{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "c0844259", "metadata": { "execution": { "iopub.execute_input": "2025-10-02T01:26:49.239355Z", "iopub.status.busy": "2025-10-02T01:26:49.239180Z", "iopub.status.idle": "2025-10-02T01:26:49.242606Z", "shell.execute_reply": "2025-10-02T01:26:49.242107Z" }, "nbsphinx": "hidden" }, "outputs": [], "source": [ "# Copyright 2025 Keysight Technologies Inc." ] }, { "cell_type": "raw", "id": "a6b0adcf", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "Rabi Experiment\n", "===============\n", "\n", "\n", "This guide shows how to perform a Rabi experiment to calibrate a :math:`\\pi`-pulse\n", "using a program. This experiment can be easily generated using the\n", ":py:class:`~keysight.qcs.experiments.RabiExperiment`\\ class.\n", "\n", "The Rabi experiment is the second step in calibrating our first quantum gates.\n", "Following the :doc:`qubit_spec` experiment, we learned the energy gap between\n", "the ground state and first excited state of our two-level system. In other words, we\n", "have determined the resonance frequency of our qubit, and can now apply pulses at\n", "this frequency to alter the qubit's state.\n", "\n", "The state of the qubit can be visualized using the Bloch sphere. The ground state\n", ":math:`|0\\rangle` is represented by the north-pole, and the excited state\n", ":math:`|1\\rangle` is represented by the south-pole as shown. By applying pulses of\n", "varying strengths to a qubit in the ground state, we can drive a rotation around the\n", "Bloch sphere by some as-yet-unknown angles.\n", "\n", ".. image:: ../figures/rabi_osc.png\n", " :align: center\n", " :width: 120%\n", "\n", "A rotation of :math:`\\pi` takes us from :math:`|0\\rangle` to :math:`|1\\rangle`, which\n", "is the operation implemented by a Pauli-X gate. The pulse that drives this rotation\n", "is called a :math:`\\pi`-pulse. Here we assume that the pulse duration is fixed, and\n", "we will vary strength by varying pulse amplitude. Our goal is to learn the required\n", ":math:`\\pi`-pulse amplitude, in order to calibrate our gate.\n", "\n", "To learn the pulse amplitude, we perform a Rabi experiment as follows:\n", "\n", "#. Initialize the qubit to the ground state.\n", "\n", "#. Apply a control pulse with the resonance frequency :math:`\\omega_r` and\n", " amplitude :math:`A`, for a fixed duration, on the target qubit.\n", "\n", "#. Measure the population of the qubit in the excited state.\n", "\n", "#. Repeat the above steps with varying amplitude :math:`A`.\n", "\n", "The observed population as a function of amplitude will be a sinusoid, corresponding\n", "to rotations around the Bloch sphere. We can read off the :math:`\\pi`-pulse amplitude\n", "as half the period of the observed oscillation." ] }, { "cell_type": "code", "execution_count": 2, "id": "f27066e8", "metadata": { "execution": { "iopub.execute_input": "2025-10-02T01:26:49.244309Z", "iopub.status.busy": "2025-10-02T01:26:49.244145Z", "iopub.status.idle": "2025-10-02T01:26:52.178696Z", "shell.execute_reply": "2025-10-02T01:26:52.177844Z" } }, "outputs": [], "source": [ "import keysight.qcs as qcs\n", "import numpy as np" ] }, { "cell_type": "raw", "id": "9613f70a", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "We start by initializing a qubit and defining an empty channel mapper to create a new\n", "instance of the :py:class:`~keysight.qcs.experiments.RabiExperiment` class. We load\n", "a ``make_calibration_set`` function that creates\n", "a calibration set for the given amount of qubit containing the linkers for the ``RX``\n", ", ``Z`` and measurement gates. Lastly, we import an experiment with simulated data\n", "to demonstrate the fitting