{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Perform noise spectroscopy in superconducting hardware\n",
    "**Reconstructing noise power spectrum density in transmon qubits using dynamical decoupling sequences**\n",
    "\n",
    "Boulder Opal enables you to reconstruct power spectral densities (PSD) of different noise sources affecting your system. The characterization of these noise PSD provides valuable information that can be used, for example, in the design of controls and hardware diagnostics.\n",
    "\n",
    "In this application note, we focus on the reconstruction of noise PSD for superconducting qubits, a system widely used in quantum computing platforms. The notebook starts by defining the model of a superconducting transmon system subject to a dephasing noise whose PSD we want to reconstruct. The reconstruction process employs a carefully designed set of dynamical decoupling (DD) pulse sequences which, in this example, will be CPMG sequences composed of customized $\\pi$ and $\\pi/2$ pulses. Once defined, the sequences are used in experiments to probe the system and obtain the measurements necessary to perform the PSD reconstruction. In the notebook, the experimental measurements will be replaced by outputs of the appropriate simulation of the physical system. Finally, we will input these measurements directly into Boulder Opal's [noise reconstruction engine](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/noise_reconstruction) to obtain the reconstructed noise spectrum."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports and initialization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import qctrlopencontrols as oc\n",
    "import qctrlvisualizer as qv\n",
    "import boulderopal as bo\n",
    "\n",
    "plt.style.use(qv.get_qctrl_style())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model of the system: transmon subject to dephasing noise\n",
    "\n",
    "We consider a single transmon subject to a dephasing noise described by the following Hamiltonian:\n",
    "\n",
    "$$\n",
    "H = \\omega_c a^\\dagger a + \\frac{\\alpha}{2} (a^\\dagger)^2 a^2 + \\frac{1}{2}\\left(\\Omega (t) b + H.c.\\right) + \\eta(t) a^\\dagger a,\n",
    "$$\n",
    "\n",
    "where $\\omega_c$ is the transmon frequency, $\\alpha$ the anharmonicity, $\\Omega (t)$ is the complex Rabi rate and $\\eta(t)$ is a time-dependent dephasing noise process consistent with the experimental power spectral density of the noise affecting the system. We can further simplify the Hamiltonian by going into the frame rotating with $\\omega_c$: \n",
    "$$\n",
    "H = \\frac{\\alpha}{2} (a^\\dagger)^2 a^2 + \\frac{1}{2}\\left(\\Omega (t) b + H.c.\\right) + \\eta(t) a^\\dagger a.\n",
    "$$ \n",
    "The cell below sets up a function (`create_hamiltonian`) that creates the Hamiltonian, assuming a three-level truncation of transmon system. The function `create_hamiltonian` also includes the dephasing noise operator corresponding to the PSD to be reconstructed as well as the pulsed controls that will take the form of the CPMG sequence subsequently. See this [user guide](https://docs.q-ctrl.com/boulder-opal/toolkit/design/simulate-quantum-systems/how-to-simulate-quantum-dynamics-subject-to-noise) for more information on setting up the Hamiltonian of a qubit under noisy conditions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define system parameters and operators.\n",
    "dim = 3  # transmon dimension\n",
    "alpha = -2 * np.pi * 400e6  # rad.Hz, transmon anharmonicity\n",
    "\n",
    "\n",
    "def create_hamiltonian(\n",
    "    graph,\n",
    "    control,  # pulse sequence control\n",
    "    noise_power_densities,  # noise PSD\n",
    "    noise_frequency_step,  # sampling rate of noise PSD\n",
    "    noise_trajectory_count,  # number of noise instances\n",
    "):\n",
    "    \"\"\"\n",
    "    Set up transmon Hamiltonian for the given pulse control and noise PSD.\n",
    "    \"\"\"\n",
    "\n",
    "    a = graph.annihilation_operator(dim)\n",
    "    n = graph.number_operator(dim)\n",
    "    duration = np.sum(control[\"durations\"])\n",
