{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "9b738055", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:17:44.580593Z", "iopub.status.busy": "2024-10-11T06:17:44.580266Z", "iopub.status.idle": "2024-10-11T06:17:44.585893Z", "shell.execute_reply": "2024-10-11T06:17:44.585109Z" }, "nbsphinx": "hidden" }, "outputs": [], "source": [ "# Copyright 2024 Keysight Technologies Inc." ] }, { "cell_type": "raw", "id": "c515c448", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "\n", ".. _envelopes:\n", "\n", "Introduction to pulse envelopes\n", "===============================\n", "\n", "This guide gives an overview of the types of pulse envelopes available in |QCS| and\n", "demonstrates how to initialize them, add them to waveforms in a programs, and plot\n", "them.\n", "\n", ".. note:: Throughout the examples in this tutorial we are using\n", " :py:class:`~keysight.qcs.channels.DCWaveform`\\s to demonstrate the\n", " envelopes. :ref:`rfwaveforms` shows how to generate the more commonly used\n", " :py:class:`~keysight.qcs.channels.RFWaveform`\\s with envelopes.\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "792379a3", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:17:44.589023Z", "iopub.status.busy": "2024-10-11T06:17:44.588735Z", "iopub.status.idle": "2024-10-11T06:17:47.731484Z", "shell.execute_reply": "2024-10-11T06:17:47.730619Z" } }, "outputs": [], "source": [ "import keysight.qcs as qcs\n", "import numpy as np" ] }, { "cell_type": "raw", "id": "a1dc2356", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "\n", "Built-In Envelopes\n", "------------------\n", "\n", "Constant Envelope\n", "^^^^^^^^^^^^^^^^^\n", "\n", "A constant envelope is the simplest pulse shape. It realizes a constant amplitude for\n", "a duration. In this example we configure a program with one AWG channel and add a\n", "DC waveform with a constant envelope to it." ] }, { "cell_type": "code", "execution_count": 3, "id": "1d640123", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:17:47.735821Z", "iopub.status.busy": "2024-10-11T06:17:47.735119Z", "iopub.status.idle": "2024-10-11T06:17:48.543812Z", "shell.execute_reply": "2024-10-11T06:17:48.542869Z" } }, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "dx": 0.001, "legendgroup": "awg_channel, labels: (0,)", "legendgrouptitle": { "text": "awg_channel, labels: (0,)" }, "name": "Drive pulse for awg_channel, labels: (0,)", "type": "scatter", "x0": 0, "xaxis": "x", "y": [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# initialize a Gaussian\n", "envelope = qcs.GaussianEnvelope(num_sigma=2)\n", "dc_wav = qcs.DCWaveform(32e-9, envelope, 1)\n", "\n", "# initialize the program and add the envelope\n", "program = qcs.Program()\n", "program.add_waveform(dc_wav, awg)\n", "\n", "# render\n", "program.render()" ] }, { "cell_type": "raw", "id": "43613c81", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "Flat-Top Gaussian Envelope\n", "^^^^^^^^^^^^^^^^^^^^^^^^^^\n", "\n", "Here we realize a Flat-Top Gaussian envelope. During an initial rise and equal lower\n", "time, the pulse is Gaussian. In the middle, for a time ``duration``, the envelope is\n", "constant and equal to its maximum value.\n", "\n", "In this example we make use of the built-in :py:class:`~keysight.qcs.variables.Scalar`\n", "class, which allows us to modify parameters after instantiation. We render the\n", "envelope once, then render it again with different parameters. This behavior is used\n", "for example in swept programs." ] }, { "cell_type": "code", "execution_count": 5, "id": "2808c250", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:17:48.676167Z", "iopub.status.busy": "2024-10-11T06:17:48.675851Z", "iopub.status.idle": "2024-10-11T06:17:48.799295Z", "shell.execute_reply": "2024-10-11T06:17:48.798330Z" } }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "dx": 1e-09, "legendgroup": "awg_channel, labels: (0,)", "legendgrouptitle": { "text": "awg_channel, labels: (0,)" }, "name": "Drive pulse for awg_channel, labels: (0,)", "type": "scatter", "x0": 0, "xaxis": "x", "y": [ 0.03431280582000545, 0.1218660129746217, 0.2342853495617262, 0.3661633927010636, 0.5057270938495457, 0.6358462565555233, 0.7371802676120509, 0.7927999266408037, 0.7927999266408037, 0.7927999266408037, 0.7927999266408037, 0.7927999266408037, 0.7927999266408037, 0.7927999266408037, 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "duration.value = 64e-9\n", "amplitude.value = 0.6\n", "rise.value = 20e-9\n", "\n", "# render\n", "program.render()" ] }, { "cell_type": "raw", "id": "b31e584f", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "Derivative Envelope\n", "^^^^^^^^^^^^^^^^^^^\n", "\n", "The derivative envelope is specified by a ``base_envelope`` and optional\n", "``step_size``. The ``base_envelope`` can be any envelope defined by |QCS|." ] }, { "cell_type": "code", "execution_count": 7, "id": "c4164218", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:17:48.879386Z", "iopub.status.busy": "2024-10-11T06:17:48.879068Z", "iopub.status.idle": "2024-10-11T06:17:49.096376Z", "shell.execute_reply": "2024-10-11T06:17:49.095667Z" } }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "dx": 0.001, "legendgroup": "awg_channel, labels: (0,)", "legendgrouptitle": { "text": "awg_channel, labels: (0,)" }, "name": "Drive pulse for awg_channel, labels: (0,)", "type": "scatter", "x0": 0, "xaxis": "x", "y": [ 2.176442532241246e-05, 2.229251048362487e-05, 2.283281520729707e-05, 2.338560717328012e-05, 2.3951159556223616e-05, 2.4529751129577114e-05, 2.512166637145873e-05, 2.572719557261181e-05, 2.634663494547405e-05, 2.6980286735831374e-05, 2.762845933596545e-05, 2.8291467399854156e-05, 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"hovermode": "x unified", "legend": { "bgcolor": "white", "bordercolor": "Black", "borderwidth": 1, "font": { "family": "Rockwell" } }, "xaxis": { "linecolor": "black", "linewidth": 1, "mirror": true, "showline": true }, "yaxis": { "linecolor": "black", "linewidth": 1, "mirror": true, "showline": true } } }, "width": 900, "xaxis": { "anchor": "y", "domain": [ 0.0, 1.0 ], "showticklabels": true, "title": { "text": "Time (s)" } }, "yaxis": { "anchor": "x", "domain": [ 0.0, 1.0 ], "title": { "text": "Fractional Voltage" } } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "base_envelope = qcs.GaussianEnvelope(num_sigma=5)\n", "envelope = qcs.DerivativeEnvelope(base_envelope)\n", "dc_wav = qcs.DCWaveform(2, envelope, 0.7)\n", "\n", "# initialize the program and add the envelope\n", "program = qcs.Program()\n", "program.add_waveform(dc_wav, awg)\n", "\n", "# render\n", "program.render(sample_rate=1e3)" ] }, { "cell_type": "raw", "id": "cf9ed2b5", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "DRAG Envelope\n", "^^^^^^^^^^^^^\n", "\n", "Derivative Removal by Adiabatic Gate (DRAG) envelopes were introduced in `Motzoi et\n", "al. `_ as a\n", "means of offsetting the noise introduced during the application of a pulse by applying\n", "another pulse in an orthogonal axis. The envelope applied orthogonal to the base\n", "envelope is described by the derivative of the base envelope scaled with some DRAG\n", "coefficient. Often, pulses applied simultaneously in different axes are stored in\n", "the real and imaginary parts of an envelope. We therefore describe the DRAG pulse of\n", "a base envelope :math:`E(t)` as\n", "\n", ".. math::\n", " E(t) + i\\beta E'(t),\n", "\n", "where :math:`\\beta` is the drag coefficient and :math:`E'(t)` is the derivative of\n", ":math:`E(t)` with respect to time.\n", "\n", "Most DRAG envelopes are not explicitly defined in |QCS|\\. However, a method that\n", "automatically constructs the relevant DRAG envelope given a base envelope using\n", "numerical differentiation is provided.