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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to characterize a transmission line using a qubit as a probe\n",
    "**Characterize transmission-line bandwidth via probe measurements and the graph-based optimization engine**\n",
    "\n",
    "The Boulder Opal optimization engine provides a large, modular collection of configuration options that allows it to be used for a range of tasks in quantum control, including estimating Hamiltonian parameters in a model using measured data. \n",
    "\n",
    "In this notebook, we show how the [optimization engine](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/graph/run_optimization) can be used to determine the hardware parameters that impact the fidelity of control operations.  Specifically, we focus on estimating the bandwidth of transmission lines via probe measurements.\n",
    "\n",
    "## Transmission-line-bandwidth characterization overview\n",
    "Our task is to identify a linear filter that alters the shape of the pulses in the control line. By feeding different control pulses and then measuring the qubit, we are able to extract information about the parameters that characterize the filter. This setup is illustrated in the figure below.\n",
    "\n",
    "![how-to-characterize-a-transmission-line-using-a-qubit-as-a-probe.svg](attachment:how-to-characterize-a-transmission-line-using-a-qubit-as-a-probe.svg)\n",
    "\n",
    "To exemplify this procedure, we will consider a one-qubit system obeying the following Hamiltonian:\n",
    "\n",
    "$$ H(t) = \\frac{1}{2} \\mathcal{L} \\left[ \\alpha(t) \\right] \\sigma_x, $$\n",
    "\n",
    "where $\\alpha(t)$ is a real time-dependent control pulse and $\\mathcal{L}$ is a filter applied to the pulse.\n",
    "This linear filter acts on the control pulse $\\alpha(t)$ according to the convolution product with some kernel $K(t)$:\n",
    "\n",
    "$$ \\mathcal{L} \\left[ \\alpha(t) \\right] = \\int_0^t \\mathrm{d} s \\; \\alpha(s) K(t-s). $$\n",
    "\n",
    "To characterize this filter, we want to determine the parameters that provide the form of the kernel $K(t)$.\n",
    "\n",
    "It is useful in many cases to approximate the linear filter using a Gaussian kernel characterized by two unknown parameters, a standard deviation $\\sigma$ and a mean $\\mu$:\n",
    "\n",
    "$$ K(t) = \\frac{1}{\\sqrt{2\\pi \\sigma^2}} \\exp \\left\\{ - \\frac{(t-\\mu)^2}{2\\sigma^2} \\right\\}. $$\n",
    "\n",
    "The standard deviation $\\sigma$ roughly represents the range of frequencies that the filter allows to pass, while the mean $\\mu$ represents a time offset between when the pulses were intended to be generated and when they are actually produced. To estimate these two parameters, we will simulate the effect of this filter on a series of pulses and then use the simulated results to find the most likely form of the filter's kernel.\n",
    "\n",
    "\n",
    "## Summary workflow\n",
    "\n",
    "\n",
    "\n",
    "### 1. Perform measurements to probe the system\n",
    "\n",
    "To estimate the parameters $\\sigma$ and $\\mu$, we subject our system to a series of Gaussian pulses with different standard deviations and delays, and measure their effect on the qubit. Each of these Gaussian wave packets will contain a different range of frequencies, and thus be differently affected by the linear filter. The different delay timings also result in a different effect of the pulses by the offset of the filter, as later pulses will have a larger portion of their area outside the time interval before the measurement. The values of the final measurements are then used to obtain an estimate of the parameters that characterize the filter.\n",
    "\n",
