# GaussianSquare

qiskit.pulse.library.GaussianSquare(duration, amp, sigma, width=None, angle=None, risefall_sigma_ratio=None, name=None, limit_amplitude=None)

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 is 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'