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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)

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

ge(x)={factive+fecho(x)x<duration2factivefecho(x)duration2<x\begin{split}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{split}

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{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:

risefall=durationwidth2\text{risefall} = \frac{\text{duration} - \text{width}}{2}


  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) (opens in a new tab)



ScalableSymbolicPulse instance.


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

Return type


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