    "As the Hamiltonian we are considering is proportional to $\\sigma_x$, we will normalize all the Gaussian pulses to produce $\\pi$ pulses, prepare the qubit initially in the state $|0 \\rangle$, and measure the population in state $| 1 \\rangle$. If no filter was present, the initial state would be flipped by the $\\pi$ pulse and the population in state $|1 \\rangle$ would be 1. Any deviations from this behavior represent the effect of the filter $\\mathcal{L}$.\n",
    "\n",
    "We will assume that the measurement results are given by some physical parameter (given in arbitrary units) linearly proportional to the population in the state $|1 \\rangle$, but not necessarily the same, because the populations might not be directly accessible by the measurement apparatus. This results in two additional parameters that connect the measured results $M$ to the population $P_1$ of state $|1 \\rangle$:\n",
    "\n",
    "$$ M = a P_1 + b. $$\n",
    "\n",
    "Together, $\\sigma$, $\\mu$, $a$, $b$ form the four variables that our optimization engine will attempt to determine.\n",
    "\n",
    "### 2. Build a graph-based optimization encoding the problem\n",
    "Next, you represent a cost function to be minimized using graphs.\n",
    "Begin by defining the parameters that you want to estimate in the graph using the `graph.optimizable_scalar` or `graph.optimization_variable` operations.\n",
    "If you have an idea of the expected value of the optimization variables, you can provide it in the form of `initial_values` for the optimization variable.\n",
    "In this case, the parameter $a$ is expected to have a value close to 1, while the parameter $b$ is expected to have a value close to 0.\n",
    "\n",
    "Construct the problem such that the optimizer will try to find the form of the evolution that would most closely match the measured points. Given a set of input points $M_i$ and the corresponding values $m_i$ that would be expected from a chosen set of the filter parameters $\\sigma, \\mu, a, b$, the cost function is:\n",
    "\n",
    "$$ C = \\sum_i \\frac{[M_i-m_i(\\sigma, \\mu, a, b)]^2}{2(\\Delta M_i)^2}, $$\n",
    "\n",
    "where $\\Delta M_i$ is the standard deviation of each of the measured input points $M_i$. Minimizing this cost function is equivalent to minimizing the negative log likelihood that a certain set of parameters $\\sigma, \\mu, a, b$ could generate the points $M_i$, for the case where the probability distribution of the errors is a Gaussian. In this case, the probability of a certain curve $m_i(\\sigma, \\mu, a, b)$ generating the points $M_i$ is the product of all the individual Gaussian probabilities:\n",
    "\n",
    "$$ P = \\prod_i \\frac{1}{\\sqrt{2\\pi (\\Delta M_i)^2}} \\exp \\left\\{ - \\frac{[M_i - m_i(\\sigma, \\mu, a, b)]^2}{2 (\\Delta M_i)^2} \\right\\}. $$\n",
    "\n",
    "It is easy to see that the negative logarithm of $P$ is the cost $C$ plus constants.\n",
    "\n",
    "Execute the optimization using `boulderopal.run_optimization` by assigning the optimization variables to output nodes of the graph. Minimizing this cost gives us the best choice of parameters that generated the original dynamics of the system, and also allows us to calculate the precision of the estimated parameters. This is done by using the Cramér–Rao bound to identify the Hessian of the cost function with the inverse of the covariance matrix for the variables estimated."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Estimating the parameters of a Gaussian filter with simulated qubit measurements\n",
    "\n",
    "The following code blocks begin by simulating the response of a qubit driven by a filtered pulse.  The results of this simulation are taken as proxy measurements on which we perform the system identification task below."
