# Gaussian¶

class Gaussian(duration: Union[int, ParameterExpression], amp: Union[complex, float, ParameterExpression], sigma: Union[float, ParameterExpression], angle: Optional[Union[float, ParameterExpression]] = None, name: Optional[str] = None, limit_amplitude: Optional[bool] = None)[source]

Bases: object

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

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

where $$f'(x)$$ is the gaussian waveform without lifting or amplitude scaling, and $$\text{A} = \text{amp} \times \exp\left(i\times\text{angle}\right)$$.

Create new pulse instance.

Parameters
• duration -- Pulse length in terms of the sampling period dt.

• amp -- The magnitude of the amplitude of the Gaussian envelope. Complex amp support will be deprecated.

• sigma -- A measure of how wide or narrow the Gaussian peak is; described mathematically in the class docstring.

• angle -- The angle of the complex amplitude of the Gaussian envelope. Default value 0.

• name -- Display name for this pulse envelope.

• limit_amplitude -- If True, then limit the amplitude of the waveform to 1. The default is True and the amplitude is constrained to 1.

Returns

ScalableSymbolicPulse instance.

Attributes

alias = 'Gaussian'