Efficient decoding up to a constant fraction of the code length for asymptotically good quantum codes

TL;DR

This paper presents an efficient decoding algorithm for quantum Tanner codes that can correct linear-weight adversarial errors, significantly improving over previous methods limited to sublinear error weights, and extends to Lifted Product codes.

Contribution

The authors develop a decoding algorithm capable of correcting linear-weight errors in quantum Tanner codes and adapt it to Lifted Product codes, with linear-time convergence.

Findings

Decoding algorithm corrects adversarial errors of linear weight.

Algorithm converges in linear time.

Extension to Lifted Product codes demonstrated.

Abstract

We introduce and analyse an efficient decoder for the quantum Tanner codes of that can correct adversarial errors of linear weight. Previous decoders for quantum low-density parity-check codes could only handle adversarial errors of weight $O(\sqrt{n \log n})$. We also work on the link between quantum Tanner codes and the Lifted Product codes of Panteleev and Kalachev, and show that our decoder can be adapted to the latter. The decoding algorithm alternates between sequential and parallel procedures and converges in linear time.