{
  "abstract": "The Solovay-Kitaev algorithm states that it is possible to efficiently compile unitaries to accuracy $ε$ in $\\text{polylog}(1/ε)$ time using any universal gate set. While Solovay and Kitaev's initial work addressed inverse-closed gate sets, recently Bouland and Giurgicǎ-Tiron showed it is possible to efficiently compile arbitrary gate sets without inverses. However, the exponent of their compilation algorithm is high. For example the inverse-free exponent for a qubit is over $8.62$, while information theoretically it is known that an inverse-free exponent of $3$ is possible in any dimension by a result of Oszmaniec, Sawicki, and Horodecki. This leads to a natural question: can one improve the exponent in Bouland and Giurgicǎ-Tiron's algorithm? And are there any cases where the inverse-free exponent is below 3, thus surpassing existing information-theoretic arguments? To answer this question, we first show that a special case of the inverse-free compiling problem -- namely Pauli gates supplemented by an irrational rotation of a qubit - admits a highly efficient compilation algorithm with an exponent at most $\\approx 2.138$. Our algorithm fuses ideas from prior algorithms of Kuperberg and Sardharwalla, Cubitt, Harrow and Linden to construct an efficient ``Pauli golf'' compilation routine. We then extend these ideas to the general inverse-free case for a qubit, where we give a compiling algorithm with exponent at most $2.988$. This result uses a novel form of approximate ``aiming'' of unitary corrections to improve the compilation efficiency. Our results give two examples of quantum compiling algorithms surpassing information-theoretic arguments, and demonstrate that there are many efficiency gains possible for inverse-free compilation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03655",
  "author_total": 3,
  "authors": [
    {
      "name": "Adam Bouland"
    },
    {
      "name": "Victor Shyaka"
    },
    {
      "name": "Chenyi Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9wwswc9t7hny7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03655",
  "fulltext_url": null,
  "id": "9wwswc9t7hny7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03655",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7220433609",
  "pdf_url": "https://arxiv.org/pdf/2610.03655",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9wwswc9t7hny7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.03655",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03655"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Breaking the cubic barrier for the inverse-free Solovay-Kitaev algorithm",
  "title_text": "Breaking the cubic barrier for the inverse-free Solovay-Kitaev algorithm",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:45Z",
  "url": "https://research.draconitic.com/paper/9wwswc9t7hny7",
  "venue": "arXiv",
  "versions": []
}