{
  "abstract": "We present the \\emph{first} analytical determination of the exact accessible dimension for every fixed architecture of arbitrary two-qubit gates on three qubits. A support word represents which pair of qubits each two-qubit gate acts on, and its reduced length is obtained by merging consecutive gates on the same pair. If the reduced length is $r$, then the set of implementable three-qubit unitaries has accessible dimension $d(w)=\\min\\{63,9r+9\\}$. Consequently, six arbitrary two-qubit gates are \\emph{necessary and sufficient for local universality}: every fixed architecture reaches a nonempty open subset of $\\mathrm{SU}(8)$ when its reduced length is at least six. The result is stronger than existence of one favorable architecture. Every reduced six-slot support word is locally universal, including the alternating nearest-neighbor line $AB,BC,AB,BC,AB,BC$. The upper bound follows from a standard parameter-counting argument. The matching lower bounds are proved by Jacobian certificates in the Pauli basis. Up to qubit relabeling and reversal, there are $22$ reduced architectures of lengths two through six. For each one, a product of rational Pauli rotations yields a nonzero maximal minor modulo the prime $1{,}000{,}003$. Thus, any obstruction to global universality with six two-qubit gates must go beyond parameter counting, connectivity, and differential rank.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22176",
  "author_total": 2,
  "authors": [
    {
      "name": "Hyunho Cha"
    },
    {
      "name": "Jungwoo Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a91my65hgn7er.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22176",
  "fulltext_url": null,
  "id": "a91my65hgn7er",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22176",
  "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": "W7214036287",
  "pdf_url": "https://arxiv.org/pdf/2609.22176",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a91my65hgn7er.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.22176",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22176"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Every architecture of six two-qubit gates is locally universal on three qubits",
  "title_text": "Every architecture of six two-qubit gates is locally universal on three qubits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/a91my65hgn7er",
  "venue": "arXiv",
  "versions": []
}