{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "5dd7a34d", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:14:08.153730Z", "iopub.status.busy": "2024-10-11T06:14:08.153411Z", "iopub.status.idle": "2024-10-11T06:14:08.159472Z", "shell.execute_reply": "2024-10-11T06:14:08.158580Z" }, "nbsphinx": "hidden" }, "outputs": [], "source": [ "# Copyright 2024 Keysight Technologies Inc." ] }, { "cell_type": "raw", "id": "840571b8", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "Coherence characterization\n", "==========================\n", "\n", ".. note::\n", "\n", " The assets are set up to map a maximum of 4 qudits to a single physical AWG and\n", " digitizer channel with an LO frequency of 5.5 GHz. For the purposes of this\n", " demonstration, we connect the output of the AWG to the digitizer so we can capture\n", " both the control and readout pulses.\n", "\n", "Coherence characterization experiments uses varying delays to probe the dynamic\n", "properties of the qubit. Here we give a guide to show how to perform a Ramsey\n", "Experiment, a Hahn Echo Experiment and a Relaxation experiment." ] }, { "cell_type": "code", "execution_count": 2, "id": "4059f4f8", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:14:08.162834Z", "iopub.status.busy": "2024-10-11T06:14:08.162527Z", "iopub.status.idle": "2024-10-11T06:14:11.525513Z", "shell.execute_reply": "2024-10-11T06:14:11.524456Z" } }, "outputs": [], "source": [ "import keysight.qcs as qcs\n", "import numpy as np\n", "from keysight.qcs.experiments import RamseyExperiment, EchoExperiment, T1Experiment\n", "from keysight.qcs.experiments import make_calibration_set" ] }, { "cell_type": "raw", "id": "53be3988", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "Relaxation Experiment\n", "---------------------\n", "Another example of decoherence is thermal relaxation which happens at a time scale\n", "commonly referred to as `T1`. This section shows how to perform a Relaxation\n", "experiment to learn that decay time `T1` using the class\n", ":py:class:`~keysight.qcs.experiments.T1Experiment`\\.\n", "\n", "A :math:`\\pi` gate is first applied to a qubit in the ground state to bring it\n", "to the excited state followed by a varying delay. The sequence is then followed\n", "by a readout pulse.\n", "\n", "\n", ".. image:: ../figures/relaxation.png\n", " :align: center\n", " :width: 120%\n", "\n", "This experiment follows the following steps:\n", " #. Initialize the qubit to the excited state by applying a :math:`\\pi``\n", "\n", " #. Apply a delay.\n", "\n", " #. Measure the population of the qubit in the excited state.\n", "\n", " #. Repeat the above steps with varying delay time." ] }, { "cell_type": "raw", "id": "dfd83b36", "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.T1Experiment`\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": 3, "id": "561d2ad7", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:14:11.530058Z", "iopub.status.busy": "2024-10-11T06:14:11.529349Z", "iopub.status.idle": "2024-10-11T06:14:11.731193Z", "shell.execute_reply": "2024-10-11T06:14:11.730314Z" } }, "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\")" ] }, { "cell_type": "code", "execution_count": 4, "id": "5e0188f2", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:14:11.734902Z", "iopub.status.busy": "2024-10-11T06:14:11.734553Z", "iopub.status.idle": "2024-10-11T06:14:11.915924Z", "shell.execute_reply": "2024-10-11T06:14:11.915210Z" } }, "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", "
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t1_experiment.compiled_program.render(\n", " channel_subplots=False,\n", " lo_frequency=5e9,\n", " sweep_index=0,\n", " sample_rate=5e9,\n", ")" ] }, { "cell_type": "raw", "id": "0b21aa9b", "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": "d47f7151", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:14:13.209809Z", "iopub.status.busy": "2024-10-11T06:14:13.209454Z", "iopub.status.idle": "2024-10-11T06:14:13.306756Z", "shell.execute_reply": "2024-10-11T06:14:13.304385Z" } }, "outputs": [], "source": [ "if run_on_hw:\n", " t1_experiment.execute()\n", "else:\n", " # load in a previously executed version of this experiment\n", " t1_experiment = qcs.load(\"T1Experiment.qcs\")" ] }, { "cell_type": "raw", "id": "e0f54140", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "For the purposes of this demonstration, we added a second \"ancilla\" qubit to the\n", "program and connected the physical output channels for our qubit to\n", "the digizer associated with the ancilla to allow us to capture the full pulse\n", "sequence." ] }, { "cell_type": "code", "execution_count": 10, "id": "fff75075", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:14:13.310907Z", "iopub.status.busy": "2024-10-11T06:14:13.310131Z", "iopub.status.idle": "2024-10-11T06:14:13.324778Z", "shell.execute_reply": "2024-10-11T06:14:13.323927Z" }, "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", "
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DurationScalar(name=_implicit, value=220 ns, dtype=float, unit=s)
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t1_experiment.plot_trace(channels=qcs.Qudits(1, \"ancilla\"))" ] }, { "cell_type": "raw", "id": "d3d38c37", "metadata": { "lines_to_next_cell": 2, "raw_mimetype": "text/restructuredtext" }, "source": [ "Ramsey Experiment\n", "-----------------\n", "\n", "\n", "This section shows how to perform a Ramsey experiment to learn the dephasing time of a\n", "qubit. This experiment can be easily generated with\n", ":py:class:`~keysight.qcs.experiments.RamseyExperiment`\\.\n", "\n", "Following the :doc:`qubit_spec` and :doc:`qubit_rabi`, we have determined the qubit's\n", "resonance frequency and :math:`\\pi`-pulse amplitude which were stored in the\n", "calibration set. Given these, we are now able to implement the :math:`\\frac{\\pi}{2}`\n", "gate to create an equal superposition between the ground and excited state.\n", "\n", "In this guide, we begin characterizing the intrinsic noise of the system by\n", "learning the decay rate of the coherence between the ground and excited states of\n", "the qubit. The time scale associated with this decoherence is commonly referred to\n", "as the :math:`T_2^*` time. The Ramsey experiment can also be used to measure the\n", "error in the measured resonance frequency of the qubit (the detuning frequency), and\n", "further tune up the calibration parameters.\n", "\n", "A :math:`\\frac{\\pi}{2}` gate applied to a qubit in the ground state creates an equal\n", "superposition state, shown below as a point on the :math:`XY` plane of the Bloch\n", "sphere. The phase of the state evolves in time, corresponding to a natural precession\n", "around the :math:`Z` axis. At the same time, dephasing occurs as the state shrinks on\n", "the Bloch sphere towards the center (the completely mixed state). After some time has\n", "elapsed, a second :math:`\\frac{\\pi}{2}` gate can be applied to drive the qubit to\n", "either the ground or excited state. The magnitude of the dephasing can then be\n", "measured as the population in the excited state. The rotation shows up in the\n", "measurement as an oscillation between the ground and excited states, while the\n", "dephasing appears as an exponentially decaying envelope. By varying the delay time, we\n", "can learn the characteristic time scale of the decay.\n", "\n", "If the offset perfectly corrects the intrinsic rotation, we would not observe\n", "any oscillation. In practice, the observed oscillation can be used to\n", "recalibrate the qubit's resonance frequency.\n", "\n", ".. image:: ../figures/ramsey_exp.png\n", " :align: center\n", " :width: 120%\n", "\n", "To learn the :math:`T_2^*` time and detuning frequency, we perform a Ramsey experiment\n", "as follows:\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 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" ] }, { "cell_type": "raw", "id": "edbd0deb", "metadata": { "lines_to_next_cell": 0, "raw_mimetype": "text/restructuredtext" }, "source": [ "We start by initializing a qubit and loading a channel mapper to\n", "create a new instance of the :py:class:`~keysight.qcs.experiments.RamseyExperiment`\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": 14, "id": "bc17cce7", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:14:13.987672Z", "iopub.status.busy": "2024-10-11T06:14:13.987311Z", "iopub.status.idle": "2024-10-11T06:14:14.008124Z", "shell.execute_reply": "2024-10-11T06:14:14.007292Z" }, "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", "
