single qubit RB does not work on OPX for sequences longer than about 1000 Cliffords

[liorella-qm]

(opened on behalf of @sarafs1926 and Charlie Guinn from Andrew Houck's lab)

the OPX variables memory depth is about 2000 variables. This means that in the current implementation of the RB code where we need to store both the sequence and inverse, we can only do up about 1000 cliffords.

However, since the number of Cliffords required to reach 1/e with fidelity alpha is ~1/(1-alpha), for fidelities approaching 99.9% we cannot execute the sequence up to the saturation point. For fidelities of 4 9's that we are targeting in our spec, we'll need to execute sequences that are about 10e4 Cliffords long.

Thus we need to find a solution for this length of sequences. One possible solution is to only save the seed and inverse in this use case. This greatly reduces the memory depth. @yomach @nirhal let's discuss how we want to do this.

[yomach]

Not sure what is currently being done, but if we change the depths in jumps >1 then we can save only some of the inverse gates.
So when delta_depth = 2, we could reach ~1300 gates.
If delta_depth = 5, we can reach ~1700 gates.
Is this good enough?

Note that in the OPX+ this limitation is gone as it has more memory.

[liorella-qm]

@sarafs1926 will @yomach 's solution work for you for now?