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

2025/07/15 by Daiki Komoto, Komoto, Daiki, Kenta Kasai +1 · 1 citation
Engineering · #Advanced Wireless Communication Techniques #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Optical Network Technologies #Power Line Communications and Noise #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2507.11534

openalex publication_date 2025/07/15 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

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.

Citations

• Quantum Error Correction Exploiting Degeneracy to Approach the Hashing Bound
• Quantum Error Correction near the Coding Theoretical Bound

Cited by

• Systematic Non-Binary Extension of LDPC-CSS Codes Preserving Orthogonality

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