{
  "abstract": "Magic-state cultivation has largely targeted single-qubit non-Clifford resources. We show that the entangled state $|CS\\rangle=CS|++\\rangle$ can be cultivated directly rather than synthesized from three $T$-type resources. Two commuting Hermitian Clifford involutions project onto four Pauli-frame branches, so no ideal branch is discarded, while a minimal six-bit $[6,2,4]$ record protects their history. The small-code state cannot itself be certified: late two-fault patterns evade its record, placing the certified boundary after surface-code growth. Under a fixed decoder that sees 136 operational detector bits per patch and withholds 168, exact audits find no accepted closed-boundary logical failure through fault order two, while order-three mechanisms exist. Escaping from the small code directly into a distance-3 patch and growing it to distance 13 in a single round keeps this certificate. Compared with a re-decoded three-$T$ comparator matched to the same binary logical-error target, the direct route uses $2\\%$ fewer active locations at $p=5\\times10^{-4}$ and $16$--$28\\%$ more at $8\\times10^{-4}$--$10^{-3}$, without charging the comparator for $T$-state storage. Counted in qubit-ticks under one rule for both routes, it uses $21$--$39\\%$ less spacetime. Adding idle-memory noise to both routes under one rule and one optimized schedule raises the direct route's cost more, to $8\\%$ and $46\\%$ above the comparator at $5\\times10^{-4}$ and $10^{-3}$, because that cost is limited by acceptance. The result is architectural: an entangled non-Clifford state can itself be cultivated with a certified output interface.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09993",
  "author_total": 2,
  "authors": [
    {
      "name": "Gunsik Min"
    },
    {
      "name": "Jun Heo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/73v7krmkj42m5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09993",
  "fulltext_url": null,
  "id": "73v7krmkj42m5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09993",
  "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": "W7212116815",
  "pdf_url": "https://arxiv.org/pdf/2609.09993",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/73v7krmkj42m5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2609.09993",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09993"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Direct Cultivation of Entangled $|CS\\rangle$ Magic States",
  "title_text": "Direct Cultivation of Entangled |CS⟩ Magic States",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:50Z",
  "url": "https://research.draconitic.com/paper/73v7krmkj42m5",
  "venue": "arXiv",
  "versions": []
}