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

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.

Quantum Physics (quant-ph); Information Theory (cs.IT)

arXiv:2507.11534 [quant-ph]

(or arXiv:2507.11534v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2507.11534 Focus to learn more arXiv-issued DOI via DataCite

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