{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Design noise-robust single-qubit gates for Rigetti Quil-T\n",
    "**Increasing robustness against control noise using Boulder Opal pulses**\n",
    "\n",
    "Boulder Opal enables you to design numerically [optimized controls](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) which can improve the performance of quantum computing hardware.  Specifically, robust control solutions are able to reduce sensitivity to dephasing and/or control noise, including slowly varying noise sources that arise as hardware drifts over time.\n",
    "\n",
    "In this application note we present an entire workflow—from gate optimization through to experimental validation on Rigetti hardware using pulse-level control through [Quil-T](https://pyquil-docs.rigetti.com/en/stable/quilt.html). We will cover:\n",
    "\n",
    "- Preparing Rigetti's JupyterHub environment for applying Boulder Opal\n",
    "- Evaluating the amplitude robustness of a default X gate\n",
    "- Designing optimized amplitude-robust controls using Boulder Opal\n",
    "- Validating performance using filter functions and quasi-static-noise-susceptibility scans\n",
    "- Validating the optimized waveform on Rigetti quantum hardware using Quil-T\n",
    "\n",
    "A related workflow on IBM hardware can be found in the [Designing noise-robust single-qubit gates for IBM Qiskit](https://docs.q-ctrl.com/boulder-opal/toolkit/apply/superconducting-systems/design-noise-robust-single-qubit-gates-for-ibm-qiskit) application note, with a detailed discussion of optimized-pulse performance published in our technical manuscript, [Error-robust quantum logic optimization using a cloud quantum computer interface](https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.15.064054).\n",
    "\n",
    "*This notebook illustrates a workflow for Rigetti's JupyterLab IDE, and some cells require a booking on Rigetti's hardware. If you want to run them, please [request access to Rigetti's Quantum Cloud Services](https://qcs.rigetti.com/request-access) to set up an account.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports and initialization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To access Rigetti's Quantum Processing Units (QPUs), you will need to upload and run this notebook within Rigetti's [JupyterLab IDE](https://docs.rigetti.com/qcs/getting-started/jupyterlab-ide).\n",
    "If you have not previously installed the following Q-CTRL packages, you should uncomment and run the next cell, in order to be able to import the packages and functions required for this notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# !pip install boulder-opal\n",
    "# !pip install qctrl-visualizer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively, to run the notebook locally without device-specific evaluations, set `run_locally = True` in the following cell.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Whether to run notebook locally or within Rigetti's JupyterLab IDE.\n",
    "run_locally = True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following cell you can also choose whether to run all the commands from scratch or to use previously obtained data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Whether to use saved data or to run experiments.\n",
    "use_saved_data = True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to authenticate your Boulder Opal session remotely, you will also need to copy your authentication token to Rigetti's JupyterHub environment. \n",
    "Ensuring that your local and JupyterHub `boulder-opal` package versions match, copy your authentication token from `~/.config/qctrl` to the same location on JupyterHub."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-03T02:03:59.576744Z",
     "start_time": "2022-11-03T02:03:57.876033Z"
    }
   },
   "outputs": [],
   "source": [
    "from copy import deepcopy\n",
    "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())\n",
    "\n",
    "\n",
    "# Rigetti imports.\n",
    "if not run_locally:\n",
    "    from pyquil import get_qc, Program\n",
    "    from pyquil.gates import RX\n",
    "    from pyquil.quilbase import DefWaveform, Frame\n",
    "\n",
    "\n",
    "# Previously obtained population data encoded with jsonpickle.\n",
    "if use_saved_data:\n",
    "    import jsonpickle\n",
    "    import jsonpickle.ext.numpy as jsonpickle_numpy\n",
    "\n",
    "    jsonpickle_numpy.register_handlers()\n",
    "\n",
    "    def read_variable(string):\n",
    "        return jsonpickle.decode(string)\n",
    "\n",
    "    robust_pickle = (\n",
    "        '{\"py/object\": \"numpy.ndarray\", \"values\": \"eJxF0m9ozVEYwPG8UJRZ0USGRSYMmTah7ZvC8j/bwlxZFMuKUF75'\n",
    "        \"sxFvvKAUjaKUkZiSiJS1FWVDocnu7W53h7u5d7/f8e+F8kKe5+z43T4vTqffec7veZ7zFKVmiHomZQvEWaYMTRYtft/KtT\"\n",
    "        \"2qjf4i1c7FA6qT+GzVxc6bMdHNrORM8d7H9XD8zDGR8PFJWhpUivk984Thc6HDm1KVpryrTKR5UqW+8qpcZfiZp7KcO6qy\"\n",
    "        \"uN/FAl4vUQF5v8aJgEuNKmS6mSZCru9Wls0PNglL06mTwvJ8pbJUPV0jLPk/xgvLoncLRe58w5V9wjKnt1hY6KgUlqUuMc\"\n",
    "        \"vvMepbdL7+xi6Ri3u7WFk+zlWWW3XK8nKZyq2VnRUi9PXn8v8fd9A1PKStWoW+nyHhBIeNDzeIgNXPVomABR9KRMCXqSog\"\n",
    "        \"mOhQe69GDOM+lwxH/Wy8vF9kOHL+sMiw7c5WYX3fDS6tMkOpK2iAWOsOYXBpVxhOn1C5/chcGGpcwgY3DgWG6vtbxADrH6\"\n",
    "        \"0Thj+jlYnuu7pXGR6vVYMUu4vSvm+DNDc3iSHqbm8XKS4cUv18z1cp/o5SfYx1D/OJFS+Wi7ifo16fR9y/S5+vPx6tI3OY\"\n",
    "        'pNA1LhHt79aqBP8AjXefpQ==\", \"shape\": [101], \"dtype\": \"float64\", \"byteorder\": \"<\"}'\n",
    "    )\n",
    "    square_pickle = (\n",
    "        '{\"py/object\": \"numpy.ndarray\", \"values\": \"eJw90M8rw3EYwHE7KQfKZA62+XEWcbKD9/gDxE1hI78S5eDoyB8g'\n",
    "        \"pJjyI9kRFzc/RnZBrZWWw2w21nezfctBOeF55pNep+fp+dXTlPaKIHVFp1hkdUHtMXg8IE447VcRNmdVFMdPhYjxWaUe2Z\"\n",
    "        \"pWT3TE2kWK7SmVIXAwKt64KrPwRbtFnpHDYfHOrU+V+HYoG++LR9gQ6RE2z83K5qFTldiZUEXibarAV6WyzF05QpMqi7+8\"\n",
    "        \"MMV5n0oSHlIJWpMtIm7239FVHnyNK18vzmiwXCKMs1Qr1kw8Y/6y/J//qz8iuB8QF6zPqxvc2UZxb/4XM/0JPBm3SDK+Oy\"\n",
    "        'bSrCypV2o+qkWO3ku/sMx9BTbmVJFfM5LN8A==\", \"shape\": [51], \"dtype\": \"float64\", \"byteorder\": \"<\"}'\n",
    "    )\n",
    "    default_pickle = (\n",
    "        '{\"py/object\": \"numpy.ndarray\", \"values\": \"eJxF0c8rRFEUB/CNHzErdhY2bBDKjAUp31nIbEVmWCgz8iMWRon4'\n",
    "        \"A5QszIKSQlkIke2TBUpZ+FESVmrmefNm3pv37t2gZOOc2230WZzVufd8zzEiBknD0DX42EYy2B9hJurf64iJmy5mofS3hF\"\n",
    "        \"jYnGZZ2DUKFlcXiI29UZbDUytzsLyyRBwkduPEwdhOgri4a2cFfAaYh5MB5mFjhnl4CDIf3xVMIHo8SHzEjqJEIHLeSwTK\"\n",
    "        \"f8qIwFkfk7gMM6nnkEimZolE+ApEYmprkkisJ5ks9r01MInbDiaB624iivVgmAmdV2Bie5z4eGliPlqem8l/joseVkBIBX\"\n",
    "        'ER+KokLqpFFXHQqT7KI64GzWPoMEZyOo+N10Zm47SfZfX7Fu5DzCreZW2efeh9Z2DWKphTAdP4A812+Ng=\", '\n",
    "        '\"shape\": [60], \"dtype\": \"float64\", \"byteorder\": \"<\"}'\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluation of default X gate amplitude robustness\n",
    "\n",
    "We will evaluate X gates on a Rigetti quantum device.\n",
    "The total Hamiltonian of the driven quantum system is:\n",
    "\n",
    "$$ H(t) = (1+\\beta_\\gamma (t)) H_c(t),$$\n",
    "\n",
    "where $\\beta_\\gamma(t)$ is a fractional time-dependent amplitude fluctuation process, and $H_c(t)$ is the control term given by\n",
    "\n",
    "\\begin{align*}\n",
    "H_c(t) = & \\frac{1}{2}\\left(\\gamma^*(t) \\sigma_- + \\gamma(t) \\sigma_+ \\right) \\\\\n",
    "= & \\frac{1}{2}\\left(I(t) \\sigma_x + Q(t) \\sigma_y \\right).\n",
    "\\end{align*}\n",
    "\n",
    "Here, $\\gamma(t) = I(t) + i Q(t)$ is the time-dependent complex-valued control pulse waveform and $\\sigma_k$, $k=x,y,z$, are the Pauli matrices.\n",
    "\n",
    "We begin by evaluating the default gate on the device; we will later use the duration of the default waveform to define our amplitude-robust waveform.\n",
    "Here we evaluate the robustness of the default waveform $\\gamma(t)$ using a quasi-static scan over $\\beta_\\gamma$.\n",
    "\n",
    "First, set up the target QPU and compiler, and obtain the device calibrations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-03T02:04:16.273685Z",
     "start_time": "2022-11-03T02:04:16.269088Z"
    }
   },
   "outputs": [],
   "source": [
    "if not run_locally:\n",
    "    qc = get_qc(\"Aspen-M-2\", compiler_timeout=100)\n",
    "    cals = qc.compiler.get_calibration_program()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we define a function that will set up a hardware experiment (program) that illustrates pulse-level control using Quil-T.\n",
    "We define a custom waveform `my_waveform`, include it as part of a custom gate definition `CustomX`, and apply our custom gate as part of a program using [parametric compilation](https://pyquil-docs.rigetti.com/en/stable/quilt_parametric.html).\n",
    "Parametric compilation allows faster evaluation of some forms of programs by allowing free parameters to be varied post-compilation.\n",
    "In our program we set a free `scale` parameter to vary the amplitude of the given waveform, apply our `CustomX` gate to the initial state $|0\\rangle$, then implement measurement on the given qubit.\n",
    "The custom waveform definition must be added to the program, along with the number of measurement shots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-03T02:04:18.859498Z",
     "start_time": "2022-11-03T02:04:18.853592Z"
    }
   },
   "outputs": [],
   "source": [
    "shot_count = 1028\n",
    "\n",
    "\n",
    "def custom_pulse_parametric_program(waveform, qubit):\n",
    "    new_waveform = DefWaveform(name=\"my_waveform\", parameters=[], entries=waveform)\n",
    "    program = Program(\n",
    "        f\"\"\"\n",
    "        DEFCAL CustomX {qubit}:\n",
    "            FENCE {qubit}\n",
    "            NONBLOCKING PULSE {qubit} \"rf\" my_waveform\n",
    "            FENCE {qubit}\"\"\",\n",
    "        \"DECLARE scale REAL[1]\",\n",
    "        f'SET-SCALE {qubit} \"rf\" scale',\n",
    "        f\"CustomX {qubit}\",\n",
    "        \"DECLARE ro BIT[1]\",\n",
    "        f\"MEASURE {qubit} ro[0]\",\n",
    "    )\n",
