{
  "abstract": "Magic $|T\\rangle$-state preparation dominates the cost of fault-tolerant quantum computation on surface codes, yet cultivation and distillation are typically provisioned statically, leaving much of the program's error budget unused. We present Gap-Priced $|T\\rangle$ States (GP$|T\\rangle$-S), a lattice surgery scheduler and factory allocator that co-optimizes both methods under a total $T$-error budget. GP$|T\\rangle$-S uses the complementary gap of each cultivated state as a fidelity estimate and dynamically adjusts the cultivation gap cutoff, converting budget slack into speed by giving the scheduler control over the cultivation post-selection. GP$|T\\rangle$-S also characterizes distillation factories by size, $|T\\rangle$-state production rate, and budget slack, and introduces cultivating factories that embed cultivation within routing channels, achieving fidelities otherwise requiring two-level distillation at a single-level footprint. GP$|T\\rangle$-S organizes these characterizations into a factory catalog, and performs distillation factory allocation over this catalog in tandem with the gap cutoff using dynamic-programming to achieve one of i) minimum spacetime volume, ii) minimum execution time, or iii) minimum space overhead, all within a user-provided $T$-error budget. Across sixteen benchmarks under high and low $T$-error budgets of $10^{-3}$ and $10^{-5}$ respectively, GP$|T\\rangle$-S consistently outperforms cultivation-only and single-factory baselines without exceeding the budget, achieving a 5.5$\\times$ geometric mean speedup in logical cycle count and a 3.4$\\times$ geometric mean reduction in space-time volume.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19299",
  "author_total": 6,
  "authors": [
    {
      "name": "Maxwell Poster"
    },
    {
      "name": "Sayam Sethi"
    },
    {
      "name": "Steven Hofmeyr"
    },
    {
      "name": "Yuhao Liu"
    },
    {
      "name": "Jonathan Baker"
    },
    {
      "name": "Costin Iancu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7dfnhtkxhq5gc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19299",
  "fulltext_url": null,
  "id": "7dfnhtkxhq5gc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19299",
  "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": "W7222320476",
  "pdf_url": "https://arxiv.org/pdf/2610.19299",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7dfnhtkxhq5gc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:18Z",
      "native_id": "2610.19299",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19299"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Gap-Priced $|T\\rangle$-States: Dynamic $|T\\rangle$ Post-Selection and Budget-Aware Factory Provisioning",
  "title_text": "Gap-Priced |T⟩-States: Dynamic |T⟩ Post-Selection and Budget-Aware Factory Provisioning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:18Z",
  "url": "https://research.draconitic.com/paper/7dfnhtkxhq5gc",
  "venue": "arXiv",
  "versions": []
}