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

Abstract

We introduce and analyse an efficient decoder for quantum Tanner codes 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.