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".. _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::\n",
" :class: admonition-blue\n",
"\n",
" 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"
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"import keysight.qcs as qcs\n",
"import numpy as np"
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"\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."
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"# initialize a constant envelope\n",
"envelope = qcs.ConstantEnvelope()\n",
"dc_wav = qcs.DCWaveform(duration=200e-9, envelope=envelope, amplitude=1)\n",
"\n",
"# instantiate an empty program\n",
"program = qcs.Program()\n",
"\n",
"# instantiate an awg channel\n",
"awg = qcs.Channels(range(1), \"awg_channel\")\n",
"\n",
"# add the envelope to the program\n",
"program.add_waveform(dc_wav, awg, pre_delay=20e-9)\n",
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"\n",
"# render\n",
"program.render()"
]
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"^^^^^^^^^^^^^^^^^\n",
"\n",
"In this example we define a DC waveform with a Gaussian envelope with a duration of\n",
"320 ns and standard deviation of 80 ns."
]
},
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"# initialize a Gaussian\n",
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"source": [
"program = qcs.Program()\n",
"program.add_waveform(\n",
" qcs.DCWaveform.create_dc_flattop(\n",
" rise_duration=rise,\n",
" hold_duration=duration,\n",
" fall_duration=50e-9,\n",
" envelope=qcs.GaussianEnvelope(),\n",
" amplitude=amplitude,\n",
" ),\n",
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")\n",
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"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|."
]
},
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"base_envelope = qcs.GaussianEnvelope(num_sigma=5)\n",
"envelope = qcs.DerivativeEnvelope(base_envelope)\n",
"dc_wav = qcs.DCWaveform(200e-9, 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()"
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"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`."
]
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"# initialize a 200ns Gaussian RF Waveform.\n",
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"gauss = qcs.RFWaveform(\n",
" duration=200e-9, envelope=qcs.GaussianEnvelope(), amplitude=0.8, rf_frequency=0\n",
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"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",
"Arbitrary envelopes can be specified with a list of sample times and corresponding\n",
"amplitudes. When rendering the envelope, linear interpolation is applied between\n",
"specified points. In this example we implement an envelope that ramps from zero to\n",
"the maximum value during the interval ``[0, 0.2]``. The amplitude then falls back\n",
"to zero on the interval ``[0.7, 1]``. This example uses a scale from 0 to 1 for\n",
"both sample times and amplitudes. The final duration and amplitude is then\n",
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"\n",
"# specify the samples for linear interpolation\n",
"times = [0, 0.2, 0.7, 1]\n",
"samples = [0, 1, 1, 0]\n",
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"# initialize the program and add the waveform\n",
"program = qcs.Program()\n",
"program.add_waveform(dc_wav, awg)\n",
"\n",
"# render\n",
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"Example 2: functional definition with sech envelope\n",
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"# define the sech envelope\n",
"def sech(times, A, sigma):\n",
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"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:"
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"# define the sine envelope\n",
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