and calibration workflow at the end of this file." ] }, { "cell_type": "code", "execution_count": 3, "id": "dca3bc84", "metadata": { "execution": { "iopub.execute_input": "2025-10-02T01:26:52.181569Z", "iopub.status.busy": "2025-10-02T01:26:52.181215Z", "iopub.status.idle": "2025-10-02T01:26:52.218165Z", "shell.execute_reply": "2025-10-02T01:26:52.217422Z" } }, "outputs": [], "source": [ "from keysight.qcs.experiments import RabiExperiment, make_calibration_set\n", "from simulated_experiments.simulated_experiments import SimulatedRabiExperiment" ] }, { "cell_type": "code", "execution_count": 4, "id": "2630a193", "metadata": { "execution": { "iopub.execute_input": "2025-10-02T01:26:52.220523Z", "iopub.status.busy": "2025-10-02T01:26:52.220327Z", "iopub.status.idle": "2025-10-02T01:26:52.612661Z", "shell.execute_reply": "2025-10-02T01:26:52.611975Z" } }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", " \n", " \n", "
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rabi_experiment.compiled_program.render(\n", " channel_subplots=False,\n", " lo_frequency=5e9,\n", " sweep_index=5,\n", " sample_rate=5e9,\n", ")" ] }, { "cell_type": "raw", "id": "8f17b3a1", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "To execute this experiment, we can simply run" ] }, { "cell_type": "code", "execution_count": 8, "id": "c80a3823", "metadata": { "execution": { "iopub.execute_input": "2025-10-02T01:26:54.787577Z", "iopub.status.busy": "2025-10-02T01:26:54.787335Z", "iopub.status.idle": "2025-10-02T01:26:54.855131Z", "shell.execute_reply": "2025-10-02T01:26:54.854435Z" } }, "outputs": [], "source": [ "if run_on_hw:\n", " rabi_experiment.execute()\n", "else:\n", " # load in a previously executed version of this experiment\n", " rabi_experiment = qcs.load(\"RabiExperiment.qcs\")" ] }, { "cell_type": "raw", "id": "06773d94", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "For the purposes of this demonstration, we added a second \"ancilla\" qubit to the\n", "Rabi program and connected the physical output channels for our qubit control to\n", "the digitizer associated with the ancilla to allow us to capture both the control\n", "and the readout pulse." ] }, { "cell_type": "code", "execution_count": 9, "id": "5412f7f5", "metadata": { "execution": { "iopub.execute_input": "2025-10-02T01:26:54.860724Z", "iopub.status.busy": "2025-10-02T01:26:54.860485Z", "iopub.status.idle": "2025-10-02T01:26:54.875561Z", "shell.execute_reply": "2025-10-02T01:26:54.874865Z" } }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", " \n", " \n", "
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FrequencyScalarRef(name=xy_pulse_frequencies, value=5.1 GHz, dtype=float, unit=Hz)
EnvelopeGaussianEnvelope(2.0)
Instantaneous PhaseScalarRef(name=x_phase, value=0 rad, dtype=float, unit=rad)
Post-phaseScalarRef(name=x_post_phase, value=0 rad, dtype=float, unit=rad)
\n", "
\n", "\n", "\n", "
\n", "
\n", "
\n", " readout_pulse\n", " \n", " 0\n", " \n", " \n", "
\n", " \n", "\n", "\n", "
\n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
\n", " Delay on ('readout_pulse', 0)\n", "
\n", "
\n", " Parameters\n", "
\n", " \n", " \n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", "
DurationScalarRef(name=readout_pulse_delay, value=0 s, dtype=float, unit=s)
\n", "
\n", "\n", "\n", "
\n", "
\n", " 		\n", " \n", "
\n", " \n", "\n", "\n", "
\n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
\n", " RFWaveform on ('readout_pulse', 0)\n", "
\n", "
\n", " Parameters\n", "
\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
DurationScalarRef(name=readout_pulse_duration, value=100 ns, dtype=float, unit=s)
AmplitudeScalarRef(name=readout_pulse_amplitudes, value=0.1, dtype=float, unit=none)
