Problem In CheckMatrix

[DiegoRuiz-Git]

Hi @oscarhiggott,

First thank you for putting this useful library on github! I think I found a bug, here is a minimal working example:

I have a dem that looks like this

stim.DetectorErrorModel('''
    error(0.01) D0
    error(0.001) D0 L0
''')

If D0 is triggered, we would expect the decoder to always choose error(0.01) D0 and to not predict that L0 was triggered. However, when running the code, the observable is always predicted as True.
I dug a bit into the source code, and I think the reason for this is that in decoder._matrices.check_matrix, the two error mechanism are merged, with a prior probability which is the sum of the two. And in it the same in decoder._matrices.observables_matrix.

Thank you

[oscarhiggott]

Thanks for flagging this. Of course this issue will only arise for a code/circuit with distance at most 2 by definition, but it would still be good to handle it correctly.

I could imagine two similarly valid approaches:

1. Both (or in general all) indistinguishable errors could still be merged, but the most probable logical observable assignment is chosen (instead of the arbitrary choice made currently).

2. Errors are only merged if they flip the same set of detectors and observables (instead of only merging errors with the same detectors, ignoring the observables, as currently done).

I would like to have both as options, and am leaning towards having (2) as the default (with an option like merge_all_indistinguishable_errors to choose (1)).

[DiegoRuiz-Git]

Thanks for the reply! As stim already merges errors if they flip the same detectors and observables in the dem, why is there a need to remerge the errors? (at least to implement solution 2.)
But maybe I'm missing some cases I don't work with usually