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Achievability of CSS codes performance limits over Pauli channels under separate ML decoding with bounded graphical complexity — arXiv:2611.02339

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.02339
License (as archived): CC0-1.0
Archived: 2026-11-03T18:51:46.381Z
SHA-256 of the archived text: ae8ea2e5c4253dba0d97efe6027e06c7b0f3e7b773341ad6228c0a3b63276845
Stable URL of this page: https://metraipolis.com/documento/dc_f05ea89e528e

How to cite

Achievability of CSS codes performance limits over Pauli channels under separate ML decoding with bounded graphical complexity — arXiv:2611.02339 — arXiv (en), https://arxiv.org/abs/2611.02339 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_f05ea89e528e (Metraipolis archive dc_f05ea89e528e, sha256 ae8ea2e5c4253dba0d97efe6027e06c7b0f3e7b773341ad6228c0a3b63276845)

BibTeX

@misc{dcf05ea89e528e,
  title = {Achievability of CSS codes performance limits over Pauli channels under separate ML decoding with bounded graphical complexity — arXiv:2611.02339},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.02339},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_f05ea89e528e; sha256 ae8ea2e5c4253dba0d97efe6027e06c7b0f3e7b773341ad6228c0a3b63276845},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.02339. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Capacity-approaching quantum error correction faces a fundamental tension: the required parity-check matrices need to become increasingly dense, while practical decoding and syndrome extraction favor sparse, bounded-degree structures. Reconciling these competing requirements remains an important open problem in quantum code design. We construct Calderbank-Shor-Steane (CSS) code ensembles that approach the CSS rate over memoryless Pauli channels under maximum-likelihood decoding while retaining sparse, bounded-degree graphical representations. The construction separates parity-check density from graphical complexity: although capacity-approaching components may require dense parity-check matrices, they are represented by sparse concatenated factor graphs. We first study a construction combining low-density parity-check (LDPC) and low-density generator-matrix (LDGM) component codes and numerically analyze the average weight distributions of the resulting codes. Motivated by these results, we introduce a second construction based on concatenated LDPC and LDGM codes and generalized irregular repeat-accumulate (GIRA) codes. We derive bounds on the average weight distribution of the resulting sum ensemble and use the Miller-Burshtein framework to prove simultaneous reliability of the two CSS decoding components. Consequently, the proposed ensemble achieves rates arbitrarily close to the CSS hashing bound under separate bit- and phase-error correction, while maintaining bounded graphical complexity, thus providing a foundation for future iterative decoders and indirect syndrome-extraction architectures.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.IT, nuovi lavori del giorno).
Categorie arXiv: Information Theory (cs.IT) ; Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2611.02339 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T18:15:52.823Z dalla pagina https://arxiv.org/list/math.IT/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).