    "\n",
    "    # Control term.\n",
    "    drive_signal = graph.pwc(**control, time_dimension=-1)\n",
    "    hamiltonian = graph.hermitian_part(drive_signal * a)\n",
    "\n",
    "    # Noise term\n",
    "    if (noise_power_densities is not None) and (noise_frequency_step is not None):\n",
    "        segment_count = (int)(np.round(duration * np.max(frequencies)) * 10)\n",
    "\n",
    "        eta_stf = graph.random.colored_noise_stf_signal(\n",
    "            power_spectral_density=noise_power_densities,\n",
    "            frequency_step=noise_frequency_step,\n",
    "            batch_shape=(noise_trajectory_count,),\n",
    "        )\n",
    "        eta_signal = graph.discretize_stf(\n",
    "            stf=eta_stf, duration=duration, segment_count=segment_count\n",
    "        )\n",
    "\n",
    "        hamiltonian += eta_signal * n\n",
    "\n",
    "    hamiltonian += -alpha * (n @ n - n) / 2\n",
    "\n",
    "    return hamiltonian"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Noise spectrum\n",
    "\n",
    "For the demonstration in this notebook, we will consider a PSD containing both a $1/f$ noise component and also a thermal broadband term. This PSD is defined in the cell below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define the non-Markovian noise power spectrum.\n",
    "def noise_spectrum(\n",
    "    frequencies, cutoff_frequency, exponent=1, scale_factor=2e10, broadband_amplitude=0\n",
    "):\n",
    "    \"\"\"\n",
    "    Set up noise power spectral density.\n",
    "    \"\"\"\n",
    "    return (\n",
    "        scale_factor / (frequencies + cutoff_frequency) ** exponent\n",
    "        + broadband_amplitude\n",
    "    )\n",
    "\n",
    "\n",
    "frequency_step = 1e3\n",
    "frequencies = np.arange(0, 5e6, frequency_step)\n",
    "power_densities = noise_spectrum(\n",
    "    frequencies=frequencies, cutoff_frequency=1e5, exponent=1, broadband_amplitude=1e4\n",
    ")\n",
    "\n",
    "color = qv.QCTRL_STYLE_COLORS[4]\n",
    "plt.plot(frequencies / 1e6, power_densities / 1e6, color=color)\n",
    "plt.suptitle(\"Dephasing noise spectral density\")\n",
    "plt.fill_between(frequencies / 1e6, 0, power_densities / 1e6, color=color, alpha=0.25)\n",
    "plt.xlabel(\"Frequency (MHz)\")\n",
    "plt.ylabel(\"Power density (1/MHz)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The noise PSD defined above produces a qubit with a T2 coherence time of about $20\\mu$s, which is commensurate with the coherence times often encountered in superconducting systems."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reconstructing the noise PSD\n",
    "\n",
    "### Generate diagnostic DD sequences with custom pulses\n",
    "\n",
    "To perform the noise reconstruction, we define a series of CPMG sequences with a fixed duration of 10$\\mu$s and varying orders (number of $\\pi$ pulses in each sequence). This is one of the most straightforward ways of probing the noise PSD. It enables us to control the amplitude and width of the fundamental filter function peaks and keep them relatively constant for CPMG pulse sequences of different orders. \n",
    "\n",
    "The CPMG pulse sequences are constructed by concatenating a series of $\\pi$ pulses appropriately spaced. An ideal sequence would be composed of perfect instantaneous $\\pi$ pulses but, in reality, the pulses in the sequences are finite and can be shaped in different ways to satisfy hardware specifications or constraints. In this example, we chose to use DRAG pulses as they help minimize the leakage to the qubit's excited state and ensure that the quality of the filter functions is maintained. The DRAG $\\pi/2$ and $\\pi$ pulses defined below are directly imported from the [Q-CTRL Open Controls library](https://github.com/qctrl/open-controls) and converted into the appropriate Boulder Opal format for later use. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def convert_pulse(pulse):\n",
    "    \"\"\"\n",
    "    Convert a pulse in Open Controls format to Boulder Opal format.\n",
    "    \"\"\"\n",
    "    return {\n",
    "        \"values\": pulse.rabi_rates * np.exp(1j * pulse.azimuthal_angles),\n",
    "        \"durations\": pulse.durations,\n",
    "    }\n",
    "\n",
    "\n",
    "omega_max = 2 * np.pi * 100e6  # rad.Hz, transmon Rabi frequency\n",
    "\n",
    "# DRAG pulses\n",
    "segment_count = 100\n",
    "\n",
    "rabi_rotation = np.pi / 1\n",
    "pi_pulse = oc.new_drag_control(\n",
    "    rabi_rotation=rabi_rotation,\n",
    "    segment_count=segment_count,\n",
    "    duration=3 * (rabi_rotation / omega_max),\n",
    "    width=(rabi_rotation / omega_max) / 2,\n",
    "    beta=2e-10,\n",
    ")\n",
    "pi_control = convert_pulse(pi_pulse)\n",
    "\n",
    "rabi_rotation = np.pi / 2\n",
    "pi_half_pulse = oc.new_drag_control(\n",
    "    rabi_rotation=rabi_rotation,\n",
    "    segment_count=segment_count,\n",
    "    duration=3 * (rabi_rotation / omega_max),\n",
    "    width=(rabi_rotation / omega_max) / 2,\n",
    "    beta=2e-10,\n",
    ")\n",
    "pi_half_control = convert_pulse(pi_half_pulse)\n",
    "\n",
    "\n",
    "qv.plot_controls(\n",
    "    {r\"$\\Omega_{\\pi}$\": pi_control, r\"$\\Omega_{\\pi/2}$\": pi_half_control}, polar=False\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The properties of the pulses can have an impact on the filtering characteristics of the DD sequences. For this reason, when defining these pulses, the filter functions of the sequences should be carefully inspected for systematic anomalies. It's useful to look out for occurrence of 0Hz peaks across different filter functions. Such anomalous peaks can introduce bias in the PSD estimates, especially in case of exponentially-shaped noise PSDs. \n",
    "\n",
    "With the custom pulses defined, we can write a function that generates the CPMG sequences using them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def custom_CPMG(duration, order, pi_control, pi_half_control):\n",
    "    \"\"\"\n",
    "    Generate a CPMG sequence using custom π and π/2 pulses.\n",
    "    \"\"\"\n",
    "\n",
    "    pi_half_values = pi_half_control[\"values\"]\n",
    "    pi_values = pi_control[\"values\"]\n",
    "\n",
    "    pi_half_durations = pi_half_control[\"durations\"]\n",
    "    pi_half_duration = np.sum(pi_half_durations)\n",
    "    pi_durations = pi_control[\"durations\"]\n",
    "    pi_duration = np.sum(pi_durations)\n",
    "\n",
    "    if order == 0:\n",
    "        seq_values = np.concatenate(\n",
    "            (pi_half_values, [0], pi_half_values * np.exp(1j * np.pi))\n",
    "        )\n",
    "        seq_durations = np.concatenate(\n",
    "            (pi_half_durations, [duration], pi_half_durations)\n",
    "        )\n",
    "\n",
    "    else:\n",
    "        seq_values = np.tile(\n",
    "            np.concatenate(([0.0], pi_values * np.exp(1j * np.pi / 2), [0.0])), order\n",
    "        )\n",
    "        tau = duration / order\n",
    "        seq_durations = np.tile(\n",
    "            np.concatenate(\n",
    "                ([(tau - pi_duration) / 2], pi_durations, [(tau - pi_duration) / 2])\n",
    "            ),\n",
    "            order,\n",
    "        )\n",
    "\n",
    "        # Add 1st π/2.\n",
    "        seq_durations[0] = seq_durations[0] - pi_half_duration / 2\n",
    "        seq_durations = np.insert(seq_durations, 0, pi_half_durations)\n",
    "        seq_values = np.insert(seq_values, 0, pi_half_values)\n",
    "\n",
    "        # Add 2nd π/2.\n",
    "        seq_durations[-1] = seq_durations[-1] - pi_half_duration / 2\n",
    "        seq_durations = np.append(seq_durations, pi_half_durations)\n",
    "        seq_values = np.append(seq_values, pi_half_values * np.exp(1j * np.pi))\n",
    "\n",
    "    return {\"durations\": seq_durations, \"values\": seq_values}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the previous function, we define a list of CPMG sequences and plot one of them as an example.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "CPMG_sequence_duration = 10e-6  # s\n",
    "CPMG_sequence_orders = np.arange(0, 40, 2)\n",
    "\n",
    "CPMG_controls = [\n",
