qiskit.pulse.library.discrete

Module for builtin discrete pulses.

Note the sampling strategy use for all discrete pulses is midpoint.

Functions


`constant`(duration, amp[, name])	Generates constant-sampled `Waveform`.
`cos`(duration, amp[, freq, phase, name])	Generates cosine wave `Waveform`.
`drag`(duration, amp, sigma, beta[, name, …])	Generates Y-only correction DRAG `Waveform` for standard nonlinear oscillator (SNO) [1].
`gaussian`(duration, amp, sigma[, name, zero_ends])	Generates unnormalized gaussian `Waveform`.
`gaussian_deriv`(duration, amp, sigma[, name])	Generates unnormalized gaussian derivative `Waveform`.
`gaussian_square`(duration, amp, sigma[, …])	Generates gaussian square `Waveform`.
`sawtooth`(duration, amp[, freq, phase, name])	Generates sawtooth wave `Waveform`.
`sech`(duration, amp, sigma[, name, zero_ends])	Generates unnormalized sech `Waveform`.
`sech_deriv`(duration, amp, sigma[, name])	Generates unnormalized sech derivative `Waveform`.
`sin`(duration, amp[, freq, phase, name])	Generates sine wave `Waveform`.
`square`(duration, amp[, freq, phase, name])	Generates square wave `Waveform`.
`triangle`(duration, amp[, freq, phase, name])	Generates triangle wave `Waveform`.
`zero`(duration[, name])	Generates zero-sampled `Waveform`.

constant

constant(duration, amp, name=None)

GitHub

Generates constant-sampled Waveform.

For $A=$ amp, samples from the function:

f(x) = A

Parameters

duration (int) – Duration of pulse. Must be greater than zero.
amp (complex) – Complex pulse amplitude.
name (Optional[str]) – Name of pulse.

Return type

Waveform

cos

cos(duration, amp, freq=None, phase=0, name=None)

GitHub

Generates cosine wave Waveform.

For $A=$ amp, $\omega=$ freq, and $\phi=$ phase, applies the midpoint sampling strategy to generate a discrete pulse sampled from the continuous function:

f(x) = A \cos(2 \pi \omega x + \phi)

Parameters

duration (int) – Duration of pulse. Must be greater than zero.
amp (complex) – Pulse amplitude.
freq (Optional[float]) – Pulse frequency, units of 1/dt. If None defaults to single cycle.
phase (float) – Pulse phase.
name (Optional[str]) – Name of pulse.

Return type

Waveform

drag

drag(duration, amp, sigma, beta, name=None, zero_ends=True)

GitHub

Generates Y-only correction DRAG Waveform for standard nonlinear oscillator (SNO) [1].

For $A=$ amp, $\sigma=$ sigma, and $\beta=$ beta, applies the midpoint sampling strategy to generate a discrete pulse sampled from the continuous function:

f(x) = g(x) + i \beta h(x),

where $g(x)$ is the function sampled in gaussian(), and $h(x)$ is the function sampled in gaussian_deriv().

If zero_ends == True, the samples from $g(x)$ are remapped as in gaussian().

References

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).

Parameters

duration (int) – Duration of pulse. Must be greater than zero.
amp (complex) – Pulse amplitude at center duration/2.
sigma (float) – Width (standard deviation) of pulse.
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.
name (Optional[str]) – Name of pulse.
zero_ends (bool) – If True, zero ends at x = -1, x = duration + 1, but rescale to preserve amp.

Return type

Waveform

gaussian

gaussian(duration, amp, sigma, name=None, zero_ends=True)

GitHub

Generates unnormalized gaussian Waveform.

For $A=$ amp and $\sigma=$ sigma, applies the midpoint sampling strategy to generate a discrete pulse sampled from the continuous function:

f(x) = A\exp\left(\left(\frac{x - \mu}{2\sigma}\right)^2 \right),

with the center $\mu=$ duration/2.

If zero_ends==True, each output sample $y$ is modifed according to:

y \mapsto A\frac{y-y^*}{A-y^*},

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.

Integrated area under the full curve is amp * np.sqrt(2*np.pi*sigma**2)

Parameters

duration (int) – Duration of pulse. Must be greater than zero.
amp (complex) – Pulse amplitude at duration/2.
sigma (float) – Width (standard deviation) of pulse.
name (Optional[str]) – Name of pulse.
zero_ends (bool) – If True, zero ends at x = -1, x = duration + 1, but rescale to preserve amp.

Return type

Waveform

gaussian_deriv

gaussian_deriv(duration, amp, sigma, name=None)

GitHub

Generates unnormalized gaussian derivative Waveform.

For $A=$ amp and $\sigma=$ sigma applies the midpoint sampling strategy to generate a discrete pulse sampled from the continuous function:

f(x) = A\frac{(x - \mu)}{\sigma^2}\exp\left(\left(\frac{x - \mu}{2\sigma}\right)^2 \right)

i.e. the derivative of the Gaussian function, with center $\mu=$ duration/2.

Parameters

duration (int) – Duration of pulse. Must be greater than zero.
amp (complex) – Pulse amplitude of corresponding Gaussian at the pulse center (duration/2).
sigma (float) – Width (standard deviation) of pulse.
name (Optional[str]) – Name of pulse.

