Achieving Thresholds via Standalone Belief Propagation on Surface Codes

TL;DR

This paper introduces novel belief propagation decoders that operate on the decoding graph, achieving near-threshold performance for surface codes under depolarizing noise, similar to MWPM, and enabling scalable hardware implementations.

Contribution

The paper presents a new BP decoding method that exchanges messages on the decoding graph, achieving thresholds close to MWPM for surface codes.

Findings

Thresholds close to MWPM for surface codes

Decoders applicable to any graphlike QEC code

Potential for hardware-accelerated implementations

Abstract

The usual belief propagation (BP) decoders are, in general, exchanging local information on the Tanner graph of the quantum error-correcting (QEC) code and, in particular, are known to not have a threshold for the surface code. We propose novel BP decoders that exchange messages on the decoding graph and obtain code capacity thresholds via standalone BP for the surface code under depolarizing noise. Our approach, similarly to the minimum weight perfect matching (MWPM) decoder, is applicable to any graphlike QEC code. The thresholds observed with our decoders are close to those obtained by MWPM. This result opens the path towards scalable hardware-accelerated implementations of MWPM-compatible decoders.