Sharp Error-Rate Transitions in Quantum QC-LDPC Codes under Joint BP Decoding
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912485819285504 |
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| author | Komoto, Daiki Kasai, Kenta |
| author_facet | Komoto, Daiki Kasai, Kenta |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11534 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp Error-Rate Transitions in Quantum QC-LDPC Codes under Joint BP Decoding Komoto, Daiki Kasai, Kenta Quantum Physics Information Theory 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. |
| title | Sharp Error-Rate Transitions in Quantum QC-LDPC Codes under Joint BP Decoding |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2507.11534 |