Automorphism Ensemble Decoding of Quantum LDPC Codes

TL;DR

AutDEC is a novel quantum decoder leveraging automorphism groups and ensemble belief propagation to improve decoding accuracy and speed for quantum LDPC codes, especially under realistic noise conditions.

Contribution

We propose AutDEC, a fast, automorphism-based ensemble decoding method that enhances quantum LDPC code decoding accuracy and efficiency, addressing limitations of traditional BP decoders.

Findings

Achieves decoding accuracy comparable to BP-OSD-0

Reduces decoding time overhead

Effective for Quantum Reed-Muller and Bivariate Bicycle codes

Abstract

We introduce AutDEC, a fast and accurate decoder for quantum error-correcting codes with large automorphism groups. Our decoder employs a set of automorphisms of the quantum code and an ensemble of belief propagation (BP) decoders. Each BP decoder is given a syndrome which is transformed by one of the automorphisms, and is run in parallel. For quantum codes, the accuracy of BP decoders is limited because short cycles occur in the Tanner graph and our approach mitigates this effect. We demonstrate decoding accuracy comparable to BP-OSD-0 with a lower time overhead for Quantum Reed-Muller (QRM) codes in the code capacity setting, and Bivariate Bicycle (BB) codes under circuit level noise. We provide a Python repository for use by the community and the results of our simulations.