437 lines
20 KiB
Plaintext
437 lines
20 KiB
Plaintext
---
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title: discrete (v0.26)
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description: API reference for qiskit.pulse.library.discrete in qiskit v0.26
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in_page_toc_min_heading_level: 2
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python_api_type: module
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python_api_name: qiskit.pulse.library.discrete
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---
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<span id="module-qiskit.pulse.library.discrete" />
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<span id="qiskit-pulse-library-discrete" />
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# qiskit.pulse.library.discrete
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Module for builtin discrete pulses.
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Note the sampling strategy use for all discrete pulses is `midpoint`.
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**Functions**
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| | |
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| ----------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------ |
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| [`constant`](#qiskit.pulse.library.discrete.constant "qiskit.pulse.library.discrete.constant")(duration, amp\[, name]) | Generates constant-sampled [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform"). |
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| [`cos`](#qiskit.pulse.library.discrete.cos "qiskit.pulse.library.discrete.cos")(duration, amp\[, freq, phase, name]) | Generates cosine wave [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform"). |
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| [`drag`](#qiskit.pulse.library.discrete.drag "qiskit.pulse.library.discrete.drag")(duration, amp, sigma, beta\[, name, …]) | Generates Y-only correction DRAG [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform") for standard nonlinear oscillator (SNO) \[1]. |
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| [`gaussian`](#qiskit.pulse.library.discrete.gaussian "qiskit.pulse.library.discrete.gaussian")(duration, amp, sigma\[, name, zero\_ends]) | Generates unnormalized gaussian [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform"). |
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| [`gaussian_deriv`](#qiskit.pulse.library.discrete.gaussian_deriv "qiskit.pulse.library.discrete.gaussian_deriv")(duration, amp, sigma\[, name]) | Generates unnormalized gaussian derivative [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform"). |
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| [`gaussian_square`](#qiskit.pulse.library.discrete.gaussian_square "qiskit.pulse.library.discrete.gaussian_square")(duration, amp, sigma\[, …]) | Generates gaussian square [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform"). |
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| [`sawtooth`](#qiskit.pulse.library.discrete.sawtooth "qiskit.pulse.library.discrete.sawtooth")(duration, amp\[, freq, phase, name]) | Generates sawtooth wave [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform"). |
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| [`sech`](#qiskit.pulse.library.discrete.sech "qiskit.pulse.library.discrete.sech")(duration, amp, sigma\[, name, zero\_ends]) | Generates unnormalized sech [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform"). |
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| [`sech_deriv`](#qiskit.pulse.library.discrete.sech_deriv "qiskit.pulse.library.discrete.sech_deriv")(duration, amp, sigma\[, name]) | Generates unnormalized sech derivative [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform"). |
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| [`sin`](#qiskit.pulse.library.discrete.sin "qiskit.pulse.library.discrete.sin")(duration, amp\[, freq, phase, name]) | Generates sine wave [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform"). |
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| [`square`](#qiskit.pulse.library.discrete.square "qiskit.pulse.library.discrete.square")(duration, amp\[, freq, phase, name]) | Generates square wave [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform"). |
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| [`triangle`](#qiskit.pulse.library.discrete.triangle "qiskit.pulse.library.discrete.triangle")(duration, amp\[, freq, phase, name]) | Generates triangle wave [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform"). |
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| [`zero`](#qiskit.pulse.library.discrete.zero "qiskit.pulse.library.discrete.zero")(duration\[, name]) | Generates zero-sampled [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform"). |
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### constant
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<Function id="qiskit.pulse.library.discrete.constant" github="https://github.com/qiskit/qiskit/tree/stable/0.17/qiskit/pulse/library/discrete.py" signature="constant(duration, amp, name=None)">
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Generates constant-sampled [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform").
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For $A=$ `amp`, samples from the function:
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$$
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f(x) = A
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$$
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**Parameters**
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* **duration** (`int`) – Duration of pulse. Must be greater than zero.
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* **amp** (`complex`) – Complex pulse amplitude.
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* **name** (`Optional`\[`str`]) – Name of pulse.
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**Return type**
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`Waveform`
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</Function>
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### cos
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<Function id="qiskit.pulse.library.discrete.cos" github="https://github.com/qiskit/qiskit/tree/stable/0.17/qiskit/pulse/library/discrete.py" signature="cos(duration, amp, freq=None, phase=0, name=None)">
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Generates cosine wave [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform").
