# Gaussian¶

class Gaussian(duration, amp, sigma, name=None, limit_amplitude=None)[source]

Bases: qiskit.pulse.library.parametric_pulses.ParametricPulse

A lifted and truncated pulse envelope shaped according to the Gaussian function whose mean is centered at the center of the pulse (duration / 2):

$\begin{split}f'(x) &= \exp\Bigl( -\frac12 \frac{{(x - \text{duration}/2)}^2}{\text{sigma}^2} \Bigr)\\ f(x) &= \text{amp} \times \frac{f'(x) - f'(-1)}{1-f'(-1)}, \quad 0 \le x < \text{duration}\end{split}$

where $$f'(x)$$ is the gaussian waveform without lifting or amplitude scaling.

This pulse would be more accurately named as LiftedGaussian, however, for historical and practical DSP reasons it has the name Gaussian.

Initialize the gaussian pulse.

Parameters
• duration (Union[int, ParameterExpression]) – Pulse length in terms of the the sampling period dt.

• amp (Union[complex, ParameterExpression]) – The amplitude of the Gaussian envelope.

• sigma (Union[float, ParameterExpression]) – A measure of how wide or narrow the Gaussian peak is; described mathematically in the class docstring.

• name (Optional[str]) – Display name for this pulse envelope.

• limit_amplitude (Optional[bool]) – If True, then limit the amplitude of the waveform to 1. The default is True and the amplitude is constrained to 1.

Methods

 draw Plot the interpolated envelope of pulse. get_waveform Return a Waveform with samples filled according to the formula that the pulse represents and the parameter values it contains. is_parameterized Return True iff the instruction is parameterized. validate_parameters Validate parameters.

Attributes

amp

The Gaussian amplitude.

Return type

Union[complex, ParameterExpression]

id

Unique identifier for this pulse.

Return type

int

limit_amplitude = True
parameters
Return type

Dict[str, Any]

sigma

The Gaussian standard deviation of the pulse width.

Return type

Union[float, ParameterExpression]