   ]
  },
  {
   "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": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1829408\") has completed.\n"
     ]
    }
   ],
   "source": [
    "# Define parameters to be estimated\n",
    "actual_sigma = 300e-9  # s\n",
    "actual_mu = 100e-9  # s\n",
    "actual_a = 1.7\n",
    "actual_b = -0.5\n",
    "\n",
    "total_duration = 1000e-9  # s\n",
    "\n",
    "# Define parameters of the Gaussian pulses to probe the filter\n",
    "max_width = total_duration / 6.0\n",
    "mean_values = np.linspace(max_width, total_duration - max_width, 6)\n",
    "width_values = np.linspace(max_width / 8.0, max_width / 2.0, 4)\n",
    "\n",
    "# Define sampled times\n",
    "segments = 150\n",
    "t_values = np.linspace(0.0, total_duration, segments + 1)\n",
    "\n",
    "\n",
    "def population(pulse_widths, pulse_means, filter_sigma, filter_mu):\n",
    "    \"\"\"\n",
    "    Calculates the transfer probability between states |0> and |1> for a\n",
    "    batch of Gaussian pulses with given widths and means, while applying\n",
    "    a Gaussian filter to the pulses with a given cutoff frequency and offset.\n",
    "    \"\"\"\n",
    "\n",
    "    def gaussian_pulse(t, mean, width):\n",
    "        return np.exp(-0.5 * ((t - mean) / width) ** 2.0) * np.sqrt(\n",
    "            0.5 * np.pi / width**2.0\n",
    "        )\n",
    "\n",
    "    graph = bo.Graph()\n",
    "\n",
    "    alpha = graph.pwc_signal(\n",
    "        gaussian_pulse(\n",
    "            t_values[None, None, :],\n",
    "            pulse_means[None, :, None],\n",
    "            pulse_widths[:, None, None],\n",
    "        ),\n",
    "        total_duration,\n",
    "    )\n",
    "\n",
    "    shift_signal = graph.convolve_pwc(\n",
    "        pwc=alpha,\n",
    "        kernel=graph.gaussian_convolution_kernel(std=filter_sigma, offset=filter_mu),\n",
    "    )\n",
    "    shift = 0.5 * shift_signal * graph.pauli_matrix(\"X\")\n",
    "\n",
    "    population = 1.0 - graph.infidelity_stf(\n",
    "        sample_times=t_values,\n",
    "        hamiltonian=shift,\n",
    "        target=graph.target(graph.pauli_matrix(\"M\")),\n",
    "    )\n",
    "    population.name = \"populations\"\n",
    "\n",
    "    graph_result = bo.execute_graph(graph=graph, output_node_names=\"populations\")\n",
    "\n",
    "    return graph_result[\"output\"][\"populations\"][\"value\"]\n",
    "\n",
    "\n",
    "populations = population(\n",
    "    pulse_widths=width_values,\n",
    "    pulse_means=mean_values,\n",
    "    filter_mu=actual_mu,\n",
    "    filter_sigma=actual_sigma,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 1152x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create measurement results with some uncertainty associated to them,\n",
    "# we will estimate the standard deviation of this error as 1% of the population\n",
    "population_errors = 0.01 * np.ones_like(populations)\n",
    "\n",
    "measurement_results = (\n",
    "    actual_a * np.random.normal(loc=populations, scale=population_errors) + actual_b\n",
    ")\n",
    "\n",
    "# Rescale error to arbitrary units\n",
    "measurement_errors = np.abs(actual_a) * population_errors\n",
    "\n",
    "# Plot inputs\n",
    "fig, axs = plt.subplots(1, 4, figsize=(16, 4))\n",
    "axs[0].set_ylabel(\"Measured values, M (a.u.)\")\n",
    "for n in range(len(width_values)):\n",
    "    axs[n].set_title(f\"Pulses with width {width_values[n] * 1e6:.2f} µs\")\n",
    "    axs[n].set_xlabel(\"Pulse center (µs)\")\n",
    "    axs[n].errorbar(\n",
    "        mean_values * 1e6,\n",
    "        measurement_results[n],\n",
    "        yerr=2.0 * measurement_errors[n],\n",
    "        fmt=\"s\",\n",
    "    )\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each of these graphs represents the average measurement results of a series of simulated experiments where the offset of the Gaussian $\\pi$ pulses vary. In each graph the width of the Gaussian control pulse is different, as indicated in their titles. The measured values $M$ plotted above are linearly proportional to the populations $P_1$:\n",
