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# 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)

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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

Parameters

• 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.

Returns

ScalableSymbolicPulse instance.

Raises

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

Return type

SymbolicPulse