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PreprintCC BY 4.0arXiv

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

  • César Hernando de la Fuente
  • Joonas Majaniemi
  • Evert van Nieuwenburg
  • Felix Frohnert
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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.

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Cite

BibTeXRIS
BibTeX
@misc{fuente2026correlated,
  title = {{Correlated decoding loses the surface code's effective distance below threshold}},
  author = {César Hernando de la Fuente and Joonas Majaniemi and Evert van Nieuwenburg and Felix Frohnert},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26785},
  eprint = {2610.26785},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26785},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Correlated decoding loses the surface code's effective distance below threshold
AU  - César Hernando de la Fuente
AU  - Joonas Majaniemi
AU  - Evert van Nieuwenburg
AU  - Felix Frohnert
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.26785
UR  - https://arxiv.org/abs/2610.26785
AB  - 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.
ER  -