A matching decoder for bivariate bicycle codes

TL;DR

This paper introduces a decoding method for bivariate bicycle quantum codes using a matching algorithm, demonstrating its effectiveness across various code families and enhancing performance with additional strategies.

Contribution

It adapts the minimum-weight perfect matching algorithm for decoding bivariate bicycle codes and introduces the 'cylinder trick' for rapid correction, broadening decoding techniques for quantum codes.

Findings

Effective decoding across multiple code families

Performance comparable to state-of-the-art methods

Enhanced decoding with belief propagation and over-matching

Abstract

The discovery of new quantum error-correcting codes that encode several logical qubits into relatively few physical qubits motivates the development of efficient and accurate methods of decoding these systems. Here, we adopt the minimum-weight perfect matching algorithm, a subroutine invaluable to decoding topological codes, to decode bivariate bicycle codes. Using the equivalence of bivariate bicycle codes to copies of the toric code, we propose a method we call the 'cylinder trick' to rapidly find a correction using matching on code symmetries. We benchmark our decoder on the gross code family, cyclic hypergraph-product codes, generalized toric codes, and recently proposed directional codes, demonstrating the general applicability of our protocol. For a subset of these codes, we find that our decoder can be significantly improved by augmenting matching with strategies including belief propagation and 'over-matching', thus achieving performance competitive with state-of-the-art approaches.