    "    program += new_waveform\n",
    "    program.num_shots = shot_count\n",
    "    return program"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, given access to the QPU through Rigetti's IDE, you can choose a target qubit and obtain the default gate waveform and its properties. You can then obtain the parametric program using the default waveform, and compile the program."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-03T02:04:20.972951Z",
     "start_time": "2022-11-03T02:04:20.966708Z"
    }
   },
   "outputs": [],
   "source": [
    "qubit = 22\n",
    "\n",
    "if not run_locally:\n",
    "    x_calibration = deepcopy(cals.get_calibration(RX(np.pi, qubit)))\n",
    "    sample_rate = cals.frames[Frame(qubits=[qubit], name=\"rf\")].sample_rate\n",
    "    default_function = x_calibration.instrs[1].waveform\n",
    "    default_waveform = default_function.samples(rate=sample_rate)\n",
    "    duration = len(default_waveform) * (1 / sample_rate)  # s\n",
    "    print(default_function)\n",
    "    default_program = custom_pulse_parametric_program(default_waveform, qubit)\n",
    "    executable = qc.compiler.native_quil_to_executable(default_program)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now you can run the program on the hardware during your booking window. Below, we take the sum over the shot results, which gives the probability of measuring the target $|1\\rangle$ state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-03T02:04:37.624322Z",
     "start_time": "2022-11-03T02:04:37.614961Z"
    }
   },
   "outputs": [],
   "source": [
    "default_scales = np.linspace(0.5, 1.5, 60)\n",
    "\n",
    "if not use_saved_data:\n",
    "    default_population = []\n",
    "    for scale in default_scales:\n",
    "        executable.write_memory(region_name=\"scale\", value=scale)\n",
    "        results = qc.run(executable)\n",
    "        default_population.append(np.sum(results.readout_data[\"ro\"]) / shot_count)\n",
    "else:\n",
    "    default_population = read_variable(default_pickle)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can then plot the state fidelity over the amplitude scan as a measure of amplitude robustness. The control amplitude error $\\beta_\\gamma$ is relative to the ideal amplitude scale, which is unity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-03T02:29:48.527983Z",
     "start_time": "2022-11-03T02:29:48.386393Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best infidelity: 7.782e-03\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(f\"Best infidelity: {1 - np.max(default_population):.3e}\")\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "ax.plot(default_scales - 1, 1 - np.array(default_population))\n",
    "ax.set_xlabel(\"Control amplitude error\")\n",
    "ax.set_ylabel(\"Infidelity\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creation and verification of amplitude-robust Boulder Opal pulses\n",
    "\n",
    "We use Boulder Opal to perform optimizations to achieve an X-gate operation on the qubit. \n",
    "We optimize a square pulse using the default pulse duration, and a smooth amplitude-robust pulse with slightly longer duration to facilitate more robust solutions.\n",
    "We then characterize the pulse robustness using filter functions and quasi-static scans."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating amplitude-robust pulses\n",
    "\n",
    "We begin by optimizing the amplitude of a square pulse for a simulation performance benchmark, using the duration of the current (or saved) default pulse. Note that pulses with different durations will require different amplitude limits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-03T02:12:16.384409Z",
     "start_time": "2022-11-03T02:12:11.706170Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1827927\") has started.\n",
      "Your task (action_id=\"1827927\") has completed.\n",
      "Optimized infidelity: 4.441e-16\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAnsAAADKCAYAAADdPYZuAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8pXeV/AAAACXBIWXMAAAsTAAALEwEAmpwYAAAeHUlEQVR4nO3deXRU5f3H8c8kM0kgCyGQkBXCTlgSQBYREEFRwA1ZRax1QflZtVpoFbXuS7VWbXHBWkVAqoKAaMuiVgERo+x72LfsCwkQssxMMvf3BzU1sgWSzJU779c5HJjnzjzP9ztnmPmce2futRmGYQgAAACW5Gd2AQAAAKg/hD0AAAALI+wBAABYGGEPAADAwgh7AAAAFkbYAwAAsDC72QX8Uu1Oz5fD7l+va1RUemT3J28DAGBl3vi8d1dUqm1C5Cm3EfZOw2H3V2JMRL2ukZF3RPFR4fW6BgAAMJc3Pu8PZBeedhu7lUxE0AMAwPrM/rwn7JkoI++I2SUAAIB6ZvbnPWHPRCVlLrNLAAAA9czsz3u+s2eSN0Ye0dYvJCnP7FIAAEA9SuwvPbTYvPXZs2eSrV+wVw8AAF9wYKW567Nnz2R3z2lkdgkAAKCeTBt71OwSfCfsrUvdoCULP1dRwRGFhYdq/F3j1KZ9K7PLAgAAqFc+EfZ2bNmpT+f8W7fd+yu1aNVcx44cM7skAAAAr/CJsLd4wecaOnywWrZJlCSFR4SbWg8AAIC3WD7seTweHdqfrs7dO+mpyc+pwl2hLhd11vBx1yogIMDs8gAAAOqV5cNe8dFiVVZWauOaTXrgsfvk7++nt1+drs8//Y+uHT2s2n1XfZ2qVctTJUnDxo+S6vlyaQAAAPXN8mHPEeCQJA0Y3F+NwsMkSYOGDjhl2Os7qI/6Duoj6czXmAMAALhQWP48ew2DG574jp7tp6O209wbAADAWiwf9iTp4kt76psvvlXx0WKVlpRq2dIV6tS1o9llAQAA1DvLH8aVpCHXX6njxSV65sE/ye5wqHuvFF113RVmlwUAAFDvfCLs+dv9NfbWURp76yizSwEAAPAqnziMCwAA4KsIewAAABZG2AMAALAwwh4AAICFEfYAAAAsjLAHAABgYYQ9AAAACyPsAQAAWBhhDwAAwMIIewAAABZG2AMAALAwwh4AAICFEfYAAAAsjLAHAABgYYQ9AAAACyPsAQAAWBhhDwAAwMIIewAAABZG2AMAALAwwh4AAICFEfYAAAAsjLAHAABgYYQ9AAAACyPsAQAAWBhhDwAAwMIIewAAABZG2AMAALAwwh4AAICFEfYAAAAsjLAHAABgYT4V9vJy8vW72x/UzGmzzS4FAADAK3wq7H08c76at0wwuwwAAACv8Zmwty51gxo0bKD2ndqaXQoAAIDX+ETYKysr16IFS3XD+OvNLgUAAMCr7GYX4A2L5i1RnwG91Dgi/Iz3W/V1qlYtT5UkDRs/SoqJ8EJ1AAAA9ceUsOfxeLQ7ba/27NirwoJCuV1uhYSGKCExTh26tFfjJo3rbK2Mg5nauW2XHnp28lnv23dQH/Ud1EeSdCC7sM5qAAAAMItXw57L5dKyJSu08qtVKj1eqrgWcWoUHiZHgEOH8w9r68Zt+ui9eerQuZ2G3HClWrZJrPWau9P2qDC/SI8/8IwkyVnulOHx6MXMl2sUAAEAAC5kXg17z/z+T0psk6gbbx+jpM7t5W/3P+k+hQWFWvvder33+vu66vor1Hdgn1qt2XdgH110cbeq218tXq7CgkKNuXVUreYFAAC4ENQ47C355HNdcc3lcjjOPx/e/Ye7FJsQc8b7RDSN0JXXXaFBwy5TYUHRea/1o4DAAAUEBlTdDgwKkN1hV2hYSK3nBgAA+KU7h7D3hSKaRqhVu0RFNousti1t8w4lJXc46xxnC3rVCrPbFRUdefY7nqNhI4bU+ZwAAAC/VOe0m27uzPlyu9wKCAxQTHy04prHKqJJYy1bukJ/evOZc1r4yUnPqm1SG429bZTs9v+Vcbz4uP7yxF/15Ct/PKf5AAAAcLJzCntPvPyonOXlyjyUpYyDWco8mKm9O/apbcdzP1FxYUGRdm3fo6nPv6m7fne7QkJPHFb1eIw6OXwLAACAcwx7NkmRzSIV2SxSXXum1Hrxe6dM1PzZn+qlx1/VxEkTzukwLwAAAM7unK6gkXEoSy6nq84WDwoK0sRJd6hbrxS9+sxr2rphW53NDQAAgHPcszftpbdls9nUJKqJ4hJiFNc8VrEJsYpNiFHTqCbnVYDNZtPwcdcpJj5G773xvvpf3ve85gEAAMDJahz2omObacIDt+nY0WJlHcpSVnqWtm1K038WLZPL6dLUWS/XqpDe/XsqsllTvTN1Rq3mAQAAwP/YDMMwajOBYRgqyCs46XQsZ1NYUKjwiHD5+VU/knzsaLFys3LVNqlNbcqqtQPZhUqsx2vj3h2ad+LvOY3qbQ0AAGCuaWOPnvi7OKpe1zlTbqn1FTRsNts5Bz3pxMmTTyWsUajCGoXWtiwAAACohmGvtKRM+3bvV8OGDdSybaJsNlvVNme5U18vWa6hN1xVowWnPv+GTvyu98x++8hvajQfAAAATu+sYS87I0evvzBNx4tLZBiG4hPjNOG3t1btmXM6XVryyRc1Dnsx8dVPr/LdslR1691NDRoGnUf5AAAAOJOzhr3P5i5SYttE3TLxJpWXOzX//U/06tOv6b5HfnNelzMbfcuIard/WLlGw0Zcdd6/5gUAAMDpnfU8ewf2HNQ1I4cqMChQjcLDdPt9v1a33l019fk3lJed540aAQAAcJ7OGvYqKipO+ordiPHXq1uvrvrb828qNyu3vmoDAABALZ31MG5UTKQO7UtXTFx0tfGRNw+XYRh6+9Xp9VYcAAAAauesYS+lR7LWfb9Bvfv3PGnbqF/dIE+lR99+/V2NF9y4ZnO124bHUNrmHQr92elWuvZMrvGcAAAAOLWzhr3jx47rymsvl8fjOekEyJI05taRGnPryBovOP21mSeNfTxrwUljtb0iBwAAAGoQ9twut2a8+b4qKyrVMaWjki/qrKTk9goICDivBQlxAAAA3nPWsDf2tlEae9soHdh7UFvWb9OieUs0a9o/1a5TWyVf1Fmdu3VSaFiIN2oFAADAOarx5dISW7dQYusWunb0MOXn5mvzum36YeUazZ0xT81bNVdy9866qE83hUeEn3Ge9AMZNVovITG+pqUBAADgNGoc9j5672NdO3qYgkOCFdksUpcPu0yXD7tMx4uPa8v6bdqyfpsk6fKrB55xnpcef7VG63G4FwAAoPZqHPYO5xfq6d8/ryHDr9Slg/vJ399fkhQSGqI+A3qrz4DeNVvQ7q/QRqHq3b+XuvfuqoBAx/lVDgAAgLOqcdi758GJ2rJ+mxZ++Jm+/TpVI266Tp26djznBZ997Smt/W6dUlf8oOWfr1C3Xl3V57LeSmzd4pznAgAAwJnVOOxJUpfundQxuYOWf/6NZk6brcTWLTTi5uGKjm1W4zkaBjfQpYP76dLB/ZR+IEOpK37QtL/8Q40aheniAb112VX9T3mKFwAAAJy7c05V/nZ/XX71QD320iNq3KSx/vzHlzXv/U90aH+63C73Oc2VkBivMb8eqUdfeEghYSFa+OFnKistO9eSAAAAcBo13rPncrq0O22PcrPzlJedp9zsfOVm56miolIrv1qlb778VjY/m6KiI/XoCw/VaM5d23fr+29Wa9PaLYpvEaebJoxVw+CG590MAAAAqqtx2Pvb828oJyNX8YlxahYTpU5dkzRo6ABFRkcqMqqpKioqlHkoSxkHM884T1HhEf3wzWr9sHKN3G63evbtoYeemaSomKhaNwMAAIDqzmnP3uQnf6vYhNhTbve3+6tVu5Zq1a7lGed5ctKzCm/cSL3791THlCT5+/vL6XSddP49zrMHAABQezUOezU9NHs2hsdQ0eEjWrrwSy1d+OVp78d59gAAAGrvnH6NWxeefOVRby8JAADgs7wa9gryDqtpVJMa3dcwDB0pPKLGTRrXc1UAAADW5dWw98rTU9UpJUmXXHaxWrZNPOV9SktKtS51g1Z8uVL9r+irAYP712pNt7tCc2fM085tu1VaUqqmUU107Zir1SklqVbzAgAAXAi8Gvb++OIUffHZl3rr5X/IZvNTQst4NQoPk8PhUGlJqXKycpWTlasWrZpr5PjhSkruUOs1PZWVatwkXPc/eo8aNwnX9k1peu/1WXr4+T+oSWREHXQFAADwy+XVsNcwuIGGj7tOw0YO0baNadq3a58KC4p0zHVMwaHB6tWvp5K6tFdsQkydrRkYFKhhI4ZU3e7crZOaREYo/UA6YQ8AAFie13+gIUkBAQHq1itF3XqleH3tY0eLlZeTr+i4aK+vDQAA4G2mhD2zVFZUaua02erdr8cpr+e76utUrVqeKkkaNn6UFMOePwAAcGHzmbDn8Xg0661/yu7vr9G3jDzlffoO6qO+g/pIkg5kF3qzPAAAgHrhZ3YB3mAYhj54Z46KjxXrjvtvlb/d3+ySAAAAvMInwt6cGfOUm5WriZMmKCAgwOxyAAAAvMbyh3ELCwq16utU2R12PXLvE1XjN942Wj37XmRiZQAAAPXP8mEvommEXnv/FbPLAAAAMIVPHMYFAADwVYQ9AAAACyPsAQAAWBhhDwAAwMIIewAAABZG2AMAALAwwh4AAICFEfYAAAAsjLAHAABgYYQ9AAAACyPsAQAAWBhhDwAAwMIIewAAABZG2AMAALAwwh4AAICFEfYAAAAsjLAHAABgYYQ9AAAACyPsAQAAWBhhDwAAwMIIewAAABZG2AMAALAwwh4AAICFEfYAAAAsjLAHAABgYYQ9AAAACyPsAQAAWBhhDwAAwMIIewAAABZG2AMAALAwwh4AAICF2c0uwBtKjpfog3fmaMeWXQoODdZ1Y4apxyUXmV0WAABAvfOJsDd35gL52+16/o2nlHEwU2+9/I7imscpJj7a7NIAAADqleUP4zrLndq0ZrOuGTlEgUGBat2+lbp076TVq9aaXRoAAEC9s3zYy8vJl5+/n6JioqrG4hJilZORY2JVAAAA3mH5w7hOp0tBDYKqjQU1DFJ5ufOk+676OlWrlqdKkq68cYR2uirqvb7ATkfrfQ0AAGCunQfz6nX+wIDTRzrLh73AwACVl5VXGysvcyooKPCk+/Yd1Ed9B/WRJB3ILlRiTES91TWtWCp3uhUU6Ki3NQAAgLm89Xl/ILvwtNssfxg3KjpSnkqP8nLyq8YyD2Upmh9nAAAAH2D5sBcYFKiUHl20aP5SOcud2rdrv7as36pefXuYXZoO5hSZXQIAAKhnZn/eWz7sSdKYW0fK7XLrkXue0Iw339fYW0dy2hUAAOATLP+dPUkKDgnWXb+73ewyAAAAvM4nwt75cFdUnvHLjnWyRnl5va/xS3b82HGFhIWYXYYpfLl3ybf7p3ff7F3y7f59uXfJO5/37orK0280YJoXH3vZ7BJM5cv9+3LvhuHb/dO77/Ll/n25d8Mwv3+f+M4eAACAryLsAQAAWBhhz0R9L+tjdgmm8uX+fbl3ybf7p3ff5cv9+3Lvkvn92wzDMEytAAAAAPWGPXsAAAAWRtgDAACwMM6zZ4KS4yX64J052rFll4JDg3XdmGHqcclFZpdVb1Z8uVI/rFyj7PRsdb+4u341cVzVtp3bdmnuzAUqOlykxNbNdfNd4xTRNMLEauuW212huTPmaee23SotKVXTqCa6dszV6pSSJMn6/c+cNlu7tu2Wy+lSaHiYrrh6oC657GJJ1u/9R3k5+frTIy+pa89k/frumyVJa79bp8/mLlZJcYnad26n8XeOVXBIsMmV1q2/PfeGDuw9KD+/E/sUwhs30mMvPSzJN/pfl7pBSxZ+rqKCIwoLD9X4u8apTftWln/dT54wpdptt8ut/lf01ehbRkiy/v/7w/mFmjtjnvbvOSi7w66uPZM18ubh8vf3V8bBTH3wzhzlZOUqOraZbpowVvEt4rxTmKknfvFR01+fZbz72kyjvKzc2LNjr/H7Ox82stKzzS6r3mxYvcnYuGaz8dH0j41Zb31QNV58rNj4/Z0PG+u/32C4nC7jkw8+Nf7yxKvmFVoPysvKjUXzlxgFeYeNyspKY8v6rcbkCVOMgrzDPtF/Vnq24XK5DcMwjOzMHOPhex43Du475BO9/+j1F6YZrzw91Zjx5vuGYZx4TiZPmGLsTttjlJeVG++9McuY/tpMk6use