Closed form logical error rate approximations for surface codes

Abstract:We propose a novel method to calculate logical error rates in surface codes, assuming independent and identically distributed physical errors. These results fit well known scaling laws for studied physical error rates and code distances, but break down in some other regimes. We show how to use our method to analyze hypothetical quantum computers with various configurations and select designs with lower error rates. Currently, this requires expensive classical simulations of quantum decoders for various distances and physical error rates or inaccurate extrapolation from minimal experimental data. Instead, we use the symmetry of the problem to count the configurations that result in a logical error with our novel software. Given a physical error rate, we can deduce the probability of a logical error, to provably good accuracy. We include an analysis of measurement errors to allow a more complete comparison of different surface code implementations. We extend this counting method to a particular locally-correlated error model.

Quantum Physics (quant-ph); Discrete Mathematics (cs.DM); Combinatorics (math.CO)

arXiv:2605.03054 [quant-ph]

(or arXiv:2605.03054v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2605.03054 Focus to learn more arXiv-issued DOI via DataCite

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