    "    custom_CPMG(CPMG_sequence_duration, order, pi_control, pi_half_control)\n",
    "    for order in CPMG_sequence_orders\n",
    "]\n",
    "\n",
    "# Plot a particular sequence.\n",
    "qv.plot_controls({r\"$\\Omega_{CPMG}$\": CPMG_controls[2]}, polar=False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that various classes of DD sequences can be chosen for noise reconstruction depending on the characteristics of the system. We picked CPMG in this example because of its simplicity and high degree of efficiency in filtering dephasing noise. However, if there were Rabi rate fluctuations in the controls acting on the system, for example, we would pick a sequence with higher robustness to this Rabi rate noise, such as the XY8 sequence."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute filter functions\n",
    "\n",
    "Next, we calculate the filter function associated with each pulse sequence. See the [How to calculate and use 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) user guide for more details."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1828086\") is queued.\n",
      "Your task (action_id=\"1828086\") has started.\n",
      "Your task (action_id=\"1828086\") has completed.\n"
     ]
    }
   ],
   "source": [
    "graph = bo.Graph()\n",
    "\n",
    "a = graph.annihilation_operator(dim)\n",
    "n = graph.number_operator(dim)\n",
    "\n",
    "ff_names = [f\"filter_function_{idx}\" for idx in range(len(CPMG_controls))]\n",
    "for name, control in zip(ff_names, CPMG_controls):\n",
    "    duration = np.sum(control[\"durations\"])\n",
    "    drive_term = graph.hermitian_part(graph.pwc(**control) * a)\n",
    "    drift_term = -alpha * (n @ n - n) / 2\n",
    "    noise = graph.constant_pwc(constant=n, duration=duration)\n",
    "\n",
    "    hamiltonian = drive_term + drift_term\n",
    "    graph.filter_function(\n",
    "        control_hamiltonian=hamiltonian,\n",
    "        noise_operator=noise,\n",
    "        frequencies=frequencies,\n",
    "        sample_count=2000,\n",
    "        projection_operator=np.diag([1, 1, 0]),\n",
    "        name=name,\n",
    "    )\n",
    "\n",
    "result = bo.execute_graph(\n",
    "    graph=graph, output_node_names=ff_names, execution_mode=\"EAGER\"\n",
    ")[\"output\"]\n",
    "\n",
    "filter_functions = np.array([result[name][\"inverse_powers\"] for name in ff_names])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(15, 5))\n",
    "ax.plot(frequencies / 1e6, filter_functions.T, linewidth=0.8)\n",
    "\n",
    "ax.set_xlabel(\"Frequency (MHz)\")\n",
    "ax.set_ylabel(\"Inverse power (Hz)\")\n",
    "fig.suptitle(\"Filter functions and power spectrum\")\n",
    "ax.set_xlim([0, 5])\n",
    "\n",
    "ax2 = ax.twinx()\n",
    "ax2.fill_between(frequencies / 1e6, power_densities / 1e6, 0, alpha=0.1, color=\"k\")\n",
    "ax2.set_ylabel(\"Spectrum power (1/MHz)\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observe the fundamental peaks for the different CPMG filter functions (colored lines) interrogating the spectral window of interest. Note that the 0 order peak corresponds to the Ramsey sequence. The FWHM of filter function peaks acts a natural limit to spectral resolution. Longer sequence durations produce narrower peeks requiring use of higher order sequences to sample the same spectral window. Ultimately, the maximal frequency that can be sampled is limited by the duration of the $\\pi$ pulses.\n",
    "\n",
    "The key to noise reconstruction is making the fundamental filter function peaks overlap adequately to ensure they sample the noise PSD uniformly, as in the figure above. Note that in general, DD sequences of different durations or classes can be mixed together in our reconstruction method. However, in such cases the sampling coverage should be carefully managed so as to ensure no part of the interrogation window is left undersampled, that is, devoid of overlapping fundamental filter function peaks.\n",
    "\n",
