Decoding Algorithms for Hypergraph Subsystem Codes and Generalized Subsystem Surface Codes

TL;DR

This paper introduces efficient decoding algorithms for hypergraph-based and surface subsystem codes, including a new construction of subsystem surface codes, achieving a noise threshold comparable to existing methods.

Contribution

It presents novel decoding algorithms for a broad class of subsystem codes and a new construction of subsystem surface codes that includes prior proposals.

Findings

Achieved a noise threshold of 1.75% for the square octagon lattice code.

Decoding algorithms are efficient for large hypergraph and surface subsystem codes.

Performance is comparable to previous methods with different algorithms.

Abstract

Topological subsystem codes can combine the advantages of both topological codes and subsystem codes. Suchara et al. proposed a framework based on hypergraphs for construction of such codes. They also studied the performance of some subsystem codes. Later Bravyi et al. proposed a subsystem surface code. Building upon these works, we propose efficient decoding algorithms for large classes of subsystem codes on hypergraphs and surfaces. We also propose a construction of the subsystem surface codes that includes the code proposed by Bravyi et al. Our simulations for the subsystem code on the square octagon lattice resulted in a noise threshold of 1.75%. This is comparable to previous result of 2% by Bombin et al. who used a different algorithm.