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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.26785

Authors: de la Fuente, César Hernando, Majaniemi, Joonas, van Nieuwenburg, Evert, Frohnert, Felix

Institutions: Riverlane (United Kingdom), Leiden University

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Universiteit Leiden

OpenAlex ID: W7223040972

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