Multi-path Summation for Decoding 2D Topological Codes

TL;DR

This paper introduces a new decoding method for 2D topological codes that improves error correction thresholds by combining belief propagation with a novel edge weighting algorithm, surpassing previous matching-based decoders.

Contribution

It develops a belief propagation-based decoding approach with a novel edge weight algorithm, enhancing minimum-weight perfect matching for surface code error correction.

Findings

Achieves a 17.76% error threshold for depolarizing errors.

Surpasses previous matching-based decoders' thresholds.

Approaches the theoretical upper bound of 18.9%.

Abstract

Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a decoder which can adapt to the wide variety of error models present in experiments. The typical approach to the problem of decoding the surface code is to reduce it to minimum-weight perfect matching in a way that provides a suboptimal threshold error rate, and is specialized to correct a specific error model. Recently, optimal threshold error rates for a variety of error models have been obtained by methods which do not use minimum-weight perfect matching, showing that such thresholds can be achieved in polynomial time. It is an open question whether these results can also be achieved by minimum-weight perfect matching. In this work, we use belief propagation and a novel algorithm for producing edge weights to increase the utility of minimum-weight perfect matching for decoding surface codes. This allows us to correct depolarizing errors using the rotated surface code, obtaining a threshold of $17.76 \pm 0.02 \%$. This is larger than the threshold achieved by previous matching-based decoders ($14.88 \pm 0.02 \%$), though still below the known upper bound of $\sim 18.9 \%$.