# Gaussian¶

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

Bases: SymbolicPulse

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.

Create new pulse instance.

Parameters
• duration (Union[int, ParameterExpression]) -- Pulse length in terms of 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

constraints

Return symbolic expression for the pulse parameter constraints.

Return type

Expr

duration
envelope

Return symbolic expression for the pulse envelope.

Return type

Expr

id

Unique identifier for this pulse.

Return type

int

limit_amplitude = True
name
parameters
Return type

Dict[str, Any]

pulse_type

Return display name of the pulse shape.

Return type

str

valid_amp_conditions

Return symbolic expression for the pulse amplitude constraints.

Return type

Expr