qiskit.pulse.library.drag

drag(duration, amp, sigma, beta, name=None, zero_ends=True)

Generates Y-only correction DRAG Waveform for standard nonlinear oscillator (SNO) [1].

For \(A=\) amp, \(\sigma=\) sigma, and \(\beta=\) beta, applies the midpoint sampling strategy to generate a discrete pulse sampled from the continuous function:

\[f(x) = g(x) + i \beta h(x),\]

where \(g(x)\) is the function sampled in gaussian(), and \(h(x)\) is the function sampled in gaussian_deriv().

If zero_ends == True, the samples from \(g(x)\) are remapped as in gaussian().

References

1. Gambetta, J. M., Motzoi, F., Merkel, S. T. & Wilhelm, F. K. “Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator.” Phys. Rev. A 83, 012308 (2011).

Parameters

• duration (int) – Duration of pulse. Must be greater than zero.

• amp (complex) – Pulse amplitude at center duration/2.

• sigma (float) – Width (standard deviation) of pulse.

• beta (float) – Y correction amplitude. For the SNO this is \(\beta=-\frac{\lambda_1^2}{4\Delta_2}\). Where \(\lambda_1\) is the relative coupling strength between the first excited and second excited states and \(\Delta_2\) is the detuning between the respective excited states.

• name (Optional[str]) – Name of pulse.

• zero_ends (bool) – If True, zero ends at x = -1, x = duration + 1, but rescale to preserve amp.

Return type

Waveform