3999nVj1bLUk8Z9of+0zTuMx+5/2ti3e79RWVlpFB0uMooOF/nU694wTrz/TbrjIWN32h7DMHzjPf/NP//dmPXWB4bL6TKOFh01npvyorFs6QrD7XYbj93/tPHV4uWGy+U2li1dYTx2/9OG2+32Sl0cxvUyZ7lTm9Zs1jUjhygwKFCt27dSl+6dtHrVWrNLqzddeyYrpUcXBYc0rDa+ac0WxcRFq1vvrnIEODT0hquUeShLOVm5JlVa9wKDAjVsxBA1iYyQn5+fOnfrpCaREUo/kO4T/cfER8vhOHEAwWazySapIO+wT/Qundi706BhA7Xv1LZqbM1369S5W0e16dBagUGBunrkUG1au0XlZeUmVuo9vtD/4gWfa+jwwWrZJlF+fn4KjwhXeES4z7zuf7RxzWaFhoWodftWknzjPf9wQaG6906RI8ChsPAwdUzuoJzMHO1O2yuPp1IDh1wqh8Ouy666VJKhXdt3e6Uuwp6X5eXky8/fT1ExUVVjcQmxysnIMbEqc2Rn5iiueWzV7cCgQDWNaqqcTOs+F8eOFisvJ1/RcdE+0/+cGfM06Y6H9OyDLygsPEydUpJ8oveysnItWrBUN4y/vtp4zs96j2zWVP52f+Xl5Hu7xHr3r7mLNOXux/TK01O1O22PJOv37/F4dGh/uoqLS/TU5Of02G+f0tyZ8+VyuXzidf9TP6xco179eshms0nyjff8y666VOu+3yiX06UjhUe0fdMOJSV3UHZGjmITYqueC0mKTYhVdoZ3gi7f2fMyp9OloAZB1caCGgapvNxpUkXmcZY7T7pWYlDDIJWXWfO5qKyo1Mxps9W7Xw9Fxzbzmf7H3jpKo28Zof27D2h32l7Z7Xaf6H3RvCXqM6CXGkeEVxt3lrvUoEGDamMNGgbJabH3gOvHXqPouGbyt9u1/vsN+vsr7+qhZydbvv/io8WqrKzUxjWb9MBj98nf309vvzpdn3/6H5943f+osKBQe3bs1U0TxlaN+UL/bdq31nfLvtcf7npEHo9Hvfr1VPJFXfT5p1+qwc8++xs0CJKz3Dt7tNmz52WBgQEnHa4oL3MqKCjQpIrMExgUeIrnolxBDaz3XHg8Hs1665+y+/tr9C0jJflW/35+fmrdvpWOFB3Ryq9WWb73jIOZ2rltlwYOGXDStsCgU78HBFrsPSCxTQsFNQiSw2FX7/491aptorZvSrN8/44AhyRpwOD+ahQeppDQEA0aOuC/vVv7df9Tq79dp9btWqppVJOqMav37/F49OZLbyulRxf95Z0X9MKbz6istFSffvRvBQSeuvfAoKDTzFa3CHteFhUdKU+lp9ohi8xDWYqOjzaxKnPExEUr81BW1W1nuVMFeYcVHWet58IwDH3wzhwVHyvWHfffKn+7vyTf6f+nPJUeFeQdtnzvu9P2qDC/SI8/8IweufcJfbV4uTat2awX//iyon/We0HeYVW4KxQVHWlixV5gs8kwDMv33zC4ocIjwiXbT0dP3LD66/6nVq9aq179e1Ybs3r/pSWlKjpcpEsH95PDYVdwaLB69++l7ZvSFBMfraz0bBk/uY5FZnq2YuKbeaU2wp6XBQYFKqVHFy2av1TOcqf27dqvLeu3qlffHmaXVm8qKyvldrnl8XhkGB65XW5VVlYquUcXZWfkaOOaTXK73Fq68AvFJcQoOtY7L35vmTNjnnKzcjVx0gQFBARUjVu9/+KjxVqXukHOcqc8Ho/SNu/QutQNat+preV77zuwj554+RFNeXaypjw7Wf0GXaJOXTvqNw9OVM9LLtLWDdu0Z+c+OcudWjR/iVJ6dDnp6x0XstKSMqVt3lH1f33NqnXau2OfOiZ38In+L760p7754lsVHy1WaUmpli1doU5dO1r+df+jfbv262jhUXXrlVJt3Or9h4SGqElkhFZ+9Z0qKytVWlKm1d+uUWzzGLVNai2bn59WfLFSbneFVny5UpLUrmPbs8xaN7hcmglKjpfon/+Yo51bdyk4tKGuG3O1pc+zt3jBUi355ItqY0NvuFLDRgzRjq279PGsBSoqKFSL1i10813j1CTSOudcKiwo1BO/e1Z2h73qfGOSdONto9Wz70WW7r/42HFNnzpDmelZMjyGGjdtrAFX9lffgSeuEWnl3n9u8YKlys8t+Nl59happLhU7Tu31fg7b7TUeeaKjx3XW3/5h3Kz8+TnZ1OzmChdPXKoOnRpL8n6/VdWVGre7E+0LnW97A6HuvdK0fU3XitHgMMnXvcfTZ8rl8utW/5v/EnbrN5/xsFMzZ+9UJmHsuTn56d2Hdto1C0jFNYoVOkHMvThu3OVk5mjZv89z15CYrxX6iLsAQAAWBiHcQEAACyMsAcAAGBhhD0AAAALI+wBAABYGGEPAADAwgh7AAAAFkbYAwAAsDDCHgAAgIUR9gAAACyMsAcAAGBhhD0AAAALI+wBAABYGGEPAADAwgh7AAAAFkbYAwAAsDDCHgAAgIUR9gAAACyMsAcAP/H9N6s1ecIU09YvLSnVI/c8rvzcgjqZz+2u0OMPPK1D+9LrZD4AFx6bYRiG2UUAgDfc96tJZ9zeq19Pjb1tpJxlToU2CvVSVdUt/PAzHS8u0c13jauzOVd8sVKb123VfQ/fXWdzArhw2M0uAAC85bnXnqz699aN2/Xhu3OrjTkCHAoICFBAQID3i5Pkcrr03fIfNHHSHXU6b49Lumvhh58pOyNHMfHRdTo3gF8+wh4AnxEWHlb17wYNG5w0Jp04jPvxrAV6+Z0XJEmLFyzVxtWbdfnVA7V4wVIdP1aibr1TdOPto/Xd8h/05b++ksvlUu9+PTV83LXy8zvx7ZiKigotmrdEa79br5KSUsXEReuaUUOVlNzhtPVt25Qmm01q1a5l1djutD2a+vybunfK/+lfcxcrKyNb0XHNNO72MUpIjJcklZWW6eNZC5S2eafKy8vVKDxMA67sr4FDBkiSgkOC1bJtS61LXa9rRg+rg2cSwIWEsAcAZ3G4oFCb12/VxEkTdLToqN6ZOkPHjhxTWHiY7nlwonKzczX99Vlq1S5RXXumSJL++fZHKsgr0K9/c7PCI8K1bdN2/f2Vd/X7px5QfIu4U66zd+c+JSQmyGaznbTts7mLdP3YaxQWHqb5sxdq5rTZevSFh2Sz2fTveUuUlZ6tiZPvUFijUB3OL9TxY8erPb5F6+bavWNv3T85AH7x+IEGAJyF4fHo5jtvVGxCjJKSO6hjcgelH8jQjbePVnRcM6X0SFarti21a/seSVJ+boHWfb9Bt937a7Xp0FpNo5powOD+6piSpFXLUk+7TmFBkRo1DjvltmtGDlW7jm0VHdtMQ4dfqdysPB0pOlr1uITEeCW2bqGIphFqm9RG3Xp3rfb4RuFhKiwoqpsnBMAFhT17AHAWjZs0rjrsK0mhYaGKjI6U3f6/t9DQRqFVe9MyDmTIMAw9N+XFavNUVFSoXce2p13H7XYrzBFyym2xzWOr/v3joefjx46rcUS4+l1+iaZPnalD+9PVoXN7de7WUW2T2lR7vCPAIbfLXcOOAVgJYQ8AzsLf37/6gO3kMZskz39PbuAxDNlsNv3hqd/J3179AIrD4TjtOiEhwSotKTtNDf+b58fDvIbnxHqdUpL01F//qO2bdmjntt166+V31K1XSrVf9JaWlCokLPjMjQKwJA7jAkAdS2gRJ8MwdOzoMUU2i6z2Jzwi/LSPi28Rp5zM3PNaMyQ0RL369dCvJo7TTRPGavW3a+V2V1Rtz87IUUKL+POaG8CFjbAHAHUsKiZKPS7prtlvf6QNqzepIO+wDu1L11eLlmnjms2nfVxScnvlZOWqpLjknNZbNH+JNq3dorycfOVk5mrT2i1qEhkhh+N/B2/27tx3xl8CA7AuDuMCQD24+c5x+vyzL/XpR//SkcKjahjSUC1aNVfbjm1O+5jYhFi1aN1c677foEsH96vxWna7Xf+et1iH8wvlcNiV2LqFJk6aULV9/+4DKistV9deybXqCcCFiStoAMAvyPbNaZr//kI9+uJDVefsq613p85UfGKcrrruijqZD8CFhT17APAL0jE5SXlX5OtI4RFFNI2o9Xxud4Ximsdo4JBL66A6ABci9uwBAABYGD/QAAAAsDDCHgAAgIUR9gAAACyMsAcAAGBhhD0AAAALI+wBAABYGGEPAADAwv4fhCMFntXxJQMAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 720x180 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph = bo.Graph()\n",
    "\n",
    "# Create Hamiltonian.\n",
    "if run_locally:\n",
    "    duration = 80e-9  # s\n",
    "    sample_rate = 1e9  # Hz\n",
    "\n",
    "drive = graph.real_optimizable_pwc_signal(\n",
    "    1, duration, 2 * np.pi * 8e6, 2 * np.pi * 1e6, name=\"drive\"\n",
    ")\n",
    "control_hamiltonian = graph.hermitian_part(drive * graph.pauli_matrix(\"P\"))\n",
    "\n",
    "# Create infidelity.\n",
    "infidelity = graph.infidelity_pwc(\n",
    "    hamiltonian=control_hamiltonian,\n",
    "    target=graph.target(graph.pauli_matrix(\"X\")),\n",
    "    name=\"infidelity\",\n",
    ")\n",
    "\n",
    "# Calculate optimization.\n",
    "square_result = bo.run_optimization(\n",
    "    graph=graph, cost_node_name=\"infidelity\", output_node_names=[\"drive\"]\n",