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For $A=$ `amp`, $\omega=$ `freq`, and $\phi=$ `phase`, applies the midpoint sampling strategy to generate a discrete pulse sampled from the continuous function:
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$$
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f(x) = A \cos(2 \pi \omega x + \phi)
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$$
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**Parameters**
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* **duration** (`int`) – Duration of pulse. Must be greater than zero.
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* **amp** (`complex`) – Pulse amplitude.
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* **freq** (`Optional`\[`float`]) – Pulse frequency, units of 1/dt. If `None` defaults to single cycle.
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* **phase** (`float`) – Pulse phase.
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* **name** (`Optional`\[`str`]) – Name of pulse.
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**Return type**
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`Waveform`
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</Function>
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### drag
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<Function id="qiskit.pulse.library.discrete.drag" github="https://github.com/qiskit/qiskit/tree/stable/0.17/qiskit/pulse/library/discrete.py" signature="drag(duration, amp, sigma, beta, name=None, zero_ends=True)">
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Generates Y-only correction DRAG [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform") for standard nonlinear oscillator (SNO) \[1].
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For $A=$ `amp`, $\sigma=$ `sigma`, and $\beta=$ `beta`, applies the `midpoint` sampling strategy to generate a discrete pulse sampled from the continuous function:
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$$
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f(x) = g(x) + i \beta h(x),
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$$
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where $g(x)$ is the function sampled in [`gaussian()`](#qiskit.pulse.library.discrete.gaussian "qiskit.pulse.library.discrete.gaussian"), and $h(x)$ is the function sampled in [`gaussian_deriv()`](#qiskit.pulse.library.discrete.gaussian_deriv "qiskit.pulse.library.discrete.gaussian_deriv").
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If `zero_ends == True`, the samples from $g(x)$ are remapped as in [`gaussian()`](#qiskit.pulse.library.discrete.gaussian "qiskit.pulse.library.discrete.gaussian").
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**References**
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1. [*Gambetta, J. M., Motzoi, F., Merkel, S. T. & Wilhelm, F. K. “Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator.” Phys. Rev. A 83, 012308 (2011).*](http://dx.doi.org/10.1103/PhysRevA.83.012308)
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**Parameters**
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* **duration** (`int`) – Duration of pulse. Must be greater than zero.
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* **amp** (`complex`) – Pulse amplitude at center `duration/2`.
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* **sigma** (`float`) – Width (standard deviation) of pulse.
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* **beta** (`float`) – Y correction amplitude. For the SNO this is $\beta=-\frac{\lambda_1^2}{4\Delta_2}$. Where $\lambda_1$ is the relative coupling strength between the first excited and second excited states and $\Delta_2$ is the detuning between the respective excited states.
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* **name** (`Optional`\[`str`]) – Name of pulse.
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* **zero\_ends** (`bool`) – If True, zero ends at `x = -1, x = duration + 1`, but rescale to preserve amp.
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**Return type**
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`Waveform`
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</Function>
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### gaussian
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<Function id="qiskit.pulse.library.discrete.gaussian" github="https://github.com/qiskit/qiskit/tree/stable/0.17/qiskit/pulse/library/discrete.py" signature="gaussian(duration, amp, sigma, name=None, zero_ends=True)">
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Generates unnormalized gaussian [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform").
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For $A=$ `amp` and $\sigma=$ `sigma`, applies the `midpoint` sampling strategy to generate a discrete pulse sampled from the continuous function:
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$$
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f(x) = A\exp\left(\left(\frac{x - \mu}{2\sigma}\right)^2 \right),
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$$
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with the center $\mu=$ `duration/2`.
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If `zero_ends==True`, each output sample $y$ is modified according to:
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$$
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y \mapsto A\frac{y-y^*}{A-y^*},
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$$
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where $y^*$ is the value of the endpoint samples. This sets the endpoints to $0$ while preserving the amplitude at the center. If $A=y^*$, $y$ is set to $1$. By default, the endpoints are at `x = -1, x = duration + 1`.
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Integrated area under the full curve is `amp * np.sqrt(2*np.pi*sigma**2)`
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**Parameters**
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* **duration** (`int`) – Duration of pulse. Must be greater than zero.
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* **amp** (`complex`) – Pulse amplitude at `duration/2`.
