---
title: GaussianSquare (v1.0)
description: API reference for qiskit.pulse.library.GaussianSquare in qiskit v1.0
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/1.0/qiskit.pulse.library.GaussianSquare
---

# GaussianSquare

*class* `qiskit.pulse.library.GaussianSquare(duration, amp, sigma, width=None, angle=0.0, risefall_sigma_ratio=None, name=None, limit_amplitude=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/1.0/qiskit/pulse/library/symbolic_pulses.py)

Bases: [`object`](https://docs.python.org/3/library/functions.html#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:

$$
\begin{aligned}
\text{risefall} &= \text{risefall\_sigma\_ratio} \times \text{sigma}\\
\text{width} &= \text{duration} - 2 \times \text{risefall}
\end{aligned}
$$

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:

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

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.
- **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**](/docs/api/qiskit/1.0/pulse#qiskit.pulse.PulseError "qiskit.pulse.PulseError") – When width and risefall\_sigma\_ratio are both empty or both non-empty.

## Attributes

### alias

Default value: `'GaussianSquare'`