FrequencyScalarRef(name=readout_frequencies, value=5.15 GHz, dtype=float, unit=Hz)
EnvelopeSineEnvelope()
Instantaneous PhaseScalarRef(name=readout_pulse_phases, value=0 rad, dtype=float, unit=rad)
Post-phaseScalarRef(name=measurement_post_phase, value=0 rad, dtype=float, unit=rad)
\n", "
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\n", " 		\n", " \n", "
\n", " \n", "\n", "\n", "
\n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
\n", " Delay on ('readout_pulse', 0)\n", "
\n", "
\n", " Parameters\n", "
\n", " \n", " \n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", "
DurationScalar(name=_implicit, value=5 ns, dtype=float, unit=s)
\n", "
\n", "\n", "\n", "
\n", "
\n", "
\n", " readout_acquisition\n", " \n", " 0\n", " \n", " \n", "
\n", " \n", "\n", "\n", "
\n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
\n", " Delay on ('readout_acquisition', 0)\n", "
\n", "
\n", " Parameters\n", "
\n", " \n", " \n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", "
DurationScalarRef(name=acquisition_delay, value=5 ns, dtype=float, unit=s)
\n", "
\n", "\n", "\n", "
\n", "
\n", " 		\n", " \n", "
\n", " \n", "\n", "\n", "
\n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
\n", " Acquisition on ('readout_acquisition', 0)\n", "
\n", "
\n", " Parameters\n", "
\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
DurationScalarRef(name=acquisition_duration, value=100 ns, dtype=float, unit=s)
Integration Filter\n", " \n", " \n", "\n", "\n", "\n", "
\n", " RFWaveform \n", "
\n", "
\n", " Parameters\n", "
\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
DurationScalarRef(name=acquisition_duration, value=100 ns, dtype=float, unit=s)
AmplitudeScalarRef(name=measurement_integrator_amplitude, value=1, dtype=float, unit=none)
FrequencyScalarRef(name=readout_frequencies, value=5.15 GHz, dtype=float, unit=Hz)
EnvelopeConstantEnvelope()
Instantaneous PhaseScalarRef(name=measurement_integrator_phase, value=0 rad, dtype=float, unit=rad)
Post-phaseScalarRef(name=measurement_integrator_post_phase, value=0 rad, dtype=float, unit=rad)
\n", "
\n", "\n", "
ClassifierClassifier(Array(name=references, shape=(1, 2), dtype=complex, unit=none))
\n", "
\n", "\n", "\n", "
\n", "
\n", " 		\n", " \n", "
\n", " \n", "\n", "\n", "
\n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
\n", " Delay on ('readout_acquisition', 0)\n", "
\n", "
\n", " Parameters\n", "
\n", " \n", " \n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", "
DurationScalar(name=_implicit, value=4.96308e-24 s, dtype=float, unit=s)
\n", "
\n", "\n", "\n", "
\n", "
\n", "
\n", " 1\n", " \n", " \n", "
\n", " \n", "\n", "\n", "
\n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
\n", " Acquisition on ('readout_acquisition', 1)\n", "
\n", "
\n", " Parameters\n", "
\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
DurationScalar(name=_implicit, value=45 ns, dtype=float, unit=s)
Integration Filter\n", " \n", " \n", "\n", "\n", "\n", "
\n", " DCWaveform \n", "
\n", "
\n", " Parameters\n", "
\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
DurationScalar(name=_implicit, value=45 ns, dtype=float, unit=s)
Amplitude1
Frequency0 Hz
EnvelopeConstantEnvelope()
Instantaneous Phase0
Post-phase0
\n", "
