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

• URL: http://arxiv.org/abs/2507.11534v2
• Date: Wed, 16 Jul 2025 14:59:31 GMT
• Title: Sharp Error-Rate Transitions in Quantum QC-LDPC Codes under Joint BP Decoding
• Authors: Daiki Komoto, Kenta Kasai,
• Abstract summary: We show that quantum quasi-cyclic low-density parity-check codes exhibit steep error-rate curves, despite the presence of error floors.<n>We find that dominant error events contributing to the error floor typically involve only a small number of bits.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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