\n", "\n", "In this example, we assemble a DRAG envelope with a Gaussian as the base shape. Here,\n", "the DRAG coefficient is :math:`\\beta=0.1`." ] }, { "cell_type": "code", "execution_count": 8, "id": "a4ee76ad", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:17:49.102229Z", "iopub.status.busy": "2024-10-11T06:17:49.101862Z", "iopub.status.idle": "2024-10-11T06:17:49.195803Z", "shell.execute_reply": "2024-10-11T06:17:49.195087Z" } }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "dx": 2e-10, "legendgroup": "awg_channel, labels: (0,)", "legendgrouptitle": { "text": "awg_channel, labels: (0,)" }, "name": "Drive pulse for awg_channel, labels: (0,)", "type": "scatter", "x0": 0, "xaxis": "x", "y": [ -0.003372531578007835, -0.010320245532864045, -0.017541802640843894, -0.025041253311834575, -0.032822254081784116, -0.04088803626028, -0.049241374493297366, -0.05788455537419348, -0.06681934624261922, -0.07604696431713259, -0.0855680463128735, -0.09538261870062682, 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# initialize a 30ns Gaussian RF Waveform at 5GHz\n", "gauss = qcs.RFWaveform(\n", " duration=30e-9, envelope=qcs.GaussianEnvelope(), amplitude=0.8, rf_frequency=5e9\n", ")\n", "\n", "# initialize the program and add the drag pulse with a coefficient of 0.05\n", "program = qcs.Program()\n", "program.add_waveform(gauss.drag(0.05), awg)\n", "\n", "# render\n", "program.render(sample_rate=5e9, plot_imaginary=True)" ] }, { "cell_type": "raw", "id": "d2237eb2", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ "Arbitrary envelopes\n", "-------------------\n", "An arbitrary envelope allows a user to specify any shape of pulse.\n", "\n", "Example 1: linear interpolation\n", "^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n", "\n", "In this example we implement a flat-top pulse with linear interpolation from zero to\n", "the maximum value during the interval ``[0, rise_time]``. The amplitude then falls\n", "back to zero on the interval ``[duration-fall_time, duration]``. Arbitrary envelopes\n", "can be specified as a list of sample times and corresponding amplitudes, in which case\n", "linear interpolation is applied between specified points." ] }, { "cell_type": "code", "execution_count": 9, "id": "edccab8f", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:17:49.200167Z", "iopub.status.busy": "2024-10-11T06:17:49.199816Z", "iopub.status.idle": "2024-10-11T06:17:49.342170Z", "shell.execute_reply": "2024-10-11T06:17:49.341391Z" } }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "dx": 0.001, "legendgroup": "awg_channel, labels: (0,)", "legendgrouptitle": { "text": "awg_channel, labels: (0,)" }, "name": "Drive pulse for awg_channel, labels: (0,)", "type": "scatter", "x0": 0, "xaxis": "x", "y": [ 0.0006, 0.0018, 0.0029999999999999996, 0.004200000000000001, 0.0054, 0.006599999999999999, 0.0078, 0.008999999999999998, 0.010199999999999999, 0.011399999999999999, 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "duration = 3\n", "rise_time = 0.5\n", "fall_time = 1\n", "amplitude = 0.6\n", "\n", "# specify the samples for linear interpolation\n", "times = [0, rise_time, duration - fall_time, duration]\n", "samples = [0, amplitude, amplitude, 0]\n", "\n", "# initialize the envelope\n", "envelope = qcs.ArbitraryEnvelope(times, samples)\n", "dc_wav = qcs.DCWaveform(duration, envelope, amplitude)\n", "\n", "# initialize the program and add the envelope\n", "program = qcs.Program()\n", "program.add_waveform(dc_wav, awg)\n", "\n", "# render\n", "program.render(sample_rate=1e3)" ] }, { "cell_type": "raw", "id": "908dd358", "metadata": { "lines_to_next_cell": 2, "raw_mimetype": "text/restructuredtext" }, "source": [ "Example 2: functional definition with sech envelope\n", "^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n", "Rather than specifying an envelope with a collection of discrete points, an envelope\n", "can be specified with a function that defines the envelope's shape.