{
  "abstract": "We present the algebraic structure of bosonic quantum error-correcting codes on genus-two Riemann surfaces. We explicitly construct the code words as automorphic forms and analytically generate the full tower of code spaces at all weights. We prove a fundamental no-go theorem: for any genus greater than one, the stabilizer group is non-amenable, forcing a strictly positive spectral gap in the stabilizer Hamiltonian. Consequently, no normalizable quantum state can satisfy all stabilizer conditions. This sharply contrasts with standard Gottesman-Kitaev-Preskill (GKP) codes, where the amenability of the stabilizer group $\\mathbb{Z}^2$ permits approximate code words with arbitrary precision.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.31156",
  "author_total": 5,
  "authors": [
    {
      "name": "David Roberts"
    },
    {
      "name": "Aaron Slipper"
    },
    {
      "name": "Alireza Parhizkar"
    },
    {
      "name": "Victor V. Albert"
    },
    {
      "name": "Mohammad Hafezi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2jvw11xce4na4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.31156",
  "fulltext_url": null,
  "id": "2jvw11xce4na4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.31156",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7204886049",
  "pdf_url": "https://arxiv.org/pdf/2608.31156",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2jvw11xce4na4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.31156",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.31156"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Bosonic codes from compact phase spaces",
  "title_text": "Bosonic codes from compact phase spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/2jvw11xce4na4",
  "venue": "arXiv",
  "versions": []
}