    "Also note that the CPMG, as well as other DD sequences, present higher order harmonics in addition to their main peak (see the smaller peaks in the plot). Those with significant presence outside the interrogation region will cause spectral leakage and lead to artifacts in the reconstructed spectrum. This can be especially problematic in reconstruction of power spectra containing complex features. In such cases, spectral leakage can be suppressed by using Slepian controls in place of DD sequences, as described in [this application note](https://docs.q-ctrl.com/boulder-opal/toolkit/apply/quantum-sensing/perform-narrow-band-magnetic-field-spectroscopy-with-nv-centers)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Apply sequences and perform measurements\n",
    "\n",
    "In a real experiment, the next step would be to apply the set of diagnostic DD sequences to the qubit and measure its population.\n",
    "Here, however, we will simulate a series of experiments where the final populations are measured after the application of CPMG sequences of various orders.\n",
    "\n",
    "We calculate the evolution of the system under each pulse sequence and measure the probabilities of the different transmon states at the end, averaged over an ensemble of different noise samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1828090\") is queued.\n",
      "Your task (action_id=\"1828090\") has started.\n",
      "Your task (action_id=\"1828090\") has completed.\n"
     ]
    }
   ],
   "source": [
    "noise_trajectory_count = 1000\n",
    "initial_state = np.array([1, 0, 0])\n",
    "\n",
    "graph = bo.Graph()\n",
    "\n",
    "names = [f\"probabilities_{idx}\" for idx in range(len(CPMG_controls))]\n",
    "for name, control in zip(names, CPMG_controls):\n",
    "    # Create Hamiltonian.\n",
    "    hamiltonian = create_hamiltonian(\n",
    "        graph=graph,\n",
    "        control=control,\n",
    "        noise_power_densities=power_densities,\n",
    "        noise_frequency_step=frequency_step,\n",
    "        noise_trajectory_count=noise_trajectory_count,\n",
    "    )\n",
    "\n",
    "    # Evolve intial state.\n",
    "    unitaries = graph.time_evolution_operators_pwc(\n",
    "        hamiltonian=hamiltonian, sample_times=np.array([np.sum(control[\"durations\"])])\n",
    "    )\n",
    "    evolved_ensemble = unitaries @ initial_state[:, None]\n",
    "\n",
    "    # Average final probabilities.\n",
    "    probabilities_ensemble = graph.abs(evolved_ensemble[:, 0, :, 0]) ** 2\n",
    "    probabilities = graph.sum(probabilities_ensemble, axis=0) / noise_trajectory_count\n",
    "    probabilities.name = name\n",
    "\n",
    "result = bo.execute_graph(graph=graph, output_node_names=names)\n",
    "\n",
    "CPMG_probabilities = np.array([result[\"output\"][name][\"value\"] for name in names])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(CPMG_sequence_orders, CPMG_probabilities)\n",
    "plt.axhline(0.5, ls=\":\", color=\"black\")\n",
    "\n",
    "plt.xlabel(\"CPMG order\")\n",
    "plt.ylabel(\"State probability\")\n",
    "plt.ylim([0, 1])\n",
    "plt.legend(labels=[rf\"$|{idx}\\rangle$\" for idx in range(3)])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Process the measurements\n",
    "\n",
    "We now construct a bounded infidelity metric $I_B=1-P_0$, where $P_0$ is the probability of the $|0\\rangle $ state. In experiments, the response of this metric to noise is nonlinear and naturally defined in the interval [0.0,0.5]. Note that the filter function formalism assumes unbounded linear response to noise. To use filter functions with greater accuracy, we first linearize the measurement values, as done below (see [Soare et al.](https://doi.org/10.1038/nphys3115) for more details)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "bounded_infidelity = 1 - CPMG_probabilities[:, 0]\n",
    "unbounded_infidelity = -np.log(1 - bounded_infidelity * 2) / 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ideally, the duration of the sequence should be significantly shorter than the qubit's T1 coherence time to minimize the impact of T1 decay over the evolution of the sequence. For durations comparable to the qubit's T1 time, the effect should be accounted for by rescaling the signal based on the decay envelope."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reconstruct the noise PSD\n",