\n", "\n", "In this example we implement a sech envelope. The envelope :math:`E(t)` is given by\n", "\n", ".. math::\n", " E(t) = A\\text{sech}\\left(\\frac{t-\\mu}{\\sigma}\\right)\n", "\n", "where :math:`A` is the scaling parameter, :math:`\\mu` is the mean and :math:`\\sigma`\n", "is the standard deviation." ] }, { "cell_type": "code", "execution_count": 10, "id": "573b95cd", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:17:49.347875Z", "iopub.status.busy": "2024-10-11T06:17:49.347556Z", "iopub.status.idle": "2024-10-11T06:17:49.445129Z", "shell.execute_reply": "2024-10-11T06:17:49.444421Z" } }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "dx": 0.001, "legendgroup": "awg_channel, labels: (0,)", "legendgrouptitle": { "text": "awg_channel, labels: (0,)" }, "name": "Drive pulse for awg_channel, labels: (0,)", "type": "scatter", "x0": 0, "xaxis": "x", "y": [ 0.0715428492621931, 0.07203315331940117, 0.07252345737660924, 0.07301376143381731, 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# define the sech envelope\n", "def sech(times, A, sigma):\n", " return A / np.cosh((times - times[-1] / 2) / sigma)\n", "\n", "\n", "A = 0.45\n", "sigma = 0.15\n", "\n", "# initialize the envelope\n", "envelope = qcs.ArbitraryEnvelope.sample(lambda t: sech(t, A, sigma), n_samples=100)\n", "\n", "duration = 1\n", "dc_wav = qcs.DCWaveform(duration, envelope, 1)\n", "\n", "# initialize the program and add the envelope\n", "program = qcs.Program()\n", "program.add_waveform(dc_wav, awg)\n", "\n", "program.render(sample_rate=1e3)" ] }, { "cell_type": "raw", "id": "ec48ea4d", "metadata": { "lines_to_next_cell": 2, "raw_mimetype": "text/restructuredtext" }, "source": [ "Example 3: functional definition with sine envelope\n", "^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n", "In this example we implement a sinusoidal envelope. The envelope :math:`E(t)` is\n", "given by\n", "\n", ".. math::\n", " E(t) = A\\sin(2\\pi f_{\\mathrm{int}} t + \\phi)\n", "\n", "where :math:`A` is the amplitude, :math:`f_{\\mathrm{int}}` is the frequency, and\n", ":math:`\\phi` is the phase of the envelope. Note that as envelopes do not explicitly\n", "depend on time, parameters such as the frequency are unitless and can be specified as\n", "integer multiples of periods. Here we specify a sine wave that covers half a period:" ] }, { "cell_type": "code", "execution_count": 11, "id": "be1d7515", "metadata": { "execution": { "iopub.execute_input": "2024-10-11T06:17:49.450108Z", "iopub.status.busy": "2024-10-11T06:17:49.449781Z", "iopub.status.idle": "2024-10-11T06:17:49.550241Z", "shell.execute_reply": "2024-10-11T06:17:49.548991Z" } }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "dx": 0.001, "legendgroup": "awg_channel, labels: (0,)", "legendgrouptitle": { "text": "awg_channel, labels: (0,)" }, "name": "Drive pulse for awg_channel, labels: (0,)", "type": "scatter", "x0": 0, "xaxis": "x", "y": [ 0.000628292167858394, 0.001884876503575182, 0.0031414608392919697, 0.004398045175008757, 0.0056546295107255465, 0.006911213846442332, 0.008167798182159123, 0.009424382517875909, 0.010680966853592698, 0.011937551189309488, 0.013193630693516737, 0.014448949755323551, 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# define the sine envelope\n", "def sine(input_times, amplitude, freq, phase):\n", " return amplitude * np.sin(2 * np.pi * freq * input_times + phase)\n", "\n", "\n", "amplitude = 0.4\n", "phase = 0\n", "freq = 0.5\n", "\n", "# initialize the envelope\n", "envelope = qcs.ArbitraryEnvelope.sample(\n", " lambda t: sine(t, amplitude, freq, phase), n_samples=100\n", ")\n", "\n", "duration = 1\n", "dc_wav = qcs.DCWaveform(duration, envelope, amplitude)\n", "\n", "# initialize the program and add the envelope\n", "program = qcs.Program()\n", "program.add_waveform(dc_wav, awg)\n", "\n", "program.render(sample_rate=1e3)" ] } ], "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 }