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(duration, amp, name=None)

Generates constant-sampled Waveform.

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

$$f(x) = A$$

Parâmetros

• duration (int) – Duration of pulse. Must be greater than zero.

• amp (complex) – Complex pulse amplitude.

• name (Optional[str]) – Name of pulse.

Tipo de retorno

Waveform

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

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:

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

Parâmetros

• 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.

Tipo de retorno

Waveform

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

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().

Referências

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).

Parâmetros

• 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.

Tipo de retorno

Waveform

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

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 modified 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)

Parâmetros

• 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.

Tipo de retorno

Waveform

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

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.

Parâmetros

• 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.

Tipo de retorno

Waveform

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

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().

Parâmetros

• 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.

Levanta

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

Tipo de retorno

Waveform

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

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

Parâmetros

• 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.

Exemplo

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 0x7f8f0678c950>]

Tipo de retorno

Waveform

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

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 modified 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.

Parâmetros

• 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.

Tipo de retorno

Waveform

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

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 $\text{sech}$.

Parâmetros

• 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.

Tipo de retorno

Waveform

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

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:

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

Parâmetros

• 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.

Tipo de retorno

Waveform

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

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

Parâmetros

• 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.

Tipo de retorno

Waveform

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

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.

Parâmetros

• 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.

Exemplo

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 0x7f8f062819d0>]

Tipo de retorno

Waveform

zero(duration, name=None)

Generates zero-sampled Waveform.

Samples from the function:

$$f(x) = 0$$

Parâmetros

• duration (int) – Duration of pulse. Must be greater than zero.

• name (Optional[str]) – Name of pulse.

Tipo de retorno

Waveform