Heuristic Search for Minimum-Distance Upper-Bound Witnesses in Quantum APM-LDPC Codes
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915940731453440 |
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| author | Kasai, Kenta |
| author_facet | Kasai, Kenta |
| contents | This paper investigates certified upper bounds on the minimum distance of an explicit family of Calderbank-Shor-Steane quantum LDPC codes constructed from affine permutation matrices. All codes considered here have active Tanner graphs of girth eight. Rather than attempting to prove a general lower bound for the full code distance, we focus on constructing low-weight non-stabilizer logical representatives, which yield valid upper bounds once they are verified to lie in the opposite parity-check kernel and outside the stabilizer row space. We develop a unified framework for such witnesses arising from latent row relations, restricted-lift subspaces including block-compressed, selected-fiber, and CRT-stripe constructions, cycle- 8 elementary trapping-set structures, and decoder-failure residuals. In every case, search is used only to generate candidates; the reported bounds begin only after explicit kernel and row-space exclusion tests have been passed. For the latent part, we also identify a block-compression criterion under which the certification becomes exact. Applying these methods to representative APM-LDPC codes sharpens previously reported upper bounds and provides concrete certified values across the explored parameter range. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15307 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Heuristic Search for Minimum-Distance Upper-Bound Witnesses in Quantum APM-LDPC Codes Kasai, Kenta Quantum Physics Information Theory This paper investigates certified upper bounds on the minimum distance of an explicit family of Calderbank-Shor-Steane quantum LDPC codes constructed from affine permutation matrices. All codes considered here have active Tanner graphs of girth eight. Rather than attempting to prove a general lower bound for the full code distance, we focus on constructing low-weight non-stabilizer logical representatives, which yield valid upper bounds once they are verified to lie in the opposite parity-check kernel and outside the stabilizer row space. We develop a unified framework for such witnesses arising from latent row relations, restricted-lift subspaces including block-compressed, selected-fiber, and CRT-stripe constructions, cycle- 8 elementary trapping-set structures, and decoder-failure residuals. In every case, search is used only to generate candidates; the reported bounds begin only after explicit kernel and row-space exclusion tests have been passed. For the latent part, we also identify a block-compression criterion under which the certification becomes exact. Applying these methods to representative APM-LDPC codes sharpens previously reported upper bounds and provides concrete certified values across the explored parameter range. |
| title | Heuristic Search for Minimum-Distance Upper-Bound Witnesses in Quantum APM-LDPC Codes |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2604.15307 |