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* **sigma** (`float`) – Width (standard deviation) of pulse.
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* **name** (`Optional`\[`str`]) – Name of pulse.
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* **zero\_ends** (`bool`) – If True, zero ends at `x = -1, x = duration + 1`, but rescale to preserve amp.
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**Return type**
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`Waveform`
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</Function>
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### gaussian\_deriv
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<Function id="qiskit.pulse.library.discrete.gaussian_deriv" github="https://github.com/qiskit/qiskit/tree/stable/0.17/qiskit/pulse/library/discrete.py" signature="gaussian_deriv(duration, amp, sigma, name=None)">
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Generates unnormalized gaussian derivative [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform").
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For $A=$ `amp` and $\sigma=$ `sigma` applies the midpoint sampling strategy to generate a discrete pulse sampled from the continuous function:
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$$
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f(x) = A\frac{(x - \mu)}{\sigma^2}\exp\left(\left(\frac{x - \mu}{2\sigma}\right)^2 \right)
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$$
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i.e. the derivative of the Gaussian function, with center $\mu=$ `duration/2`.
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**Parameters**
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* **duration** (`int`) – Duration of pulse. Must be greater than zero.
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* **amp** (`complex`) – Pulse amplitude of corresponding Gaussian at the pulse center (`duration/2`).
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* **sigma** (`float`) – Width (standard deviation) of pulse.
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* **name** (`Optional`\[`str`]) – Name of pulse.
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**Return type**
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`Waveform`
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</Function>
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### gaussian\_square
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<Function id="qiskit.pulse.library.discrete.gaussian_square" github="https://github.com/qiskit/qiskit/tree/stable/0.17/qiskit/pulse/library/discrete.py" signature="gaussian_square(duration, amp, sigma, risefall=None, width=None, name=None, zero_ends=True)">
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Generates gaussian square [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform").
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For $d=$ `duration`, $A=$ `amp`, $\sigma=$ `sigma`, and $r=$ `risefall`, applies the `midpoint` sampling strategy to generate a discrete pulse sampled from the continuous function:
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$$
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\begin{split}f(x) = \begin{cases}
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g(x - r) ) & x\leq r \\
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A & r\leq x\leq d-r \\
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g(x - (d - r)) & d-r\leq x
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\end{cases}\end{split}
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$$
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where $g(x)$ is the Gaussian function sampled from in [`gaussian()`](#qiskit.pulse.library.discrete.gaussian "qiskit.pulse.library.discrete.gaussian") with $A=$ `amp`, $\mu=1$, and $\sigma=$ `sigma`. I.e. $f(x)$ represents a square pulse with smooth Gaussian edges.
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If `zero_ends == True`, the samples for the Gaussian ramps are remapped as in [`gaussian()`](#qiskit.pulse.library.discrete.gaussian "qiskit.pulse.library.discrete.gaussian").
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**Parameters**
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* **duration** (`int`) – Duration of pulse. Must be greater than zero.
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* **amp** (`complex`) – Pulse amplitude.
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* **sigma** (`float`) – Width (standard deviation) of Gaussian rise/fall portion of the pulse.
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* **risefall** (`Optional`\[`float`]) – Number of samples over which pulse rise and fall happen. Width of square portion of pulse will be `duration-2*risefall`.
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* **width** (`Optional`\[`float`]) – The duration of the embedded square pulse. Only one of `width` or `risefall` should be specified as the functional form requires `width = duration - 2 * risefall`.
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* **name** (`Optional`\[`str`]) – Name of pulse.
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* **zero\_ends** (`bool`) – If True, zero ends at `x = -1, x = duration + 1`, but rescale to preserve amp.
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**Raises**
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[**PulseError**](qiskit.pulse.PulseError "qiskit.pulse.PulseError") – If `risefall` and `width` arguments are inconsistent or not enough info.
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**Return type**
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`Waveform`
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</Function>
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### sawtooth
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<Function id="qiskit.pulse.library.discrete.sawtooth" github="https://github.com/qiskit/qiskit/tree/stable/0.17/qiskit/pulse/library/discrete.py" signature="sawtooth(duration, amp, freq=None, phase=0, name=None)">
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Generates sawtooth wave [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform").
