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# GaussianSquare¶

class GaussianSquare(duration: , amp: Union[complex, float, qiskit.circuit.parameterexpression.ParameterExpression], sigma: , width: Optional[Union[float, qiskit.circuit.parameterexpression.ParameterExpression]] = None, angle: Optional[Union[float, qiskit.circuit.parameterexpression.ParameterExpression]] = None, risefall_sigma_ratio: Optional[Union[float, qiskit.circuit.parameterexpression.ParameterExpression]] = None, name: Optional[str] = None, limit_amplitude: Optional[bool] = None)[source]

Bases: object

A square pulse with a Gaussian shaped risefall on both sides lifted such that its first sample is zero.

Exactly one of the risefall_sigma_ratio and width parameters has to be specified.

If risefall_sigma_ratio is not None and width is None:

$\begin{split}\text{risefall} &= \text{risefall_sigma_ratio} \times \text{sigma}\\ \text{width} &= \text{duration} - 2 \times \text{risefall}\end{split}$

If width is not None and risefall_sigma_ratio is None:

$\text{risefall} = \frac{\text{duration} - \text{width}}{2}$

In both cases, the lifted gaussian square pulse $$f'(x)$$ is defined as:

$\begin{split}f'(x) &= \begin{cases} \exp\biggl(-\frac12 \frac{(x - \text{risefall})^2}{\text{sigma}^2}\biggr) & x < \text{risefall}\\ 1 & \text{risefall} \le x < \text{risefall} + \text{width}\\ \exp\biggl(-\frac12 \frac{{\bigl(x - (\text{risefall} + \text{width})\bigr)}^2} {\text{sigma}^2} \biggr) & \text{risefall} + \text{width} \le x \end{cases}\\ f(x) &= \text{A} \times \frac{f'(x) - f'(-1)}{1-f'(-1)}, \quad 0 \le x < \text{duration}\end{split}$

where $$f'(x)$$ is the gaussian square 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 and square pulse. Complex amp support will be deprecated.

• sigma – A measure of how wide or narrow the Gaussian risefall is; see the class docstring for more details.

• width – The duration of the embedded square pulse.

• angle – The angle of the complex amplitude of the pulse. Default value 0.

• risefall_sigma_ratio – The ratio of each risefall duration to sigma.

• 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.

Raises

PulseError – When width and risefall_sigma_ratio are both empty or both non-empty.

Attributes

alias = 'GaussianSquare'