    "\n",
    "We now reconstruct the noise in several simple steps. First, we select the frequency band that corresponds to the spectral range being interrogated by the filter function peaks - this is the spectral window over which we have the ability to reconstruct the PSD."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "filter_function_peaks = frequencies[np.argmax(filter_functions, axis=1)]\n",
    "lower_sample_frequency = filter_function_peaks[0]\n",
    "upper_sample_frequency = filter_function_peaks[-1]\n",
    "\n",
    "sample_selection = (frequencies >= lower_sample_frequency) & (\n",
    "    frequencies <= upper_sample_frequency\n",
    ")\n",
    "sample_frequencies = frequencies[sample_selection]\n",
    "sample_spectrum = power_densities[sample_selection]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we pass the measurements along with their corresponding filter functions `boulderopal.noise_reconstruction.reconstruct`, as described in the [How to perform noise spectroscopy on arbitrary noise channels](https://docs.q-ctrl.com/boulder-opal/toolkit/design/characterize-hardware/how-to-perform-noise-spectroscopy-on-arbitrary-noise-channels) user guide.\n",
    "Here we use convex optimization to perform a non-parametric spectrum reconstruction without specific assumptions about the shape of the noise PSD."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1828092\") is queued.\n",
      "Your task (action_id=\"1828092\") has started.\n",
      "Your task (action_id=\"1828092\") has completed.\n"
     ]
    }
   ],
   "source": [
    "shot_noise = 1e-4\n",
    "\n",
    "# Configure CVX reconstruction method.\n",
    "method = bo.noise_reconstruction.ConvexOptimization(\n",
    "    power_density_lower_bound=0,\n",
    "    power_density_upper_bound=1e6,\n",
    "    regularization_hyperparameter=1e-11,\n",
    ")\n",
    "\n",
    "sample_filter_functions = [\n",
    "    bo.noise_reconstruction.FilterFunction(sample_frequencies, filter_function)\n",
    "    for filter_function in filter_functions[:, sample_selection]\n",
    "]\n",
    "\n",
    "result = bo.noise_reconstruction.reconstruct(\n",
    "    filter_functions=[sample_filter_functions],\n",
    "    infidelities=unbounded_infidelity,\n",
    "    infidelity_uncertainties=np.ones_like(unbounded_infidelity) * shot_noise,\n",
    "    method=method,\n",
    ")\n",
    "\n",
    "# Extract reconstructed PSD.\n",
    "reconstructed_spectrum = result[\"output\"][0][\"psd\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(15, 5))\n",
    "ax.fill_between(\n",
    "    sample_frequencies / 1e6,\n",
    "    sample_spectrum / 1e6,\n",
    "    0,\n",
    "    color=\"lightgray\",\n",
    "    label=\"True spectrum\",\n",
    ")\n",
    "ax.plot(\n",
    "    sample_frequencies / 1e6,\n",
    "    reconstructed_spectrum / 1e6,\n",
    "    \"-\",\n",
    "    label=\"Reconstructed spectrum\",\n",
    ")\n",
    "\n",
    "ax.set_xlabel(\"Frequency (MHz)\")\n",
    "ax.set_ylabel(\"Power density (MHz$^{-1}$)\")\n",
    "ax.legend()\n",
    "fig.suptitle(\"Power spectrum reconstruction with Boulder Opal\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we can compare the reconstructed spectrum (solid line) with the true noise PSD used to simulate the results (shaded). \n",
    "\n",
    "Note the discrepancies near each of the extremities of the spectrum. These artifacts originate from a reduced sampling level. The sides of the band are probed by a single filter function in contrast to the middle, where every frequency point is sampled by at least two overlapping filter function peaks. Those artifacts can be reduced by narrowing the spectral width of the filter function peaks. Furthermore, these reconstructed results can be used to propose an analytic model of noise PSD with relatively few degrees of freedom and perform a parametric reconstruction that would resolve such artifacts."
   ]
  }
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