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For $A=$ `amp`, $T=$ `period`, and $\phi=$ `phase`, applies the midpoint sampling strategy to generate a discrete pulse sampled from the continuous function:
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$$
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f(x) = 2 A \left( g(x) - \left\lfloor \frac{1}{2} + g(x) \right\rfloor\right)
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$$
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where $g(x) = x/T + \phi/\pi$.
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**Parameters**
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* **duration** (`int`) – Duration of pulse. Must be greater than zero.
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* **amp** (`complex`) – Pulse amplitude. Wave range is $[-$ `amp` $,$ `amp` $]$.
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* **freq** (`Optional`\[`float`]) – Pulse frequency, units of 1./dt. If `None` defaults to 1./duration.
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* **phase** (`float`) – Pulse phase.
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* **name** (`Optional`\[`str`]) – Name of pulse.
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**Example**
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```python
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import matplotlib.pyplot as plt
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from qiskit.pulse.library import sawtooth
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import numpy as np
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duration = 100
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amp = 1
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freq = 1 / duration
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sawtooth_wave = np.real(sawtooth(duration, amp, freq).samples)
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plt.plot(range(duration), sawtooth_wave)
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```
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```
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[<matplotlib.lines.Line2D at 0x7f47cc2fe090>]
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```
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**Return type**
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`Waveform`
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</Function>
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### sech
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<Function id="qiskit.pulse.library.discrete.sech" github="https://github.com/qiskit/qiskit/tree/stable/0.17/qiskit/pulse/library/discrete.py" signature="sech(duration, amp, sigma, name=None, zero_ends=True)">
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Generates unnormalized sech [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform").
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For $A=$ `amp` and $\sigma=$ `sigma`, applies the `midpoint` sampling strategy to generate a discrete pulse sampled from the continuous function:
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$$
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f(x) = A\text{sech}\left(\frac{x-\mu}{\sigma} \right)
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$$
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with the center $\mu=$ `duration/2`.
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If `zero_ends==True`, each output sample $y$ is modified according to:
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$$
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y \mapsto A\frac{y-y^*}{A-y^*},
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$$
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where $y^*$ is the value of the endpoint samples. This sets the endpoints to $0$ while preserving the amplitude at the center. If $A=y^*$, $y$ is set to $1$. By default, the endpoints are at `x = -1, x = duration + 1`.
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**Parameters**
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* **duration** (`int`) – Duration of pulse. Must be greater than zero.
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* **amp** (`complex`) – Pulse amplitude at duration/2.
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* **sigma** (`float`) – Width (standard deviation) of pulse.
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* **name** (`Optional`\[`str`]) – Name of pulse.
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* **zero\_ends** (`bool`) – If True, zero ends at `x = -1, x = duration + 1`, but rescale to preserve amp.
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**Return type**
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`Waveform`
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</Function>
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### sech\_deriv
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<Function id="qiskit.pulse.library.discrete.sech_deriv" github="https://github.com/qiskit/qiskit/tree/stable/0.17/qiskit/pulse/library/discrete.py" signature="sech_deriv(duration, amp, sigma, name=None)">
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Generates unnormalized sech derivative [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform").
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For $A=$ `amp`, $\sigma=$ `sigma`, and center $\mu=$ `duration/2`, applies the midpoint sampling strategy to generate a discrete pulse sampled from the continuous function:
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$$
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f(x) = \frac{d}{dx}\left[A\text{sech}\left(\frac{x-\mu}{\sigma} \right)\right],
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$$
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i.e. the derivative of $\text{sech}$.
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**Parameters**
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* **duration** (`int`) – Duration of pulse. Must be greater than zero.
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* **amp** (`complex`) – Pulse amplitude at center.
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* **sigma** (`float`) – Width (standard deviation) of pulse.
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* **name** (`Optional`\[`str`]) – Name of pulse.
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**Return type**
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`Waveform`
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</Function>
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### sin
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<Function id="qiskit.pulse.library.discrete.sin" github="https://github.com/qiskit/qiskit/tree/stable/0.17/qiskit/pulse/library/discrete.py" signature="sin(duration, amp, freq=None, phase=0, name=None)">
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Generates sine wave [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform").
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For $A=$ `amp`, $\omega=$ `freq`, and $\phi=$ `phase`, applies the midpoint sampling strategy to generate a discrete pulse sampled from the continuous function:
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$$
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f(x) = A \sin(2 \pi \omega x + \phi)
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$$
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**Parameters**
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* **duration** (`int`) – Duration of pulse. Must be greater than zero.
