{
  "abstract": "Bivariate bicycle (BB) codes of Bravyi \\emph{et al.}~\\cite{Bravyi2024} are quantum low-density parity-check codes with weight-$6$ checks, exemplified by $[[144,12,12]]$ with $kd^2/n=12$. We develop the algebraic structure theory of BB-type codes with weight-$8$ checks (weight-$4$ generator polynomials) and use it, together with an exactly validated search pipeline, to construct and certify new codes. We prove an exact dimension formula $k=2\\dim R/(A,B)$ (forcing even $k$), a $4\\ell m$-element symmetry group on generator pairs, an $X/Z$ distance equality $d_X=d_Z$, and a family of subgroup-coset kernel vectors giving rigorous distance upper bounds and a design rule for high-distance constructions; all distances are computed exhaustively by a cross-validated bit-mask verifier. At $n=144$ the pipeline returns a census of $53$ codes whose strongest members surpass the BB benchmark: $[[144,6,d\\ge 15]]$ exceeds the benchmark distance $12$ (certified $d\\ge 15$), $[[144,10,12]]$ reaches it with weight-$8$ checks, and $[[144,16,10]]$ encodes a third more logical qubits at $kd^2/n=11.11$ ($7.4\\%$ below benchmark) while decoding no worse. At $n=72$, $[[72,14,8]]$ attains $kd^2/n=12.44$---more than twice the same-length BB code---and decodes better; a circuit-level memory experiment places our weight-$8$ codes at $\\approx 0.1\\%$ pseudo-threshold versus $\\approx 0.4\\%$ for the BB reference under an identical model, quantifying the threshold cost of the heavier checks. All structural statements are verified numerically on the whole census.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06572",
  "author_total": 3,
  "authors": [
    {
      "name": "Liangdong Lu"
    },
    {
      "name": "Ruipan Yang"
    },
    {
      "name": "Guanmin Guo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5s43g3qae6km7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06572",
  "fulltext_url": null,
  "id": "5s43g3qae6km7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06572",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7212024023",
  "pdf_url": "https://arxiv.org/pdf/2609.06572",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5s43g3qae6km7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.06572",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06572"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum bivariate bicycle codes with weight-8 checks surpassing the BB benchmark",
  "title_text": "Quantum bivariate bicycle codes with weight-8 checks surpassing the BB benchmark",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/5s43g3qae6km7",
  "venue": "arXiv",
  "versions": []
}