    ")\n",
    "print(f\"Optimized infidelity: {square_result['cost']:.3e}\")\n",
    "qv.plot_controls({r\"$\\gamma$\": square_result[\"output\"][\"drive\"]})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we optimize a smooth, robust pulse. \n",
    "We allow a slightly longer duration than the default pulse, which often helps to provide the necessary control freedom to increase robustness.\n",
    "The returned pulse `sample_count` is defined using the hardware `sample_rate` obtained above for the default pulse.\n",
    "The smoothing using `graph.filter_and_resample_pwc` is performed using a sinc filter to eliminate frequencies above the cutoff frequency, and we also apply a `graph.signals.gaussian_pulse_pwc` envelope for higher-fidelity signal generation on the hardware."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-03T02:12:28.898611Z",
     "start_time": "2022-11-03T02:12:19.148438Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1827941\") is queued.\n",
      "Your task (action_id=\"1827941\") has started.\n",
      "Your task (action_id=\"1827941\") has completed.\n",
      "\n",
      "Optimized robust infidelity: 1.806e-11\n",
      "Optimized noise-free infidelity: 4.787e-12\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "robust_duration = duration + 20e-9\n",
    "optimization_count = 16\n",
    "sample_count = round(robust_duration * sample_rate)\n",
    "max_rabi_rate = 2 * np.pi * 60e6  # rad/s\n",
    "cutoff_frequency = 2 * np.pi * 15e6  # rad/s\n",
    "\n",
    "graph = bo.Graph()\n",
    "\n",
    "# Create Hamiltonian.\n",
    "drive_pwc = graph.complex_optimizable_pwc_signal(\n",
    "    optimization_count, robust_duration, max_rabi_rate\n",
    ")\n",
    "filtered_drive = graph.filter_and_resample_pwc(\n",
    "    drive_pwc,\n",
    "    kernel=graph.sinc_convolution_kernel(cutoff_frequency),\n",
    "    segment_count=sample_count,\n",
    ")\n",
    "envelope = graph.signals.gaussian_pulse_pwc(\n",
    "    robust_duration, sample_count, amplitude=1.0, flat_duration=robust_duration / 2\n",
    ")\n",
    "filtered_drive *= envelope\n",
    "filtered_drive.name = \"drive\"\n",
    "drive_term = filtered_drive * graph.pauli_matrix(\"P\")\n",
    "control_hamiltonian = graph.hermitian_part(drive_term)\n",
    "\n",
    "# Create noise-free infidelity.\n",
    "noise_free_infidelity = graph.infidelity_pwc(\n",
    "    hamiltonian=control_hamiltonian,\n",
    "    target=graph.target(graph.pauli_matrix(\"X\")),\n",
    "    name=\"noise_free_infidelity\",\n",
    ")\n",
    "\n",
    "# Create robust infidelity.\n",
    "infidelity = graph.infidelity_pwc(\n",
    "    hamiltonian=control_hamiltonian,\n",
    "    target=graph.target(graph.pauli_matrix(\"X\")),\n",
    "    noise_operators=[0.1 * control_hamiltonian],\n",
    "    name=\"infidelity\",\n",
    ")\n",
    "\n",
    "# Calculate optimization.\n",
    "robust_result = bo.run_optimization(\n",
    "    graph=graph,\n",
    "    cost_node_name=\"infidelity\",\n",
    "    output_node_names=[\"drive\", \"infidelity\", \"noise_free_infidelity\"],\n",
    ")\n",
    "print()\n",
    "print(\n",
    "    f\"Optimized robust infidelity: {robust_result['output']['infidelity']['value']:.3e}\"\n",
    ")\n",
    "print(\n",
    "    \"Optimized noise-free infidelity: \"\n",
    "    f\"{robust_result['output']['noise_free_infidelity']['value']:.3e}\"\n",
    ")\n",
    "qv.plot_controls({r\"$\\gamma$\": robust_result[\"output\"][\"drive\"]})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We write the complex wavefunction as a list for implementation on the hardware.\n",
    "The number of samples returned by the `filtered_drive` output corresponds to the nanosecond wavefunction resolution of the device."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-03T02:12:36.709996Z",
     "start_time": "2022-11-03T02:12:36.702018Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Robust waveform duration: 1e-07\n",
      "Waveform samples: 100\n"
     ]
    }
   ],
   "source": [
    "durations = robust_result[\"output\"][\"drive\"][\"durations\"]\n",
    "values = robust_result[\"output\"][\"drive\"][\"values\"]\n",
    "robust_waveform = list((values / np.max(np.abs(values)))[np.array(durations > 1e-10)])\n",
    "print(\"Robust waveform duration:\", robust_duration)\n",
    "print(\"Waveform samples:\", len(robust_waveform))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Robustness characterization with filter functions and quasi-static scans\n",
    "\n",
    "[Filter functions](https://docs.q-ctrl.com/boulder-opal/toolkit/design/design-model-based-controls/estimate-noise-resilience/how-to-calculate-and-use-filter-functions-for-arbitrary-controls) provide a useful way to determine the sensitivity of pulses to different time varying noise mechanisms.\n",
    "The next cell generates filter functions for the Q-CTRL robust pulse and the primitive square pulse under amplitude noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1827957\") is queued.\n",
      "Your task (action_id=\"1827957\") has started.\n",
