{
  "abstract": "We compute exactly the acceptance and logical error rates for the distance $d=3$ and $d=5$ magic state cultivation circuits from Clifft [arXiv:2604.27058] and SOFT [arXiv:2512.23037] using Pauli propagation and binary tensor contraction. Actual $T$-gates are studied, not the $S$-gate proxy used for sampling. The calculation includes every fault order at several circuit-level noise strengths ($p$). We provide a series expansion form to the logical error rates, through order $(p/(1-p))^{10}$. The analytical results recover the numerical values from Clifft and SOFT at both $d=3$ and $d=5$ to within their sampling uncertainty. Then, we show that the $d=3$ and $d=5$ circuits actually have fault distances of $d_{\\text{fault}}=2$ and $d_{\\text{fault}}=3$ respectively, explaining the similar distance degrading effects from the companion code of [Quantum 10, 2134 (2026)].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18922",
  "author_total": 2,
  "authors": [
    {
      "name": "Kwok Ho Wan"
    },
    {
      "name": "Ainhoa Zapirain"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9bw27f1r3s1wj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18922",
  "fulltext_url": null,
  "id": "9bw27f1r3s1wj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18922",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7213513163",
  "pdf_url": "https://arxiv.org/pdf/2609.18922",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9bw27f1r3s1wj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.18922",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18922"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Exact logical error rates for magic state cultivation",
  "title_text": "Exact logical error rates for magic state cultivation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/9bw27f1r3s1wj",
  "venue": "arXiv",
  "versions": []
}