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

arXiv (Cornell University)

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.

Authors 4

1. César Hernando de la Fuente
2. Joonas Majaniemi

   Riverlane (United Kingdom)

   Affiliation as printed

   Riverlane , 59 St Andrews Street , CB2 3BZ Cambridge , United Kingdom

3. Evert van Nieuwenburg Aachen Applied Quantum Algorithms and Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Applied Quantum Algorithms and Instituut-Lorentz , Leiden University , Niels Bohrweg 1 , 2333 CA Leiden , The Netherlands

4. Felix Frohnert Aachen Applied Quantum Algorithms and Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Applied Quantum Algorithms and Instituut-Lorentz , Leiden University , Niels Bohrweg 1 , 2333 CA Leiden , The Netherlands