      "Your task (action_id=\"1827957\") has completed.\n"
     ]
    }
   ],
   "source": [
    "sample_count = 4096\n",
    "frequencies = np.logspace(-2, np.log10(max_rabi_rate), 2000)\n",
    "drive_labels = [\"Q-CTRL pulse\", \"Square pulse\"]\n",
    "drives = {\n",
    "    \"Q-CTRL pulse\": robust_result[\"output\"][\"drive\"],\n",
    "    \"Square pulse\": square_result[\"output\"][\"drive\"],\n",
    "}\n",
    "\n",
    "graph = bo.Graph()\n",
    "for label, drive in drives.items():\n",
    "    drive = graph.pwc(**drive)\n",
    "    hamiltonian = graph.hermitian_part(drive * graph.pauli_matrix(\"P\"))\n",
    "    graph.filter_function(\n",
    "        control_hamiltonian=hamiltonian,\n",
    "        noise_operator=hamiltonian,\n",
    "        frequencies=frequencies,\n",
    "        sample_count=sample_count,\n",
    "        name=label,\n",
    "    )\n",
    "filter_functions = bo.execute_graph(\n",
    "    graph=graph, output_node_names=drive_labels, execution_mode=\"EAGER\"\n",
    ")[\"output\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We next calculate the [pulse robustness against quasi-static noise](https://docs.q-ctrl.com/boulder-opal/toolkit/design/design-error-robust-quantum-logic-gates/how-to-evaluate-control-susceptibility-to-quasi-static-noise), comparing the robust $\\pi$-pulse with the primitive square pulse.\n",
    "We can assess robustness to quasi-static errors in the control amplitude by scanning over the amplitude scaling factor $\\beta_\\gamma$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-03T02:13:37.482420Z",
     "start_time": "2022-11-03T02:13:28.068387Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1827968\") is queued.\n",
      "Your task (action_id=\"1827968\") has started.\n",
      "Your task (action_id=\"1827968\") has completed.\n"
     ]
    }
   ],
   "source": [
    "amplitude_error = 0.5\n",
    "amplitude_scalings = np.linspace(1 - amplitude_error, 1 + amplitude_error, 21)\n",
    "\n",
    "graph = bo.Graph()\n",
    "for label, drive in drives.items():\n",
    "    durations = drive[\"durations\"]\n",
    "    values = drive[\"values\"]\n",
    "    drive_pwc = graph.pwc(durations, values)\n",
    "    duration = np.sum(drive_pwc.durations)\n",
    "    noise = graph.constant_pwc(\n",
    "        constant=amplitude_scalings, duration=duration, batch_dimension_count=1\n",
    "    )\n",
    "    drive_term = noise * drive_pwc * graph.pauli_matrix(\"P\")\n",
    "    control_hamiltonian = graph.hermitian_part(drive_term)\n",
    "    infidelities = graph.infidelity_pwc(\n",
    "        hamiltonian=control_hamiltonian,\n",
    "        target=graph.target(graph.pauli_matrix(\"X\")),\n",
    "        name=label,\n",
    "    )\n",
    "robustness_scans = bo.execute_graph(graph=graph, output_node_names=drive_labels)[\n",
    "    \"output\"\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 2, figsize=(15, 5))\n",
    "fig.suptitle(\"Robustness verification\", y=1.1)\n",
    "\n",
    "axs[0].set_xlabel(\"Frequency (Hz)\")\n",
    "axs[0].set_ylabel(\"Inverse power\")\n",
    "axs[0].set_title(\"Amplitude filter functions\")\n",
    "axs[0].set_xlim(np.min(frequencies), np.max(frequencies))\n",
    "for label, filter_function in filter_functions.items():\n",
    "    axs[0].loglog(frequencies, filter_function[\"inverse_powers\"], label=label)\n",
    "\n",
    "axs[1].set_title(\"Robustness scan\")\n",
    "axs[1].set_ylabel(\"Infidelity\")\n",
    "axs[1].set_xlabel(\"Control amplitude error\")\n",
    "for label, infidelities in robustness_scans.items():\n",
    "    axs[1].plot(amplitude_scalings - 1, infidelities[\"value\"], label=label)\n",
    "\n",
    "\n",
    "hs, ls = axs[0].get_legend_handles_labels()\n",
    "fig.legend(handles=hs, labels=ls, loc=\"center\", bbox_to_anchor=(0.5, 1.0), ncol=2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Left plot: Filter functions for the control pulses under amplitude noise. The hallmark of robustness is the lower filter function values at low frequencies, which is clearly demonstrated for the Q-CTRL pulse optimized with Boulder Opal. \n",
    "Right plot: Simulated infidelity as a function of control amplitude scaling error. The Q-CTRL solution shows flat behavior for a large range of scaling values as compared to the primitive pulse, indicating robustness against amplitude error."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Experimental robustness verification with a quasi-static scan\n",
    "\n",
    "We now compare the implementation and performance of the pulses on Rigetti hardware.\n",
    "As for the theoretical validation above, we perform a quasi-static scan over the control pulse amplitude.\n",
    "We include the default X-gate for this Rigetti backend as an extra point of comparison.\n",
    "\n",
    "For each pulse, as for the default pulse earlier:\n",
    "* First compile the custom pulse program for execution on the hardware; recall that this is a parametric program with respect to amplitude scaling,\n",
    "* Define the amplitude scan parameters,\n",