    "\n",
    "$$ M = a P_1 + b. $$\n",
    "\n",
    "The measured values are assumed to be subject to errors with Gaussian probability distributions that have a standard deviation that is 1% of $a$. This means that we are assuming that the error in the value of the of the population is of about 1%. The error bars in the graphs represent two times the standard deviation, having therefore a reliability of 95%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimating the parameters of the filter\n",
    "\n",
    "The next step involves performing an optimization in which the four unknown parameters are estimated. This is done by the optimizer by trying to find the form of the evolution that would most closely match the measured points. The optimization engine involves performing a simulation of system evolution in order to fit the measured data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "graph = bo.Graph()\n",
    "\n",
    "# Parameters to estimate\n",
    "mu = graph.optimizable_scalar(lower_bound=0.0, upper_bound=total_duration, name=\"mu\")\n",
    "sigma = graph.optimizable_scalar(\n",
    "    lower_bound=total_duration / 100, upper_bound=total_duration, name=\"sigma\"\n",
    ")\n",
    "a = graph.optimizable_scalar(\n",
    "    lower_bound=-10.0, upper_bound=10.0, initial_values=1.0, name=\"a\"\n",
    ")\n",
    "b = graph.optimizable_scalar(\n",
    "    lower_bound=-10.0, upper_bound=10.0, initial_values=0.0, name=\"b\"\n",
    ")\n",
    "\n",
    "\n",
    "# Define Gaussian pulse, normalized to generate pi-pulses\n",
    "def gauss_pulse(t, mean, width):\n",
    "    return graph.exp(-0.5 * ((t - mean) / width) ** 2.0) * graph.sqrt(\n",
    "        0.5 * np.pi / width**2.0\n",
    "    )\n",
    "\n",
    "\n",
    "# Create Hamiltonian term\n",
    "# Create a 2D batch of signals with all values of mean and width you want to simulate.\n",
    "# This batch is preserved through the entire computation, which ends up being faster than\n",
    "# looping through all values.\n",
    "alpha = graph.pwc_signal(\n",
    "    values=gauss_pulse(\n",
    "        t_values[None, None, :], mean_values[None, :, None], width_values[:, None, None]\n",
    "    ),\n",
    "    duration=total_duration,\n",
    "    name=\"alpha\",\n",
    ")\n",
    "\n",
    "gaussian_kernel = graph.gaussian_convolution_kernel(std=sigma, offset=mu)\n",
    "alpha_filtered = graph.convolve_pwc(pwc=alpha, kernel=gaussian_kernel)\n",
    "shift = 0.5 * alpha_filtered * graph.pauli_matrix(\"X\")\n",
    "\n",
    "# Calculate |0> -> |1> transfer probability\n",
    "calculated_populations = 1.0 - graph.infidelity_stf(\n",
    "    sample_times=t_values,\n",
    "    hamiltonian=shift,\n",
    "    target=graph.target(graph.pauli_matrix(\"M\")),\n",
    "    name=\"infidelities\",\n",
    ")\n",
    "\n",
    "# Create measured points\n",
    "calculated_points = a * calculated_populations + b\n",
    "calculated_points.name = \"calculated_points\"\n",
    "\n",
    "# Calculate cost\n",
    "cost = graph.sum(\n",
    "    (calculated_points - measurement_results) ** 2.0 / (2.0 * measurement_errors**2.0),\n",
    "    name=\"cost\",\n",
    ")\n",
    "\n",
    "# Calculate Hessian\n",
    "hessian = graph.hessian(cost, [mu, sigma, a, b], name=\"hessian\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1829409\") has started.\n",
      "Your task (action_id=\"1829409\") has completed.\n"
     ]
    }
   ],
   "source": [
    "# Estimate the parameters\n",
    "result = bo.run_optimization(\n",
    "    graph=graph,\n",
    "    cost_node_name=\"cost\",\n",
    "    output_node_names=[\"mu\", \"sigma\", \"a\", \"b\", \"hessian\"],\n",
    "    optimization_count=10,\n",
    ")\n",
    "\n",
    "estimated_mu = result[\"output\"][\"mu\"][\"value\"]\n",
    "estimated_sigma = result[\"output\"][\"sigma\"][\"value\"]\n",
    "estimated_a = result[\"output\"][\"a\"][\"value\"]\n",
    "estimated_b = result[\"output\"][\"b\"][\"value\"]\n",
    "\n",
    "# Calculate 2-sigma uncertainties (error bars give 95% precision)\n",
    "hessian = result[\"output\"][\"hessian\"][\"value\"]\n",
    "uncertainties = 2.0 * np.sqrt(np.diag(np.linalg.inv(hessian)))\n",
    "uncertainty_mu, uncertainty_sigma, uncertainty_a, uncertainty_b = uncertainties"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1829410\") has started.\n",
      "Your task (action_id=\"1829410\") has completed.\n",
      "Your task (action_id=\"1829411\") has completed.\n"
     ]
    }
   ],
   "source": [
    "mean_range = np.linspace(0.1 * total_duration, 0.9 * total_duration, 30)\n",
    "\n",
    "calculated_curves = estimated_b + estimated_a * population(\n",
    "    pulse_widths=width_values,\n",
    "    pulse_means=mean_range,\n",
    "    filter_mu=estimated_mu,\n",
    "    filter_sigma=estimated_sigma,\n",
    ")\n",
    "\n",
    "ideal_curves = actual_b + actual_a * population(\n",
    "    pulse_widths=width_values,\n",
    "    pulse_means=mean_range,\n",
    "    filter_mu=actual_mu,\n",
    "    filter_sigma=actual_sigma,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "actual sigma = 0.3 µs\n",
      "estimated sigma = (0.300 ± 0.028) µs\n",
      "\n",
      "actual mu = 0.1 µs\n",
      "estimated mu = (0.097 ± 0.008) µs\n",
      "\n",
      "actual a = 1.7 au\n",
      "estimated a = (1.729 ± 0.100) au\n",
      "\n",
      "actual b = -0.5 au\n",
      "estimated b = (-0.531 ± 0.099) au\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1152x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Print parameter estimates\n",
    "print(f\"\\nactual sigma = {actual_sigma/1e-6} µs\")\n",
    "print(\n",
    "    f\"estimated sigma = ({estimated_sigma/1e-6:.3f} ± {uncertainty_sigma/1e-6:.3f}) µs\"\n",
    ")\n",
    "\n",
    "print(f\"\\nactual mu = {actual_mu/1e-6} µs\")\n",
    "print(f\"estimated mu = ({estimated_mu/1e-6:.3f} ± {uncertainty_mu/1e-6:.3f}) µs\")\n",
    "\n",
    "print(f\"\\nactual a = {actual_a} au\")\n",
    "print(f\"estimated a = ({estimated_a:.3f} ± {uncertainty_a:.3f}) au\")\n",
    "\n",
    "print(f\"\\nactual b = {actual_b} au\")\n",
    "print(f\"estimated b = ({estimated_b:.3f} ± {uncertainty_b:.3f}) au\")\n",
    "\n",
    "# Plot results\n",
    "fig, axs = plt.subplots(1, 4, figsize=(16, 4))\n",
    "axs[0].set_ylabel(\"Measurement values, M (a.u.)\")\n",
    "\n",
    "for n in range(len(width_values)):\n",
    "    axs[n].set_title(f\"Pulses with width {width_values[n] * 1e6:.2f} µs\")\n",
    "    axs[n].set_xlabel(\"Pulse center (µs)\")\n",
    "    axs[n].errorbar(\n",
    "        mean_values * 1e6,\n",
    "        measurement_results[n],\n",
    "        yerr=2.0 * measurement_errors[n],\n",
    "        fmt=\"s\",\n",
    "        color=\"C0\",\n",
    "        label=\"Measured values\",\n",
    "    )\n",
    "    axs[n].plot(\n",
    "        mean_range * 1e6, ideal_curves[n], color=\"C0\", label=\"Ideal values\", alpha=0.3\n",
    "    )\n",
    "    axs[n].plot(\n",
    "        mean_range * 1e6,\n",
    "        calculated_curves[n],\n",
    "        \"--\",\n",
    "        label=\"Estimated values\",\n",
    "        color=\"C1\",\n",
    "    )\n",
    "    axs[n].legend(loc=3)\n",
    "\n",
    "plt.show()"
   ]
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    "In the graphs above, we can compare the curves that represent the values that would be measured if the system followed the estimated filter (dashed), and the values that would be measured if perfect measurements were performed on a system subject to the real filter (solid). Each graph corresponds to sets of experiments where pulses of the same width are applied at different points in time, as indicated in their titles and $x$ axis. The close match between the two curves highlights the fact that the estimated parameters are close to the real values.\n",
    "\n",
    "Above we also provide explicit estimates of the parameters $\\sigma$ (`sigma`) and $\\mu$ (`mu`) of the Gaussian kernel of the linear filter.  The errors estimated for the variables above have a certainty of 2 times the standard deviation, or 95%."
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