{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "a5295d78", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:13:58.356776Z", "iopub.status.busy": "2024-10-11T06:13:58.356475Z", "iopub.status.idle": "2024-10-11T06:13:58.363786Z", "shell.execute_reply": "2024-10-11T06:13:58.362985Z" }, "nbsphinx": "hidden" }, "outputs": [], "source": [ "# Copyright 2024 Keysight Technologies Inc." ] }, { "cell_type": "raw", "id": "9ffe085a", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "Error Amplification\n", "===================\n", "\n", "The Rabi experiment (:py:class:`~keysight.qcs.experiments.RabiExperiment`) is\n", "performed in order to tune the amplitude of our pulses to perform rotation gates. This\n", "step is crucial in our calibration workflow as imprecisions in its value lead to\n", "rotation angles that do not match our expectations, resulting in errors that propagate\n", "throughout our computations.\n", "\n", "The Error Amplification experiment (also referred to as ping-pong in the literature)\n", "is a simple protocol to determine the accuracy of the rotation pulse amplitude. It\n", "relies on a simple concept: any given number of :math:`\\pi` pulse pairs\n", "should get the system back to its initial state. If the effective rotation\n", "angle is not exactly :math:`\\pi`, increasing the number of :math:`\\pi` pulse pairs\n", "accumulates the errors and increases the deviation." ] }, { "cell_type": "code", "execution_count": 2, "id": "c81fa268", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:13:58.368340Z", "iopub.status.busy": "2024-10-11T06:13:58.368014Z", "iopub.status.idle": "2024-10-11T06:14:01.563459Z", "shell.execute_reply": "2024-10-11T06:14:01.562511Z" } }, "outputs": [], "source": [ "import numpy as np\n", "\n", "import keysight.qcs as qcs\n", "from keysight.qcs.experiments import ErrorAmplification, make_calibration_set" ] }, { "cell_type": "raw", "id": "439591f2", "metadata": { "lines_to_next_cell": 0, "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.ErrorAmplification` class. We\n", "use the :py:func:`~keysight.qcs.experiments.make_calibration_set` function that\n", "creates a calibration set for the given amount of qubit containing the linkers for the\n", " ``RX``, ``Z`` and measurement gates." ] }, { "cell_type": "code", "execution_count": 3, "id": "8ebb70a7", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:14:01.567976Z", "iopub.status.busy": "2024-10-11T06:14:01.567502Z", "iopub.status.idle": "2024-10-11T06:14:01.897545Z", "shell.execute_reply": "2024-10-11T06:14:01.896595Z" } }, "outputs": [], "source": [ "# set the following to True when connected to hardware\n", "run_on_hw = False\n", "\n", "n_qubits = 1\n", "qubits = qcs.Qudits(range(n_qubits))\n", "calibration_set = make_calibration_set(n_qubits)\n", "\n", "# generate an empty channel mapper\n", "mapper = qcs.ChannelMapper(\"ip_addr\")\n", "\n", "# create Error Amplification experiment\n", "error_amp_exp = ErrorAmplification(\n", " backend=mapper, calibration_set=calibration_set, n_amplifications=3, qubits=qubits\n", ")" ] }, { "cell_type": "raw", "id": "45b79bdf", "metadata": { "lines_to_next_cell": 0, "raw_mimetype": "text/restructuredtext" }, "source": [ "``n_amplifications`` is an integer that determines the maximal number of :math:`\\pi`\n", "pulse pairs sent to the driven system.\n", "For instance, ``n_amplifications`` = 3, 4 different pulse sequences are prepared (0,\n", "2, 4 and 6 :math:`\\pi` pulses).\n", "We can view the operations in the program with the following command:" ] }, { "cell_type": "code", "execution_count": 4, "id": "02f687b0", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:14:01.901599Z", "iopub.status.busy": "2024-10-11T06:14:01.901229Z", "iopub.status.idle": "2024-10-11T06:14:01.979110Z", "shell.execute_reply": "2024-10-11T06:14:01.978057Z" }, "lines_to_next_cell": 0 }, "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", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
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\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=xy_pulse_durations, value=30 ns, dtype=float, unit=s)
AmplitudeScalarRef(name=_implicit, value=None, dtype=float, unit=none)
FrequencyScalarRef(name=xy_pulse_frequencies, value=5.1 GHz, dtype=float, unit=Hz)
EnvelopeGaussianEnvelope(2.0)
Instantaneous PhaseScalarRef(name=rx_phase, value=0 rad, dtype=float, unit=rad)
Post-phaseScalarRef(name=rx_post_phase, value=0 rad, dtype=float, unit=rad)
\n", "
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\n", " Delay on ('xy_pulse', 0)\n", "
\n", "
\n", " Parameters\n", "
\n", " \n", " \n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", "
DurationMax(ScalarRef(name=readout_pulse_duration, value=100 ns, dtype=float, unit=s), ScalarRef(name=acquisition_duration, value=100 ns, dtype=float, unit=s))
\n", "
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\n", " readout_pulse\n", " \n", " 0\n", " \n", " \n", "
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\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=180 ns, dtype=float, unit=s)
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\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=measurement_phase, 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", " Delay on ('readout_pulse', 0)\n", "
\n", "
\n", " Parameters\n", "
\n", " \n", " \n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", "
DurationScalar(name=_implicit, value=0 s, 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", "
DurationScalar(name=_implicit, value=180 ns, dtype=float, unit=s)
\n", "
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\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", "
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ClassifierClassifier(Array(name=references, shape=(1, 2), dtype=complex, unit=none))
\n", "
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\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=0 s, dtype=float, unit=s)
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\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "metadata": { "text/html": { "isolated": true } }, "output_type": "display_data" } ], "source": [ "error_amp_exp.compiled_program.draw()" ] }, { "cell_type": "raw", "id": "9954aef3", "metadata": { "lines_to_next_cell": 0, "raw_mimetype": "text/restructuredtext" }, "source": [ "We use the :py:meth:`~keysight.programs.render` method to visualize this with the\n", ":py:class:`~keysight.channels.ChannelMapper`\\. The first index controls the number of\n", ":math:`\\pi` pulse pairs displayed (up to ``n_amplifications``) whereas the second one\n", "relates to the amplitude array provided when configuring the repetitions." ] }, { "cell_type": "code", "execution_count": 7, "id": "ea4f4df0", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:14:02.159325Z", "iopub.status.busy": "2024-10-11T06:14:02.159002Z", "iopub.status.idle": "2024-10-11T06:14:03.043177Z", "shell.execute_reply": "2024-10-11T06:14:03.042207Z" } }, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "dx": 2e-10, "legendgroup": "xy_pulse, labels: (0,)", "legendgrouptitle": { "text": "xy_pulse, labels: (0,)" }, "name": "Drive pulse for xy_pulse, labels: (0,)", "type": "scatter", "x0": 0, "xaxis": "x", "y": [ 0.0013592873771704843, 0.003898180660176664, 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "error_amp_exp.compiled_program.render(\n", " channel_subplots=False, sweep_index=(2, 4), lo_frequency=4.9e9, sample_rate=5.0e9\n", ")" ] }, { "cell_type": "raw", "id": "6a4cad77", "metadata": { "lines_to_next_cell": 0, "raw_mimetype": "text/restructuredtext" }, "source": [ "To execute this experiment, we can simply run" ] }, { "cell_type": "code", "execution_count": 9, "id": "19a69368", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:14:03.263181Z", "iopub.status.busy": "2024-10-11T06:14:03.262791Z", "iopub.status.idle": "2024-10-11T06:14:03.336065Z", "shell.execute_reply": "2024-10-11T06:14:03.334961Z" } }, "outputs": [], "source": [ "if run_on_hw:\n", " error_amp_exp.execute()\n", "else:\n", " # load in a previously executed version of this experiment\n", " error_amp_exp = qcs.load(\"ErrorAmplification.qcs\")" ] }, { "cell_type": "raw", "id": "84c5d1c2", "metadata": { "lines_to_next_cell": 0, "raw_mimetype": "text/restructuredtext" }, "source": [ "..note::\n", " For the purposes of this demonstration, we added a second \"ancilla\" qubit to the\n", " ErrorAmplification program and connected the physical output channels for our qubit\n", " to the digizer associated with the ancilla to allow us to capture the full pulse\n", " sequence." ] }, { "cell_type": "code", "execution_count": 10, "id": "543d14d8", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:14:03.340190Z", "iopub.status.busy": "2024-10-11T06:14:03.339836Z", "iopub.status.idle": "2024-10-11T06:14:03.364297Z", "shell.execute_reply": "2024-10-11T06:14:03.363307Z" }, "lines_to_next_cell": 0 }, "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", " \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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EnvelopeGaussianEnvelope(2.0)
