{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "a2a719fc", "metadata": { "execution": { "iopub.execute_input": "2025-10-02T01:26:17.860883Z", "iopub.status.busy": "2025-10-02T01:26:17.860680Z", "iopub.status.idle": "2025-10-02T01:26:17.865213Z", "shell.execute_reply": "2025-10-02T01:26:17.864387Z" }, "nbsphinx": "hidden" }, "outputs": [], "source": [ "# Copyright 2025 Keysight Technologies Inc." ] }, { "cell_type": "raw", "id": "6a244568", "metadata": { "lines_to_next_cell": 0, "raw_mimetype": "text/restructuredtext" }, "source": [ "Hahn Echo Experiment\n", "====================\n", "\n", "This section shows how to perform a Hahn Echo experiment. This experiment can\n", "be easily generated with :py:class:`~keysight.qcs.experiments.EchoExperiment`\\.\n", "\n", "With the previous Ramsey experiment we showed a way to characterize the decay\n", "rate of the coherence between the ground and excited states of the qubit.\n", "We now show how to perform a `T_2` Hahn Echo experiment to obtain a more\n", "precise estimate of the qubit's decay time. Indeed, unlike the `T_2^*`\n", "previously measured, the `T_2` obtained using a Hahn Echo experiement allows\n", "to get a measure of the decoherence while eliminating low frequency fluctuations.\n", "Here we are following the same process as the Ramsey experiment above with the\n", "addition of an additional Z rotation also called a refocusing pulse in between\n", "the two :math:`\\frac{\\pi}{2}` pulses. This `Z` rotation will counteract the\n", "natural precession of the qubit's state and is refocusing any slow noise\n", "by doing so.\n", "\n", ".. image:: ../figures/hahn_echo.png\n", " :align: center\n", " :width: 120%\n", "\n", "The experiment therefore follows the following steps:\n", "\n", "#. Initialize the qubit to an equal superposition state between the ground and\n", " excited state (in the :math:`XY` plane of the Bloch sphere) by applying a\n", " :math:`\\frac{\\pi}{2}` gate.\n", "\n", "#. Apply a delay.\n", "\n", "#. Apply a :math:`Z` rotation to offset the natural precession.\n", "\n", "#. Apply a second :math:`\\frac{\\pi}{2}` gate to drive the qubit toward either the\n", " ground or excited state.\n", "\n", "#. Measure the population of the qubit in the excited state.\n", "\n", "#. Repeat the above steps with varying delay time.\n", "\n" ] }, { "cell_type": "raw", "id": "c8c71354", "metadata": { "lines_to_next_cell": 0, "raw_mimetype": "text/restructuredtext" }, "source": [ "We start again by initializing a qubit and loading a channel mapper to\n", "create a new instance of the :py:class:`~keysight.qcs.experiments.EchoExperiment`\n", "class. Next, we generate a calibration set for the qubit\n", "using :py:func:`~keysight.qcs.experiments.make_calibration_set`. This file includes\n", "the quantum operations and variables we will need to run the experiment." ] }, { "cell_type": "code", "execution_count": 2, "id": "230b1f6b", "metadata": { "execution": { "iopub.execute_input": "2025-10-02T01:26:17.867776Z", "iopub.status.busy": "2025-10-02T01:26:17.867472Z", "iopub.status.idle": "2025-10-02T01:26:21.055652Z", "shell.execute_reply": "2025-10-02T01:26:21.055045Z" }, "lines_to_next_cell": 2 }, "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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The sequence is then followed by a measurement." ] }, { "cell_type": "code", "execution_count": 3, "id": "b1e505cd", "metadata": { "execution": { "iopub.execute_input": "2025-10-02T01:26:21.058071Z", "iopub.status.busy": "2025-10-02T01:26:21.057723Z", "iopub.status.idle": "2025-10-02T01:26:21.107827Z", "shell.execute_reply": "2025-10-02T01:26:21.107220Z" } }, "outputs": [], "source": [ "# configure the repetitions for this experiment\n", "start_delay = 40e-9\n", "end_delay = 80e-9\n", "steps = 3\n", "scan_values = np.linspace([start_delay] * n_qubits, [end_delay] * n_qubits, steps)\n", "echo_experiment.configure_repetitions(delays=scan_values, n_shots=1)" ] }, { "cell_type": "raw", "id": "c8c1cc37", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "Compiling this program to the waveform level using the\n", ":py:class:`~keysight.qcs.programs.ParameterizedLinker`\\s in the calibration set\n", "results in the following program:" ] }, { "cell_type": "code", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "echo_experiment.compiled_program.render(channel_subplots=False, sample_rate=5e9)" ] }, { "cell_type": "raw", "id": "f398549d", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "To execute this experiment, we can simply run" ] }, { "cell_type": "code", "execution_count": 5, "id": "0bc9e23b", "metadata": { "execution": { "iopub.execute_input": "2025-10-02T01:26:23.413507Z", "iopub.status.busy": "2025-10-02T01:26:23.413233Z", "iopub.status.idle": "2025-10-02T01:26:23.507165Z", "shell.execute_reply": "2025-10-02T01:26:23.506394Z" } }, "outputs": [], "source": [ "if run_on_hw:\n", " echo_experiment.execute()\n", "else:\n", " # load in a previously executed version of this experiment\n", " echo_experiment = qcs.load(\"EchoExperiment_data.hdf5\")" ] }, { "cell_type": "raw", "id": "faef9394", "metadata": { "lines_to_next_cell": 0, "raw_mimetype": "text/restructuredtext" }, "source": [ "The draw and plot methods can then be used just like for the Ramsey experiment." ] }, { "cell_type": "code", "execution_count": 6, "id": "16719e65", "metadata": { "execution": { "iopub.execute_input": "2025-10-02T01:26:23.511319Z", "iopub.status.busy": "2025-10-02T01:26:23.510960Z", "iopub.status.idle": "2025-10-02T01:26:23.565731Z", "shell.execute_reply": "2025-10-02T01:26:23.565202Z" } }, "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=readout_frequencies, value=5.15 GHz, dtype=float, unit=Hz)
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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)
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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=165 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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DurationArray(name=_implicit, shape=(1,), dtype=float, unit=s)
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\n", " Delay on ('readout_acquisition', 0)\n", "
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DurationScalarRef(name=acquisition_delay, value=5 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=260 ns, dtype=float, unit=s)
Integration Filter\n", " \n", " \n", "\n", "\n", "\n", "
\n", " RFWaveform \n", "
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DurationScalarRef(name=acquisition_duration, value=260 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=4.96308e-24 s, dtype=float, unit=s)
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\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=260 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=260 ns, dtype=float, unit=s)
Amplitude1
Frequency0 Hz
EnvelopeConstantEnvelope()
Instantaneous Phase0
Post-phase0
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