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* **amp** (`complex`) – Pulse amplitude.
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* **freq** (`Optional`\[`float`]) – Pulse frequency, units of 1/dt. If `None` defaults to single cycle.
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* **phase** (`float`) – Pulse phase.
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* **name** (`Optional`\[`str`]) – Name of pulse.
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**Return type**
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`Waveform`
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</Function>
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### square
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<Function id="qiskit.pulse.library.discrete.square" github="https://github.com/qiskit/qiskit/tree/stable/0.17/qiskit/pulse/library/discrete.py" signature="square(duration, amp, freq=None, phase=0, name=None)">
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Generates square wave [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform").
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For $A=$ `amp`, $T=$ `period`, and $\phi=$ `phase`, applies the midpoint sampling strategy to generate a discrete pulse sampled from the continuous function:
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$$
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f(x) = A \text{sign}\left[ \sin\left(\frac{2 \pi x}{T} + 2\phi\right) \right]
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$$
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with the convention $\text{sign}(0) = 1$.
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**Parameters**
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* **duration** (`int`) – Duration of pulse. Must be greater than zero.
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* **amp** (`complex`) – Pulse amplitude. Wave range is $[-$ `amp` $,$ `amp` $]$.
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* **freq** (`Optional`\[`float`]) – Pulse frequency, units of 1./dt. If `None` defaults to 1./duration.
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* **phase** (`float`) – Pulse phase.
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* **name** (`Optional`\[`str`]) – Name of pulse.
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**Return type**
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`Waveform`
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</Function>
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### triangle
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<Function id="qiskit.pulse.library.discrete.triangle" github="https://github.com/qiskit/qiskit/tree/stable/0.17/qiskit/pulse/library/discrete.py" signature="triangle(duration, amp, freq=None, phase=0, name=None)">
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Generates triangle wave [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform").
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For $A=$ `amp`, $T=$ `period`, and $\phi=$ `phase`, applies the midpoint sampling strategy to generate a discrete pulse sampled from the continuous function:
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$$
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f(x) = A \left(-2\left|\text{sawtooth}(x, A, T, \phi)\right| + 1\right)
|
||
$$
|
||
|
||
This a non-sinusoidal wave with linear ramping.
|
||
|
||
**Parameters**
|
||
|
||
* **duration** (`int`) – Duration of pulse. Must be greater than zero.
|
||
* **amp** (`complex`) – Pulse amplitude. Wave range is $[-$ `amp` $,$ `amp` $]$.
|
||
* **freq** (`Optional`\[`float`]) – Pulse frequency, units of 1./dt. If `None` defaults to 1./duration.
|
||
* **phase** (`float`) – Pulse phase.
|
||
* **name** (`Optional`\[`str`]) – Name of pulse.
|
||
|
||
**Example**
|
||
|
||
```python
|
||
import matplotlib.pyplot as plt
|
||
from qiskit.pulse.library import triangle
|
||
import numpy as np
|
||
|
||
duration = 100
|
||
amp = 1
|
||
freq = 1 / duration
|
||
triangle_wave = np.real(triangle(duration, amp, freq).samples)
|
||
plt.plot(range(duration), triangle_wave)
|
||
```
|
||
|
||
```
|
||
[<matplotlib.lines.Line2D at 0x7f47cbe3a790>]
|
||
```
|
||
|
||
|
||
|
||
**Return type**
|
||
|
||
`Waveform`
|
||
</Function>
|
||
|
||
### zero
|
||
|
||
<Function id="qiskit.pulse.library.discrete.zero" github="https://github.com/qiskit/qiskit/tree/stable/0.17/qiskit/pulse/library/discrete.py" signature="zero(duration, name=None)">
|
||
Generates zero-sampled [`Waveform`](qiskit.pulse.Waveform "qiskit.pulse.Waveform").
|
||
|
||
Samples from the function:
|
||
|
||
$$
|
||
f(x) = 0
|
||
$$
|
||
|
||
**Parameters**
|
||
|
||
* **duration** (`int`) – Duration of pulse. Must be greater than zero.
|
||
* **name** (`Optional`\[`str`]) – Name of pulse.
|
||
|
||
**Return type**
|
||
|
||
`Waveform`
|
||
</Function>
|
||
|