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# qiskit.pulse.library.Sech

qiskit.pulse.library.Sech(duration, amp, sigma, angle=0.0, name=None, zero_ends=True, limit_amplitude=None)

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An unnormalized sech pulse.

The sech function is centered around the halfway point of the pulse, and the envelope of the pulse is given by:

$f(x) = \text{A}\text{sech}\left( \frac{x-\mu}{\text{sigma}}\right) , 0 <= x < duration$

where $\text{A} = \text{amp} \times\exp\left(i\times\text{angle}\right)$, and $\mu=\text{duration}/2$.

If zero_ends is set to True, the output y is modified: .. math:

y\left(x\right) \mapsto \text{A}\frac{y-y^{*}}{\text{A}-y^{*}},

where $y^{*}$ is the value of $y$ at the endpoints (at $x=-1 and :math:x=\text{duration}+1$). This shifts the endpoints value to zero, while also rescaling to preserve the amplitude at :math:text{duration}/2.

Parameters

• duration (int |ParameterExpression) – Pulse length in terms of the sampling period dt.
• amp (float |ParameterExpression) – The magnitude of the amplitude of the pulse (the value at the midpoint duration/2).
• sigma (float |ParameterExpression) – A measure of how wide or narrow the sech peak is in terms of dt; described mathematically in the class docstring.
• angle (ParameterExpression |float | None) – The angle in radians of the complex phase factor uniformly scaling the pulse. Default value 0.
• name (str | None) – Display name for this pulse envelope.
• zero_ends (bool | None) – If True, zeros the ends at x = -1, x = duration + 1, but rescales to preserve amp. Default value True.
• 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.

Return type

ScalableSymbolicPulse