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Dim2
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Post-phaseScalarRef(name=sx_post_phase, value=0 rad, dtype=float, unit=rad)
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ramsey_experiment.compiled_program.render(\n", " channel_subplots=False,\n", " lo_frequency=5e9,\n", " sweep_index=2,\n", " sample_rate=5e9,\n", ")" ] }, { "cell_type": "raw", "id": "b4ab8e27", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "To execute this experiment, we can simply run" ] }, { "cell_type": "code", "execution_count": 18, "id": "a2802143", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:14:14.255194Z", "iopub.status.busy": "2024-10-11T06:14:14.254596Z", "iopub.status.idle": "2024-10-11T06:14:14.273777Z", "shell.execute_reply": "2024-10-11T06:14:14.272752Z" } }, "outputs": [], "source": [ "if run_on_hw:\n", " ramsey_experiment.execute()\n", "else:\n", " # load in a previously executed version of this experiment\n", " ramsey_experiment = qcs.load(\"RamseyExperiment.qcs\")" ] }, { "cell_type": "raw", "id": "c3e848b2", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "For the purposes of this demonstration, we added a second \"ancilla\" qubit to the\n", "Ramsey program and connected the physical output channels for our qubit to\n", "the digizer associated with the ancilla to allow us to capture the full pulse\n", "sequence." ] }, { "cell_type": "code", "execution_count": 19, "id": "9b53ee64", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:14:14.281145Z", "iopub.status.busy": "2024-10-11T06:14:14.280535Z", "iopub.status.idle": "2024-10-11T06:14:14.313017Z", "shell.execute_reply": "2024-10-11T06:14:14.312003Z" } }, "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", " \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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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ramsey_experiment.plot_trace(channels=qcs.Qudits(1, \"ancilla\"))" ] }, { "cell_type": "raw", "id": "d899c6af", "metadata": { "lines_to_next_cell": 2, "raw_mimetype": "text/restructuredtext" }, "source": [ "Here we can see two control pulses separated by our varying delays.\n", ".. note::\n", "\n", " The local oscillator (LO) frequency was set to 5 GHz for this\n", " example, and that we also limited the number of delay sweep points to keep\n", " the visualization easy to interpret" ] }, { "cell_type": "raw", "id": "f58695fd", "metadata": { "lines_to_next_cell": 0, "raw_mimetype": "text/restructuredtext" }, "source": [ "Hahn Echo Experiment\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", " #. 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": "eb56a720", "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": 21, "id": "fa4e4ffd", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:14:14.448410Z", "iopub.status.busy": "2024-10-11T06:14:14.447012Z", "iopub.status.idle": "2024-10-11T06:14:14.470684Z", "shell.execute_reply": "2024-10-11T06:14:14.468520Z" } }, "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", "
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The sequence is then followed by a measurement.\n", "#" ] }, { "cell_type": "code", "execution_count": 22, "id": "3124cedb", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:14:14.475149Z", "iopub.status.busy": "2024-10-11T06:14:14.474261Z", "iopub.status.idle": "2024-10-11T06:14:14.497822Z", "shell.execute_reply": "2024-10-11T06:14:14.495040Z" } }, "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": "dd786822", "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:\n", "echo_experiment.compiled_program.render(channel_subplots=False, sample_rate=5e9)" ] }, { "cell_type": "raw", "id": "544aadf0", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "To execute this experiment, we can simply run" ] }, { "cell_type": "code", "execution_count": 23, "id": "e260dc5b", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:14:14.505057Z", "iopub.status.busy": "2024-10-11T06:14:14.504251Z", "iopub.status.idle": "2024-10-11T06:14:14.536015Z", "shell.execute_reply": "2024-10-11T06:14:14.533711Z" } }, "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": "3be97f95", "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.\n", 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