{
  "abstract": "For the standard Clifford+$T$ gate set, deterministic, ancilla-free synthesis now attains the minimal $T$-count for general single-qubit unitaries (Morisaki et al., arXiv:2510.05816). The $\\sqrt{T}$ gate rotates by half the angle of $T$, generating a finer lattice of implementable operations. Access to this magic state is expected to lower the cost of deterministic and ancilla-free synthesis of general single-qubit unitaries (Kliuchnikov et al., arXiv:2203.10064), but no direct Clifford+$\\sqrt{T}$ algorithm existed for this case. We provide one by extending the integer lattice-point enumeration method of Morisaki et al. We adopt a resource state cost model based on the magic-state catalysis approach of Gidney and Fowler (arXiv:1812.01238). On Haar-random targets synthesized to precisions ranging from $\\varepsilon=10^{-3}$ to $10^{-8}$, the cost of Clifford+$\\sqrt{T}$ circuits scales as $2.4\\log_2(1/\\varepsilon)$ compared to $3.0\\log_2(1/\\varepsilon)$ for $T$-count-optimal Clifford+$T$ circuits. Once a one-time catalyst state is amortized, the Clifford+$\\sqrt{T}$ circuits are never costlier than their Clifford+$T$ counterparts.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16659",
  "author_total": 5,
  "authors": [
    {
      "name": "Mathias Weiden"
    },
    {
      "name": "Jae Won Kim"
    },
    {
      "name": "Justin Kalloor"
    },
    {
      "name": "John Kubiatowicz"
    },
    {
      "name": "Costin Iancu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/42793qpqnandx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16659",
  "fulltext_url": null,
  "id": "42793qpqnandx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16659",
  "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": "W7213431427",
  "pdf_url": "https://arxiv.org/pdf/2609.16659",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/42793qpqnandx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2609.16659",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16659"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Approximate synthesis of general single-qubit unitaries over the Clifford+$\\sqrt{T}$ gate set",
  "title_text": "Approximate synthesis of general single-qubit unitaries over the Clifford+√T gate set",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:35Z",
  "url": "https://research.draconitic.com/paper/42793qpqnandx",
  "venue": "arXiv",
  "versions": []
}