Correlated decoding loses the surface code's effective distance below threshold

Abstract:Correlated decoding improves matching and clustering surface-code decoders by reweighting one decoding subgraph conditioned on the other's correction. We show that standard reweighting can cause correlated decoders to fail on size-$(d-1)/2$ fault configurations that a distance-$d$ code should correct, reducing error suppression deep below threshold. Under circuit-level noise, a single first-pass edge can discount several correlated edges, even though their joint occurrence requires additional independent faults, so the decoder favors an over-discounted correction. Regularizing the reweighting rule restores the nominal distance scaling and a clear correlated-decoding advantage.

arXiv:2610.26785 [quant-ph]

(or arXiv:2610.26785v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.26785 Focus to learn more arXiv-issued DOI via DataCite

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