Instantaneous PhaseScalarRef(name=rx_phase, value=0 rad, dtype=float, unit=rad)
Post-phaseScalarRef(name=rx_post_phase, value=0 rad, dtype=float, unit=rad)
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\n", " RFWaveform on ('xy_pulse', 0)\n", "
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\n", " Parameters\n", "
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DurationScalarRef(name=xy_pulse_durations, value=30 ns, dtype=float, unit=s)
AmplitudeScalarRef(name=_implicit, value=None, dtype=float, unit=none)
FrequencyScalarRef(name=xy_pulse_frequencies, value=5.1 GHz, dtype=float, unit=Hz)
EnvelopeGaussianEnvelope(2.0)
Instantaneous PhaseScalarRef(name=rx_phase, value=0 rad, dtype=float, unit=rad)
Post-phaseScalarRef(name=rx_post_phase, value=0 rad, dtype=float, unit=rad)
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\n", " RFWaveform on ('xy_pulse', 0)\n", "
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\n", " Parameters\n", "
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DurationScalarRef(name=xy_pulse_durations, value=30 ns, dtype=float, unit=s)
AmplitudeScalarRef(name=_implicit, value=None, dtype=float, unit=none)
FrequencyScalarRef(name=xy_pulse_frequencies, value=5.1 GHz, dtype=float, unit=Hz)
EnvelopeGaussianEnvelope(2.0)
Instantaneous PhaseScalarRef(name=rx_phase, value=0 rad, dtype=float, unit=rad)
Post-phaseScalarRef(name=rx_post_phase, value=0 rad, dtype=float, unit=rad)
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\n", " RFWaveform on ('xy_pulse', 0)\n", "
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\n", " Parameters\n", "
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DurationScalarRef(name=xy_pulse_durations, value=30 ns, dtype=float, unit=s)
AmplitudeScalarRef(name=_implicit, value=None, dtype=float, unit=none)
FrequencyScalarRef(name=xy_pulse_frequencies, value=5.1 GHz, dtype=float, unit=Hz)
EnvelopeGaussianEnvelope(2.0)
Instantaneous PhaseScalarRef(name=rx_phase, value=0 rad, dtype=float, unit=rad)
Post-phaseScalarRef(name=rx_post_phase, value=0 rad, dtype=float, unit=rad)
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\n", " RFWaveform on ('xy_pulse', 0)\n", "
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\n", " Parameters\n", "
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DurationScalarRef(name=xy_pulse_durations, value=30 ns, dtype=float, unit=s)
AmplitudeScalarRef(name=_implicit, value=None, dtype=float, unit=none)
FrequencyScalarRef(name=xy_pulse_frequencies, value=5.1 GHz, dtype=float, unit=Hz)
EnvelopeGaussianEnvelope(2.0)
Instantaneous PhaseScalarRef(name=rx_phase, value=0 rad, dtype=float, unit=rad)
Post-phaseScalarRef(name=rx_post_phase, value=0 rad, dtype=float, unit=rad)
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\n", " RFWaveform on ('xy_pulse', 0)\n", "
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\n", " Parameters\n", "
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DurationScalarRef(name=xy_pulse_durations, value=30 ns, dtype=float, unit=s)
AmplitudeScalarRef(name=_implicit, value=None, dtype=float, unit=none)
FrequencyScalarRef(name=xy_pulse_frequencies, value=5.1 GHz, dtype=float, unit=Hz)
EnvelopeGaussianEnvelope(2.0)
Instantaneous PhaseScalarRef(name=rx_phase, value=0 rad, dtype=float, unit=rad)
Post-phaseScalarRef(name=rx_post_phase, value=0 rad, dtype=float, unit=rad)
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\n", " RFWaveform on ('xy_pulse', 0)\n", "
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\n", " Parameters\n", "
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DurationScalarRef(name=xy_pulse_durations, value=30 ns, dtype=float, unit=s)
AmplitudeScalarRef(name=_implicit, value=None, dtype=float, unit=none)
FrequencyScalarRef(name=xy_pulse_frequencies, value=5.1 GHz, dtype=float, unit=Hz)
EnvelopeGaussianEnvelope(2.0)
Instantaneous PhaseScalarRef(name=rx_phase, value=0 rad, dtype=float, unit=rad)
Post-phaseScalarRef(name=rx_post_phase, value=0 rad, dtype=float, unit=rad)
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\n", " Delay on ('xy_pulse', 0)\n", "
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\n", " Parameters\n", "
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DurationMax(ScalarRef(name=readout_pulse_duration, value=350 ns, dtype=float, unit=s), ScalarRef(name=acquisition_duration, value=350 ns, dtype=float, unit=s))
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\n", " readout_pulse\n", " \n", " 0\n", " \n", " \n", "
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\n", " Delay on ('readout_pulse', 0)\n", "