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\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "metadata": { "text/html": { "isolated": true } }, "output_type": "display_data" } ], "source": [ "rabi_experiment.compiled_program.draw()" ] }, { "cell_type": "raw", "id": "1db29ac1", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "The ancilla qubit is mapped to the digitizer channel ``1`` and has a single\n", "acquisition that spans the duration of the control pulse." ] }, { "cell_type": "code", "execution_count": 11, "id": "aa5b9b0f", "metadata": { "execution": { "iopub.execute_input": "2025-10-02T01:26:54.905066Z", "iopub.status.busy": "2025-10-02T01:26:54.904824Z", "iopub.status.idle": "2025-10-02T01:26:55.128349Z", "shell.execute_reply": "2025-10-02T01:26:55.127811Z" } }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "dx": 2.0833333333333334e-10, "legendgroup": "qudits, labels: (0,)", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rabi_experiment.plot_trace()" ] }, { "cell_type": "raw", "id": "1f458ca2", "metadata": { "lines_to_next_cell": 2, "raw_mimetype": "text/restructuredtext" }, "source": [ "Here we can see the control pulse with our varying amplitudes. Note that our local\n", "oscillator (LO) frequency was set to 5 GHz for this example.\n", "\n", "Fitting and calibration workflow\n", "--------------------------------\n", "\n", "Let's walk through how to extract the desired drive amplitude from the Rabi experiment\n", "and how to update the corresponding variables in our calibration set. For this\n", "example, we load in an experiment with simulated data that we imported at the\n", "beginning of the file:" ] }, { "cell_type": "code", "execution_count": 12, "id": "b79d9b26", "metadata": { "execution": { "iopub.execute_input": "2025-10-02T01:26:55.135945Z", "iopub.status.busy": "2025-10-02T01:26:55.135735Z", "iopub.status.idle": "2025-10-02T01:26:55.157811Z", "shell.execute_reply": "2025-10-02T01:26:55.157161Z" } }, "outputs": [], "source": [ "rabi_experiment = SimulatedRabiExperiment(calibration_set, qubits)" ] }, { "cell_type": "code", "execution_count": 13, "id": "57206350", "metadata": { "execution": { "iopub.execute_input": "2025-10-02T01:26:55.160024Z", "iopub.status.busy": "2025-10-02T01:26:55.159847Z", "iopub.status.idle": "2025-10-02T01:26:55.288389Z", "shell.execute_reply": "2025-10-02T01:26:55.287850Z" } }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "IQ Value: %{y}
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rabi_experiment.plot_iq(plot_type=\"linear\")" ] }, { "cell_type": "raw", "id": "946983b3", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "The :py:meth:`~keysight.qcs.experiments.Experiment.fit` method takes this I/Q data\n", "and fits it to a decaying sinusoidal model, as specified by the built-in\n", ":py:class:`~keysight.qcs.analysis.DecayingSinusoid`. In order to specify how to\n", "prepare the I/Q data for fitting (in this case, we want to fit the magnitude), the\n", ":py:class:`~keysight.qcs.experiments.RabiExperiment` uses the\n", ":py:class:`~keysight.qcs.analysis.IQuadrature` pre-processor, which extracts the\n", "I-quadrature out of the complex I/Q data.\n", "\n", "The result of the fit is an :py:class:`~keysight.qcs.analysis.EstimateCollection`,\n", "which contains individual :py:class:`~keysight.qcs.analysis.Estimate`\\s for each\n", "qubit that was fitted." ] }, { "cell_type": "code", "execution_count": 14, "id": "5f1dcd9d", "metadata": { "execution": { "iopub.execute_input": "2025-10-02T01:26:55.291750Z", "iopub.status.busy": "2025-10-02T01:26:55.291551Z", "iopub.status.idle": "2025-10-02T01:26:55.722026Z", "shell.execute_reply": "2025-10-02T01:26:55.721426Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "EstimateCollection(1)\n", "Estimate(amplitude=1.3380733863826824, decay_rate=2.125015503505198, frequency=39.84246405002836, phase=-1.5244173129014738, ...)\n" ] } ], "source": [ "ec = rabi_experiment.fit()\n", "print(ec)\n", "print(ec.estimates[0])" ] }, { "cell_type": "raw", "id": "518659f0", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "We can represent estimate parameters and its values and estimate collection\n", "in a tabular form by calling the\n", ":py:meth:`~keysight.qcs.analysis.Estimate.draw` method:" ] }, { "cell_type": "code", "execution_count": 15, "id": "23957671", "metadata": { "execution": { "iopub.execute_input": "2025-10-02T01:26:55.723968Z", "iopub.status.busy": "2025-10-02T01:26:55.723769Z", "iopub.status.idle": "2025-10-02T01:26:55.731373Z", "shell.execute_reply": "2025-10-02T01:26:55.730514Z" } }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
