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)[source]#

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:

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

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:

\[\text{risefall} = \frac{\text{duration} - \text{width}}{2}\]


  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)

  • duration (int | ParameterExpression) – Pulse length in terms of the sampling period dt.

  • amp (float | ParameterExpression) – The amplitude of the rise and fall and of the echoed pulse.

  • sigma (float | ParameterExpression) – A measure of how wide or narrow the risefall is; see the class docstring for more details.

  • width (ParameterExpression | float | None) – The duration of the embedded square pulse.

  • angle (ParameterExpression | float | None) – The angle in radians of the complex phase factor uniformly scaling the echoed pulse. Default value 0.

  • active_amp (ParameterExpression | float | None) – The amplitude of the active pulse.

  • active_angle (ParameterExpression | float | None) – The angle in radian of the complex phase factor uniformly scaling the active pulse. Default value 0.

  • risefall_sigma_ratio (ParameterExpression | float | None) – The ratio of each risefall duration to sigma.

  • name (str | None) – Display name for this pulse envelope.

  • limit_amplitude (bool | None) – If True, then limit the amplitude of the waveform to 1. The default is True and the amplitude is constrained to 1.


ScalableSymbolicPulse instance.


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

Return type: