{
  "abstract": "In this paper, we present a polynomial-time quantum algorithm for computing a minimum-sized generating set of solvable black-box groups. Next, we consider the class $Γ_d$ of black-box groups, where every non-abelian composition factor is isomorphic to a subgroup of the symmetric group $S_d$ for a fixed $d$. We design polynomial-time quantum algorithms to compute the direct product decomposition of abelian factor groups and solve the constructive membership problem for factor groups of groups from $Γ_d$. With the help of these algorithms, we design a quantum algorithm for computing a chief series of black-box groups from $Γ_d$. Using the chief series, we construct a polynomial-time quantum algorithm for computing minimum generating sets of black-box groups from $Γ_d$. Finally, we show that the minimum generating set problem for general black-box groups is in $\\textrm{NP} \\cap \\textrm{coAM}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40260",
  "author_total": 4,
  "authors": [
    {
      "name": "Bireswar Das"
    },
    {
      "name": "Udit Kumar"
    },
    {
      "name": "Kavita Samant"
    },
    {
      "name": "Dhara Thakkar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6aww4hscbmp6c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40260",
  "fulltext_url": null,
  "id": "6aww4hscbmp6c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.40260",
  "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",
      "cs.CC"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7215049824",
  "pdf_url": "https://arxiv.org/pdf/2609.40260",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6aww4hscbmp6c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.40260",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40260"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Algorithms for Minimum Generating Set",
  "title_text": "Quantum Algorithms for Minimum Generating Set",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/6aww4hscbmp6c",
  "venue": "arXiv",
  "versions": []
}