Fast offline decoding with local message-passing automata

Ethan Lake

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arXiv · 2506.03266

Fast offline decoding with local message-passing automata

Ethan Lake

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Abstract

We present a local offline decoder for topological codes that operates according to a parallelized message-passing framework. The decoder works by passing messages between anyons, with the contents of received messages used to move nearby anyons towards one another. We prove the existence of a threshold, and show that in a system of linear size $L$, decoding terminates with an $O((\log L)^\eta)$ average-case runtime, where $\eta$ is a small constant. For the toric code subject to i.i.d Pauli noise, our decoder has $\eta=1$ and a threshold at a noise strength of $p_c\approx 7.3\%$.

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Ethan Lake. 2025-06-03. Fast offline decoding with local message-passing automata. https://arxiv.org/abs/2506.03266

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