{
  "abstract": "Quantum Fourier transforms (QFT) for general groups were recognized to be fundamental already early in the field. A canonical example of non-abelian QFT for the symmetric group was outlined by Beals (1997). Later, a more detailed analysis of this algorithm was carried out by Kawano and Sekigawa (2016). In this paper, we revisit that construction. After a careful analysis, we revise their gate complexity to $\\widetilde{\\mathcal{O}}(n^{3.5})$ and circuit depth to $\\widetilde{\\mathcal{O}}(n^3)$. Moreover, we observe that their construction is not optimal in the choice of transversal elements, so we propose simpler realization of the symmetric group QFT.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28569",
  "author_total": 3,
  "authors": [
    {
      "name": "Carli Bruinsma"
    },
    {
      "name": "Dmitry Grinko"
    },
    {
      "name": "Maris Ozols"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/49nbdanpbvynq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28569",
  "fulltext_url": null,
  "id": "49nbdanpbvynq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28569",
  "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",
      "math.RT"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7204787393",
  "pdf_url": "https://arxiv.org/pdf/2608.28569",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/49nbdanpbvynq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2608.28569",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28569"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Fourier transform for the symmetric group",
  "title_text": "Quantum Fourier transform for the symmetric group",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/49nbdanpbvynq",
  "venue": "arXiv",
  "versions": []
}