{
  "abstract": "T-state cultivation is a resource-efficient protocol producing logical T states but recent benchmarks show that its logical error rate is considerably higher than intended i.e. than S-state cultivation, which is the analogous protocol for producing logical S states. In this paper, we explain this T-S discrepancy by analytically showing, under circuit-level depolarising noise, that distance-3 (-5) T-state cultivation has fault distance 2 (3) due to Pauli hook errors that propagate to coherent Clifford errors after its final double-check circuit; such errors remain Pauli in S-state cultivation, which consequently retains fault distance 3 (5). As part of our analysis we derive a general formula, and an $\\mathcal O(n^3)$-time algorithm for fixed logical-qubit count, for the acceptance probability of a logical mixed state afflicted with a Clifford error, where $n$ is the physical qubit count. We then design flags that detect the malignant hook errors in cultivation, improving the pre-escape logical error rate from $Θ(p^3)$ to $Θ(p^5)$. At noise level $p =10^{-3}$, this is a 4.9$\\times$ improvement, costing a 1.36$\\times$ increase in attempts per accepted shot.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17706",
  "author_total": 4,
  "authors": [
    {
      "name": "Tim Chan"
    },
    {
      "name": "Armands Strikis"
    },
    {
      "name": "Zhu Sun"
    },
    {
      "name": "Zhenyu Cai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8pg3scspm3y9j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17706",
  "fulltext_url": null,
  "id": "8pg3scspm3y9j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17706",
  "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": "W7213507716",
  "pdf_url": "https://arxiv.org/pdf/2609.17706",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8pg3scspm3y9j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:48Z",
      "native_id": "2609.17706",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17706"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Diagnosing and Restoring the Degraded Fault Distance of Magic State Cultivation",
  "title_text": "Diagnosing and Restoring the Degraded Fault Distance of Magic State Cultivation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:48Z",
  "url": "https://research.draconitic.com/paper/8pg3scspm3y9j",
  "venue": "arXiv",
  "versions": []
}