_{-} + \\gamma^*(t)\\sigma_{+}\\right) + \\frac{\\alpha(t)}{2} \\sigma_{z} + \\eta(t) \\sigma_{z} , \n",
    "$$\n",
    "where $\\gamma(t)$ and $\\alpha(t)$ are, respectively, complex and real time-dependent pulses, $\\sigma_{\\pm}$ are the qubit ladder operators and $\\sigma_{z}$ is the Pauli-Z operator. $\\eta(t)$ and $\\beta_{\\gamma}(t)$ are small, slowly-varying stochastic processes corresponding to dephasing and amplitude noise, respectively.\n",
    "\n",
    "The functions of time $\\gamma(t)$ and $\\alpha(t)$ are not predetermined, and instead are optimized by the Boulder Opal optimization engine in order to achieve some target operation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import qctrlvisualizer as qv\n",
    "import boulderopal as bo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start by defining operators and parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# Define physical constants\n",
    "gamma_max = 2 * np.pi * 0.5e6  # Hz\n",
    "alpha_max = 2 * np.pi * 0.5e6  # Hz\n",
    "segment_count = 50\n",
    "duration = 10e-6  # s\n",
    "sinc_cutoff_frequency = 5e6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we show how to create a data flow graph for optimizing the single-qubit system described above. Comments in the code explain the details of each step. Note that we are using a filter to produce smooth pulses as explained in our [How to add smoothing and band-limits to optimized controls](https://docs.q-ctrl.com/boulder-opal/toolkit/design/design-model-based-controls/how-to-add-smoothing-and-band-limits-to-optimized-controls) user guide. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# Define the data flow graph describing the system\n",
    "graph = bo.Graph()\n",
    "\n",
    "# Create a complex piecewise-constant (PWC) signal, with optimizable modulus\n",
    "# and phase, representing gamma(t)\n",
    "gamma = graph.complex_optimizable_pwc_signal(\n",
    "    segment_count=segment_count, duration=duration, maximum=gamma_max\n",
    ")\n",
    "# Create a real PWC signal, with optimizable amplitude, representing\n",
    "# alpha(t)\n",
    "alpha = graph.real_optimizable_pwc_signal(\n",
    "    segment_count=segment_count,\n",
    "    minimum=-alpha_max,\n",
    "    maximum=alpha_max,\n",
    "    duration=duration,\n",
    ")\n",
    "\n",
    "# Create filtered signals\n",
    "sinc_kernel = graph.sinc_convolution_kernel(sinc_cutoff_frequency)\n",
    "rediscretized_gamma = graph.filter_and_resample_pwc(\n",
    "    pwc=gamma, kernel=sinc_kernel, segment_count=256, name=\"gamma\"\n",
    ")\n",
    "rediscretized_alpha = graph.filter_and_resample_pwc(\n",
    "    pwc=alpha, kernel=sinc_kernel, segment_count=256, name=\"alpha\"\n",
    ")\n",
    "\n",
    "# Create PWC operators representing the Hamiltonian terms\n",
    "drive = graph.hermitian_part(rediscretized_gamma * graph.pauli_matrix(\"M\"))\n",
    "shift = rediscretized_alpha * graph.pauli_matrix(\"Z\") / 2\n",
    "\n",
    "# Create a constant PWC operator representing the dephasing noise\n",
    "# (note that we scale by 1/duration to ensure consistent units between\n",
    "# the noise Hamiltonian and the control Hamiltonian)\n",
    "dephasing = graph.pauli_matrix(\"Z\") / duration\n",
    "\n",
    "# Create the noise list with the dephasing and drive operators\n",
    "noise_list = [dephasing, drive]\n",
    "\n",
    "# Create the target operator\n",
    "target_operator = graph.target(operator=graph.pauli_matrix(\"Y\"))\n",
    "\n",
    "# Create infidelity\n",
    "cost = graph.infidelity_pwc(\n",
    "    hamiltonian=drive + shift,\n",
    "    noise_operators=noise_list,\n",
    "    target=target_operator,\n",
    "    name=\"robust_cost\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Execute graph-based optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1828093\") has started.\n",
      "Your task (action_id=\"1828093\") has completed.\n",
      "Optimized cost:\t 6.510974451916839e-10\n"
     ]
    }
   ],
   "source": [
    "optimization_result = bo.run_optimization(\n",
    "    graph=graph,\n",
    "    cost_node_name=\"robust_cost\",\n",
    "    output_node_names=[\"alpha\", \"gamma\"],\n",
    "    optimization_count=4,\n",
    ")\n",
    "print(\"Optimized cost:\\t\", optimization_result[\"cost\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We may use the [`qctrlvisualizer`](https://docs.q-ctrl.com/references/qctrl-visualizer/qctrlvisualizer) package to plot the optimized pulses, which are available in the result object. By setting `polar=False`, we plot $\\gamma(t) = I(t) + i Q(t)$ in terms of its real and imaginary parts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 720x540 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qv.plot_controls(\n",
    "    {\n",
    "        \"$\\\\alpha$\": optimization_result[\"output\"][\"alpha\"],\n",
    "        \"$\\\\gamma$\": optimization_result[\"output\"][\"gamma\"],\n",
    "    },\n",
    "    polar=False,\n",
    ")"
   ]
  }
 ],
 "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
}