Sharp Error-Rate Transitions in Quantum QC-LDPC Codes under Joint BP Decoding

TL;DR

This paper reveals that quantum QC-LDPC codes decoded with joint BP show sharp error-rate transitions and error floors caused by trapping sets, highlighting potential paths to improve quantum error correction.

Contribution

First observation of threshold-like behavior in quantum LDPC codes with non-vanishing rate under joint BP decoding, linking error floors to trapping sets.

Findings

Quantum QC-LDPC codes exhibit steep error-rate curves.

Error floors are linked to small trapping sets.

Identifying trapping sets may reduce error floors.

Abstract

In this study, we report that quantum quasi-cyclic low-density parity-check codes decoded via joint belief propagation (BP) exhibit steep error-rate curves, despite the presence of error floors. To the best of our knowledge, this is the first observation of such threshold-like behavior for quantum LDPC codes with non-vanishing coding rate, excluding those decoded with non-binary BP decoders. Moreover, we find that dominant error events contributing to the error floor typically involve only a small number of bits. These findings suggest that the error floor is caused by trapping sets--specific subgraph structures in the Tanner graph--and indicate that identifying and avoiding such structures may lead to further reduction of the error floor.