---
title: gaussian_square_echo (v1.1)
description: API reference for qiskit.pulse.library.gaussian_square_echo in qiskit v1.1
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/1.1/qiskit.pulse.library.gaussian_square_echo
---

# qiskit.pulse.library.gaussian\_square\_echo

`qiskit.pulse.library.gaussian_square_echo(duration, amp, sigma, width=None, angle=0.0, active_amp=0.0, active_angle=0.0, risefall_sigma_ratio=None, name=None, limit_amplitude=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/1.1/qiskit/pulse/library/symbolic_pulses.py#L1067-L1267)

An echoed Gaussian square pulse with an active tone overlaid on it.

The Gaussian Square Echo pulse is composed of three pulses. First, a Gaussian Square pulse $f_{echo}(x)$ with amplitude `amp` and phase `angle` playing for half duration, followed by a second Gaussian Square pulse $-f_{echo}(x)$ with opposite amplitude and same phase playing for the rest of the duration. Third a Gaussian Square pulse $f_{active}(x)$ with amplitude `active_amp` and phase `active_angle` playing for the entire duration. The Gaussian Square Echo pulse $g_e()$ can be written as:

$$
\begin{aligned}
g_e(x) &= \begin{cases}            f_{\text{active}} + f_{\text{echo}}(x)                & x < \frac{\text{duration}}{2}\\
f_{\text{active}} - f_{\text{echo}}(x)                & \frac{\text{duration}}{2} < x        \end{cases}\\
\end{aligned}
$$

One case where this pulse can be used is when implementing a direct CNOT gate with a cross-resonance superconducting qubit architecture. When applying this pulse to the target qubit, the active portion can be used to cancel IX terms from the cross-resonance drive while the echo portion can reduce the impact of a static ZZ coupling.

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}


$$

**References**

1. [*Jurcevic, P., Javadi-Abhari, A., Bishop, L. S., Lauer, I., Bogorin, D. F., Brink, M., Capelluto, L., G\{“u}nl\{“u}k, O., Itoko, T., Kanazawa, N. & others Demonstration of quantum volume 64 on a superconducting quantum computing system. (Section V)*](https://iopscience.iop.org/article/10.1088/2058-9565/abe519)

**Parameters**

- **duration** ([*int*](https://docs.python.org/3/library/functions.html#int) *| ParameterValueType*) – Pulse length in terms of the sampling period dt.
- **amp** ([*float*](https://docs.python.org/3/library/functions.html#float)  *|*[*ParameterExpression*](/docs/api/qiskit/1.1/qiskit.circuit.ParameterExpression "qiskit.circuit.ParameterExpression")) – The amplitude of the rise and fall and of the echoed pulse.
- **sigma** ([*float*](https://docs.python.org/3/library/functions.html#float)  *|*[*ParameterExpression*](/docs/api/qiskit/1.1/qiskit.circuit.ParameterExpression "qiskit.circuit.ParameterExpression")) – A measure of how wide or narrow the risefall is; see the class docstring for more details.
- **width** ([*float*](https://docs.python.org/3/library/functions.html#float)  *|*[*ParameterExpression*](/docs/api/qiskit/1.1/qiskit.circuit.ParameterExpression "qiskit.circuit.ParameterExpression") *| None*) – The duration of the embedded square pulse.
- **angle** ([*float*](https://docs.python.org/3/library/functions.html#float)  *|*[*ParameterExpression*](/docs/api/qiskit/1.1/qiskit.circuit.ParameterExpression "qiskit.circuit.ParameterExpression") *| None*) – The angle in radians of the complex phase factor uniformly scaling the echoed pulse. Default value 0.
- **active\_amp** ([*float*](https://docs.python.org/3/library/functions.html#float)  *|*[*ParameterExpression*](/docs/api/qiskit/1.1/qiskit.circuit.ParameterExpression "qiskit.circuit.ParameterExpression") *| None*) – The amplitude of the active pulse.
- **active\_angle** ([*float*](https://docs.python.org/3/library/functions.html#float)  *|*[*ParameterExpression*](/docs/api/qiskit/1.1/qiskit.circuit.ParameterExpression "qiskit.circuit.ParameterExpression") *| None*) – The angle in radian of the complex phase factor uniformly scaling the active pulse. Default value 0.
- **risefall\_sigma\_ratio** ([*float*](https://docs.python.org/3/library/functions.html#float)  *|*[*ParameterExpression*](/docs/api/qiskit/1.1/qiskit.circuit.ParameterExpression "qiskit.circuit.ParameterExpression") *| None*) – The ratio of each risefall duration to sigma.
- **name** ([*str*](https://docs.python.org/3/library/stdtypes.html#str) *| None*) – Display name for this pulse envelope.
- **limit\_amplitude** ([*bool*](https://docs.python.org/3/library/functions.html#bool) *| None*) – 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/1.1/pulse#qiskit.pulse.PulseError "qiskit.pulse.PulseError") – When width and risefall\_sigma\_ratio are both empty or both non-empty.

**Return type**

[SymbolicPulse](/docs/api/qiskit/1.1/qiskit.pulse.library.SymbolicPulse "qiskit.pulse.library.SymbolicPulse")