Enhancements to DRAG protocol

[andrea-pasquale]

Currently our DRAG calibration is checking for phase errors using a sequence with $X_\pi - X_{-\pi}$.
Similar to the flipping protocol it is possible to apply a sequence which is $(X_\pi - X_{-\pi})^N$ which should generate more clearly oscillations. Both qua-libs and qiskit-experiments allow to do this.

Moreover, if we want something which doesn't involve oscillation there is another way of selecting the value of $\beta$ which involves testing just two sequences which should highlight phase errors. There is an example of this procedure in qua-libs again. This second fitting procedure was first tested at Yale, see for example https://rsl.yale.edu/sites/default/files/2024-08/2013-RSL-Thesis-Matthew-Reed.pdf.

Finally, we have already mentioned a few times that after finding the correct value for $\beta$ in order to address both leakage and phase errors it is possible to use a waveform where we introduce a detuning

$$ s(t) \rightarrow e^{i \delta \omega t} s(t) $$

which is explained here and also here.
In this case we should add this waveform to qibolab.

[alecandido]

In this case we should add this waveform to qibolab.

Not sure what you mean exactly, but we can definitely modify waveforms, if needed.

I would say that in this case, adding a detuning just means changing the modulation frequency, so it has no effect on the envelope (you can certainly pre-modulate the envelope with a small detuning, but it seems a bit impractical...).

[andrea-pasquale]

Perhaps it is better to discuss offline, according to the references which I've provided above I think that they are using a different waveform since they say "By introducing a frequency detuning parameter $\delta f$ to the waveform". Moreover, according to the data provided by them the detuning could be up to a few tens of MHz which it will probably not work if we use it as demodulation frequency.