Transmission coefficient calibration

[alecandido]

The present goal of the spectroscopies is mainly to locate the peak frequency, lying on the horizontal axis. This makes pretty much irrelevant the normalization on the vertical one, and it allows Qibocal to just represent this information as arbitrary units.

However, it becomes relevant when the function fitted is going to involve parameters with a direct physical interpretation, beyond those just related to the horizontal features (as the position and width of the Lorentzian), as it will happen in #883.

In this case, the arbitrary units are going to swallow part of the physical information, requiring every fit to account for an unknown offset and scaling (assuming linearity of the units).

It is not particularly relevant which are the units overall (being Volts or the unit step in the ADC), but it is relevant to express them in terms of the input provided by the DAC, i.e. measuring the transmission coefficient. A possible way of doing this could be to first run a spectroscopy, and then check the pulses' response on a frequency that is far from the peak, passed as a parameter of a dedicated routine. This could happen for a few amplitudes with very long pulses:

• 0 amplitude (i.e. just a long delay), will set the offset (the ADC baseline when nothing is being played)
• 1 a.u. amplitude, to measure 1 a.u. in the DAC to which response it corresponds in the ADC, setting the scaling (i.e. to which reading a transmission coefficient 1 corresponds)
• 10 a.u. amplitude, to confirm the linearity of the units in the amplitude, or establish its limits (this is just a validation step, and we could check for even more than a single value)

This routine should be thought as the equivalent of the single-shot classification for probabilities, as you need it to define the meaning of the probabilities, as some classification parameters, and you can then consume them to provide the probabilities to be used by the other routines. Analogously, this routine will just define the meaning of the transmission coefficient, and store it in the Qibocal portion of the platform (where T1, T2, and the others are stored - i.e. parameters.json for Qibolab 0.1, hopefully not for 0.2[*]) that will be then used by other routines like #883.

[alecandido]

On second thought, it seems that all the routines displaying signals could gain more physical meaning by reporting about a transmission coefficient.

However, a more challenge task, but that we should face in the process of implementing this (possibly as a second iteration) is how to define the transmission coefficients for non-rectangular pulses (most likely we should rely on the integral, and thus possibly providing the integrals of the envelopes already in Qibolab - in the worst case just summing the samples).