I've been experimenting with subsystem codes decoded with BP-OSD decoders. The performance seems pretty bad compared to subspace code. I believe this is expected since the information used is the syndrome of the stabilizers only.
This paper claims major improvements using syndromes of the gauge operators as well. The method seems to be closely linked to MWPM decoding. Can the process be generalized to other decoders, for example BP-OSD?
Any references or feedback would be appreciated.
Gauge-fixing does not require the use of MWPM Decoding. You should think about measuring gauge operators as adding those operators to the generating set of the stabilizer group. This makes your syndrome larger, giving you more information. If you decode properly, this will always improve your logical error rate.
That being said, decoding a generic code is hard. All efficient decoders make some approximations, and the validity of those approximations is code-dependent. Strictly speaking, it is possible that adding gauges could hurt you while using an approximate decoder. However, that seems unlikely to me.
