discrete

constant(duration, amp, name=None)

Generates constant-sampled SamplePulse.

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

Parameters

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

Return type

SamplePulse

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

Generates cosine wave SamplePulse.

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

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

SamplePulse

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

Generates Y-only correction DRAG SamplePulse 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:

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

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).

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, make the first and last sample zero, but rescale to preserve amp.

Return type

SamplePulse

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

Generates unnormalized gaussian SamplePulse.

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

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

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

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 $1$.

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, make the first and last sample zero, but rescale to preserve amp.

Return type

SamplePulse

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

Generates unnormalized gaussian derivative SamplePulse.

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

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

SamplePulse

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

Generates gaussian square SamplePulse.

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:

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, make the first and last sample zero, but rescale to preserve amp.

Raises

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

Return type

SamplePulse

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

Generates sawtooth wave SamplePulse.

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

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.
• period (Optional[float]) – Pulse period, units of dt. (Deprecated, use freq instead)
• phase (float) – Pulse phase.
• name (Optional[str]) – Name of pulse.

Example

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

[<matplotlib.lines.Line2D at 0x7f1bfbc7c910>]

Return type

SamplePulse

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

Generates unnormalized sech SamplePulse.

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

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

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

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 $1$.

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, make the first and last sample zero, but rescale to preserve amp.

Return type

SamplePulse

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

Generates unnormalized sech derivative SamplePulse.

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:

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

SamplePulse

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

Generates sine wave SamplePulse.

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

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

SamplePulse

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

Generates square wave SamplePulse.

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

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.
• period (Optional[float]) – Pulse period, units of dt. (Deprecated, use freq instead)
• phase (float) – Pulse phase.
• name (Optional[str]) – Name of pulse.

Return type

SamplePulse

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

Generates triangle wave SamplePulse.

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

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.
• period (Optional[float]) – Pulse period, units of dt. (Deprecated, use freq instead)
• phase (float) – Pulse phase.
• name (Optional[str]) – Name of pulse.

Example

import matplotlib.pyplot as plt
from qiskit.pulse.pulse_lib import triangle
import numpy as np
 
duration = 100
amp = 1
period = duration
triangle_wave = np.real(triangle(duration, amp, period).samples)
plt.plot(range(duration), triangle_wave)

[<matplotlib.lines.Line2D at 0x7f1bf94d9a90>]

Return type

SamplePulse

zero(duration, name=None)

Generates zero-sampled SamplePulse.

Samples from the function:

Parameters

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

Return type

SamplePulse