RFC: score function for a rough estimation of the circuit quality/complexity

[Roger-luo]

this is a feature request. It worth discussing what exactly the score function is about:

• noise modeling
• gate count

cc: @weinbe58 @jon-wurtz @kaihsin I'm wondering what did you guys use for the hackthon back in Jan?

[david-pl]

@Roger-luo I think #592 would basically implement this feature: the fidelity would naturally reduce whenever there is a noise channel, which should also lead to deeper circuits having a lower fidelity.

The only open question here is whether we want to have some heuristic scoring function for noise-less circuits? For example, add a penalty for each gate and a larger one for two-qubit gates. Not sure though.