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"black", "linewidth": 1, "mirror": true, "showline": true } } }, "width": 900, "xaxis": { "anchor": "y", "domain": [ 0.0, 1.0 ], "showticklabels": true, "title": { "text": "x180_pulse_amplitudes" } }, "yaxis": { "anchor": "x", "domain": [ 0.0, 1.0 ], "title": { "text": "I/Q Magnitude" } } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rabi_experiment.plot()" ] }, { "cell_type": "raw", "id": "36fe4b87", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "We can then get the calibration value associated to this Rabi Experiment by\n", "calling\n", ":py:meth:`~keysight.qcs.experiments.RabiExperiment.get_updated_calibration_values`.\n", "This method will compute the new values for the calibration variable(s) of this\n", "experiment using the fit results." ] }, { "cell_type": "code", "execution_count": 17, "id": "6d583446", "metadata": { "execution": { "iopub.execute_input": "2025-10-02T01:26:57.006571Z", "iopub.status.busy": "2025-10-02T01:26:57.006355Z", "iopub.status.idle": "2025-10-02T01:26:57.439693Z", "shell.execute_reply": "2025-10-02T01:26:57.438835Z" } }, "outputs": [ { "data": { "text/plain": [ "{'x180_pulse_amplitudes': [0.03826112037115306]}" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rabi_experiment.get_updated_calibration_values()" ] }, { "cell_type": "raw", "id": "af5823fc", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "To check the current state of that variable in the calibration_set to confirm\n", "its update, one can do:" ] }, { "cell_type": "code", "execution_count": 18, "id": "be6ac85b", "metadata": { "execution": { "iopub.execute_input": "2025-10-02T01:26:57.441949Z", "iopub.status.busy": "2025-10-02T01:26:57.441767Z", "iopub.status.idle": "2025-10-02T01:26:57.447603Z", "shell.execute_reply": "2025-10-02T01:26:57.446711Z" } }, "outputs": [ { "data": { "text/plain": [ "array([0.5])" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rabi_experiment.calibration_set.variables.x180_pulse_amplitudes.value" ] }, { "cell_type": "raw", "id": "ab0b5e16", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "The update is then done as follows:" ] }, { "cell_type": "code", "execution_count": 19, "id": "ab9bf927", "metadata": { "execution": { "iopub.execute_input": "2025-10-02T01:26:57.449755Z", "iopub.status.busy": "2025-10-02T01:26:57.449516Z", "iopub.status.idle": "2025-10-02T01:26:57.929680Z", "shell.execute_reply": "2025-10-02T01:26:57.928919Z" } }, "outputs": [ { "data": { "text/plain": [ "array([0.03826112])" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rabi_experiment.set_updated_calibration_values()\n", "rabi_experiment.calibration_set.variables.x180_pulse_amplitudes.value" ] }, { "cell_type": "raw", "id": "5a8fae0b", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "The last line printing the new updated value, thus confirming that the update\n", "has been successful." ] } ], "metadata": { "jupytext": { "cell_metadata_filter": "raw_mimetype,nbsphinx,-all", "main_language": "python", "notebook_metadata_filter": "-all", "text_representation": { "extension": ".py", "format_name": "percent" } }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.12" } }, "nbformat": 4, "nbformat_minor": 5 }