Return type

Waveform

gaussian_square

gaussian_square(duration, amp, sigma, risefall=None, width=None, name=None, zero_ends=True)

GitHub

Generates gaussian square Waveform.

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:

\begin{split}f(x) = \begin{cases} g(x - r) ) & x\leq r \\ A & r\leq x\leq d-r \\ g(x - (d - r)) & d-r\leq x \end{cases}\end{split}

where $g(x)$ is the Gaussian function sampled from in gaussian() with $A=$ amp, $\mu=1$ , and $\sigma=$ sigma. I.e. $f(x)$ represents a square pulse with smooth Gaussian edges.

If zero_ends == True, the samples for the Gaussian ramps are remapped as in gaussian().

Parameters

duration (int) – Duration of pulse. Must be greater than zero.
amp (complex) – Pulse amplitude.
sigma (float) – Width (standard deviation) of Gaussian rise/fall portion of the pulse.
risefall (Optional[float]) – Number of samples over which pulse rise and fall happen. Width of square portion of pulse will be duration-2*risefall.
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.
name (Optional[str]) – Name of pulse.
zero_ends (bool) – If True, zero ends at x = -1, x = duration + 1, but rescale to preserve amp.

Raises

PulseError – If risefall and width arguments are inconsistent or not enough info.

Return type

Waveform

sawtooth

sawtooth(duration, amp, freq=None, phase=0, name=None)

GitHub

Generates sawtooth wave Waveform.

For $A=$ amp, $T=$ period, and $\phi=$ phase, applies the midpoint sampling strategy to generate a discrete pulse sampled from the continuous function:

f(x) = 2 A \left( g(x) - \left\lfloor \frac{1}{2} + g(x) \right\rfloor\right)

where $g(x) = x/T + \phi/\pi$ .

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

import matplotlib.pyplot as plt
from qiskit.pulse.library import sawtooth
import numpy as np
 
duration = 100
amp = 1
freq = 1 / duration
sawtooth_wave = np.real(sawtooth(duration, amp, freq).samples)
plt.plot(range(duration), sawtooth_wave)

[<matplotlib.lines.Line2D at 0x7fc352516090>]

../_images/qiskit.pulse.library.discrete_0_1.png

Return type

Waveform

sech

sech(duration, amp, sigma, name=None, zero_ends=True)

GitHub

Generates unnormalized sech Waveform.

For $A=$ amp and $\sigma=$ sigma, applies the midpoint sampling strategy to generate a discrete pulse sampled from the continuous function:

f(x) = A\text{sech}\left(\frac{x-\mu}{\sigma} \right)

with the center $\mu=$ duration/2.

If zero_ends==True, each output sample $y$ is modifed according to:

y \mapsto A\frac{y-y^*}{A-y^*},

Parameters

duration (int) – Duration of pulse. Must be greater than zero.
amp (complex) – Pulse amplitude at duration/2.
sigma (float) – Width (standard deviation) of pulse.
name (Optional[str]) – Name of pulse.
zero_ends (bool) – If True, zero ends at x = -1, x = duration + 1, but rescale to preserve amp.

Return type

Waveform

sech_deriv

sech_deriv(duration, amp, sigma, name=None)

GitHub

Generates unnormalized sech derivative Waveform.

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:

f(x) = \frac{d}{dx}\left[A\text{sech}\left(\frac{x-\mu}{\sigma} \right)\right],

i.e. the derivative of $\text{sech}$ .

Parameters

duration (int) – Duration of pulse. Must be greater than zero.
amp (complex) – Pulse amplitude at center.
sigma (float) – Width (standard deviation) of pulse.
name (Optional[str]) – Name of pulse.

Return type

Waveform

sin

sin(duration, amp, freq=None, phase=0, name=None)

GitHub

Generates sine wave Waveform.

For $A=$ amp, $\omega=$ freq, and $\phi=$ phase, applies the midpoint sampling strategy to generate a discrete pulse sampled from the continuous function:

f(x) = A \sin(2 \pi \omega x + \phi)

Parameters

duration (int) – Duration of pulse. Must be greater than zero.
amp (complex) – Pulse amplitude.
freq (Optional[float]) – Pulse frequency, units of 1/dt. If None defaults to single cycle.
phase (float) – Pulse phase.
name (Optional[str]) – Name of pulse.

Return type

Waveform

square

square(duration, amp, freq=None, phase=0, name=None)

GitHub

Generates square wave Waveform.

For $A=$ amp, $T=$ period, and $\phi=$ phase, applies the midpoint sampling strategy to generate a discrete pulse sampled from the continuous function:

f(x) = A \text{sign}\left[ \sin\left(\frac{2 \pi x}{T} + 2\phi\right) \right]

with the convention $\text{sign}(0) = 1$ .

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.

Return type

Waveform

triangle

triangle(duration, amp, freq=None, phase=0, name=None)

GitHub

Generates triangle wave Waveform.

For $A=$ amp, $T=$ period, and $\phi=$ phase, applies the midpoint sampling strategy to generate a discrete pulse sampled from the continuous function:

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

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 0x7fc352006190>]

../_images/qiskit.pulse.library.discrete_1_1.png

Return type

Waveform

zero

zero(duration, name=None)

GitHub

Generates zero-sampled 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

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