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\n", " Parameters\n", "
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DurationScalar(name=_implicit, value=240 ns, dtype=float, unit=s)
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\n", " RFWaveform on ('readout_pulse', 0)\n", "
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\n", " Parameters\n", "
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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=measurement_phase, value=0 rad, dtype=float, unit=rad)
Post-phaseScalarRef(name=measurement_post_phase, value=0 rad, dtype=float, unit=rad)
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\n", " Delay on ('readout_pulse', 0)\n", "
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\n", " Parameters\n", "
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DurationScalar(name=_implicit, value=250 ns, dtype=float, unit=s)
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\n", " readout_acquisition\n", " \n", " 0\n", " \n", " \n", "
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\n", " Delay on ('readout_acquisition', 0)\n", "
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\n", " Parameters\n", "
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DurationScalar(name=_implicit, value=240 ns, dtype=float, unit=s)
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\n", " Acquisition on ('readout_acquisition', 0)\n", "
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DurationScalarRef(name=acquisition_duration, value=350 ns, dtype=float, unit=s)
Integration Filter\n", " \n", " \n", "\n", "\n", "\n", "
\n", " RFWaveform \n", "
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\n", " Parameters\n", "
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DurationScalarRef(name=acquisition_duration, value=350 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)
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ClassifierClassifier(Array(name=references, shape=(1, 2), dtype=complex, unit=none))
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\n", " Delay on ('readout_acquisition', 0)\n", "
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\n", " Parameters\n", "
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DurationScalar(name=_implicit, value=0 s, dtype=float, unit=s)
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\n", " Acquisition on ('readout_acquisition', 1)\n", "
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\n", " Parameters\n", "
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DurationScalar(name=_implicit, value=350 ns, dtype=float, unit=s)
Integration Filter\n", " \n", " \n", "\n", "\n", "\n", "
\n", " DCWaveform \n", "
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\n", " Parameters\n", "
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DurationScalar(name=_implicit, value=350 ns, dtype=float, unit=s)
Amplitude1
Frequency0 Hz
EnvelopeConstantEnvelope()
Instantaneous Phase0
Post-phase0
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\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "metadata": { "text/html": { "isolated": true } }, "output_type": "display_data" } ], "source": [ "error_amp_exp.compiled_program.draw()" ] }, { "cell_type": "raw", "id": "0cc51382", "metadata": { "lines_to_next_cell": 0, "raw_mimetype": "text/restructuredtext" }, "source": [ "We can visualize the generated pulses directly with the following command:" ] }, { "cell_type": "code", "execution_count": 12, "id": "6e7bfb5e", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:14:03.423694Z", "iopub.status.busy": "2024-10-11T06:14:03.423371Z", "iopub.status.idle": "2024-10-11T06:14:04.048930Z", "shell.execute_reply": "2024-10-11T06:14:04.043506Z" } }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "dx": 2.0833333333333334e-10, "legendgroup": "ancilla, labels: (1,)", "legendgrouptitle": { "text": "ancilla, labels: (1,)" }, "name": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "error_amp_exp.plot_trace(channels=qcs.Qudits(1, \"ancilla\"))" ] }, { "cell_type": "raw", "id": "be2ff016", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "This concludes the tutorial for running an error amplification experiment,\n", "using the Keysight QCS System. For detailed information on all available\n", "arguments and functionalities, please refer to the API documentation for\n", ":py:class:`~keysight.qcs.experiments.ErrorAmplification`." ] } ], "metadata": { "jupytext": { "cell_metadata_filter": "nbsphinx,raw_mimetype,-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": "3.9.6" } }, "nbformat": 4, "nbformat_minor": 5 }