    "* Run the program; this must be performed within a hardware booking window,\n",
    "* Take the sum over the shot results, which gives the probability of measuring the target $|1\\rangle$ state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-03T02:16:35.898728Z",
     "start_time": "2022-11-03T02:16:35.888751Z"
    }
   },
   "outputs": [],
   "source": [
    "# Square pulse.\n",
    "square_waveform = np.ones(round(duration * sample_rate))\n",
    "square_scales = np.linspace(0, 0.4, 51)\n",
    "\n",
    "if not use_saved_data:\n",
    "    program = custom_pulse_parametric_program(square_waveform, qubit)\n",
    "    executable = qc.compiler.native_quil_to_executable(program)\n",
    "    square_population = []\n",
    "    for scale in square_scales:\n",
    "        executable.write_memory(region_name=\"scale\", value=scale)\n",
    "        results = qc.run(executable)\n",
    "        square_population.append(np.sum(results.readout_data[\"ro\"]) / shot_count)\n",
    "else:\n",
    "    robust_population = read_variable(robust_pickle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-03T02:16:40.121370Z",
     "start_time": "2022-11-03T02:16:40.109456Z"
    }
   },
   "outputs": [],
   "source": [
    "# Q-CTRL robust pulse.\n",
    "robust_scales = np.linspace(0, 2, 101)\n",
    "\n",
    "if not use_saved_data:\n",
    "    program = custom_pulse_parametric_program(robust_waveform, qubit)\n",
    "    executable = qc.compiler.native_quil_to_executable(program)\n",
    "    robust_population = []\n",
    "    for scale in robust_scales:\n",
    "        executable.write_memory(region_name=\"scale\", value=scale)\n",
    "        results = qc.run(executable)\n",
    "        robust_population.append(np.sum(results.readout_data[\"ro\"]) / shot_count)\n",
    "else:\n",
    "    square_population = read_variable(square_pickle)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can then plot the state fidelity over the amplitude scan as a measure of amplitude robustness. Note that in the cell below we calibrate the amplitude such that the best-performing scaling factor is set to amplitude 1, and control amplitude error $\\beta_\\gamma$ is relative to this ideal amplitude."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-03T02:33:19.045044Z",
     "start_time": "2022-11-03T02:33:18.839636Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "drive_populations = [robust_population, square_population, default_population]\n",
    "drive_scales = [robust_scales, square_scales, default_scales]\n",
    "labels = drive_labels + [\"Default pulse\"]\n",
    "\n",
    "for index, label in enumerate(labels):\n",
    "    scales = drive_scales[index]\n",
    "    populations = np.array(drive_populations[index])\n",
    "    scale_max_population = scales[np.argmax(populations)]\n",
    "    points = plt.plot(\n",
    "        scales / scale_max_population - 1,\n",
    "        1 - populations,\n",
    "        \".\",\n",
    "        label=f\"{label} run on Rigetti\",\n",
    "        markersize=10,\n",
    "    )\n",
    "    if label in robustness_scans:\n",
    "        plt.plot(\n",
    "            amplitude_scalings - 1,\n",
    "            robustness_scans[label][\"value\"] + 0.04,\n",
    "            \"--\",\n",
    "            color=points[0].get_color(),\n",
    "            label=f\"{label} simulation\",\n",
    "        )\n",
    "plt.xlabel(\"Control amplitude error\")\n",
    "plt.ylabel(\"Infidelity\")\n",
    "plt.xlim((-0.5, 0.5))\n",
    "plt.ylim((0.0, 0.6))\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The experimental quasi-static scans demonstrate the broader low-infidelity region of the Q-CTRL robust pulse.\n",
    "Here the data obtained from the quantum computer is displayed as lines for the Q-CTRL, square and default pulses; the pulses have been centered to 0 error using the best-obtained fidelity value.\n",
    "The theoretical quasi-static scan data is displayed as dashed lines with colors matched to the corresponding pulse type.\n",
    "The default pulse is calibrated on the device, and obtains the lowest infidelity with no amplitude error.\n",
    "The model-based optimized pulses have their lowest infidelity values around 4%, and the theoretical data is shifted to match this value; these pulses could be improved by tuning pulse characteristics using [closed-loop hardware optimization](https://docs.q-ctrl.com/boulder-opal/toolkit/automate/automate-closed-loop-optimization/how-to-automate-closed-loop-hardware-optimization).\n",
    "Note that the default pulse is similarly susceptible to amplitude noise as the square pulse, while the Q-CTRL pulse leverages its longer duration and higher power to provide substantial robustness gains."
   ]
  }
 ],
 "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"
  },
  "notify_time": "5",
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": true,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": true,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
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}
