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About this paper
Shaked Regev, Daniel Dilley, Ryan Bennink
A combinatorial framework estimates surface-code logical error rates by counting physical error patterns associated with minimum-length logical paths, reducing reliance on repeated decoder simulations. The analysis provides closed-form approximations and bounds for unrotated and rotated codes, and extends to local correlations, global noise fluctuations, and repeated measurement errors.
Key insights
- Minimum-weight failures dominate when the combined parameter p d² is much smaller than one; once p d² is not small, higher-weight configurations can materially increase the logical error rate.
- Rotated codes have more minimum-length logical paths and therefore higher logical failure rates at equal distance, while their lower qubit overhead can make them preferable at a fixed hardware budget.
- Correlations change which errors dominate: local correlations favor long clusters, whereas rare high-error global environments can control asymptotic logical performance.
Summary by alphaXiv.
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