Fast offline decoding with local message-passing automata

TL;DR

This paper introduces a fast, local, message-passing decoder for topological codes that efficiently corrects errors with a proven threshold and logarithmic average runtime, improving decoding speed and reliability.

Contribution

It presents a novel parallelized message-passing decoder for topological codes with proven thresholds and logarithmic average decoding time, enhancing decoding efficiency.

Findings

Decoder operates with $O((\log L)^\eta)$ runtime

Threshold for the toric code at approximately 7.3% noise

Decoding terminates efficiently in linear systems

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 $p_c\approx 7.3\%$.