{
  "abstract": "Consider a quantum state vector proportional to any given column of the character table of the symmetric group ($S_n$), corresponding to a superposition over the irreps weighted by the character values. It was recently argued that sampling from this state is classically hard under reasonable complexity-theoretic assumptions, while there exists an efficient quantum algorithm for preparing this character state using the quantum Fourier transform (QFT) over $S_n$ [arXiv:2501.12579]. We give an alternative, simpler algorithm to prepare this character state with a sequence of Hamiltonian evolutions, as well as an efficient implementation with reconfigurable qubits that uses only nearest-neighbor gates in 1D. The gate complexity, accounting for Hamiltonian simulation errors, depends on the choice of the column: For fixed target state error, the estimated sufficient total gate count ranges from as few as $O(n)$ gates for the $n$-cycle column, to $\\widetilde O(n^{1.75})$ gates near the conjecturally classically hard parameter regime, to provably $\\widetilde O(n^{2.5})$ gates in the worst case. In contrast, the QFT subroutine in the prior approach uses $\\widetilde O(n^3)$ gates. Our gate count estimates come from leading-order state-dependent Trotter error analysis, and the proven worst-case bound relies on a QSVT-based Hamiltonian simulation method; numerical benchmarks of the Trotter-based protocol suggest that the estimates are conservative. Furthermore, we generalize our protocol to give an explicit algorithm for the quantum character transform (QCT) over $S_n$ using $\\widetilde O(n^{2.5})$ gates and $O(n)$ qubits. An application to entanglement entropy of symmetric orbifold conformal field theories is also discussed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05752",
  "author_total": 2,
  "authors": [
    {
      "name": "Dikshant Rathore"
    },
    {
      "name": "Leo Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bxpspfad08jkk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05752",
  "fulltext_url": null,
  "id": "bxpspfad08jkk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05752",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7220742130",
  "pdf_url": "https://arxiv.org/pdf/2610.05752",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bxpspfad08jkk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.05752",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05752"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "An efficient Hamiltonian-based quantum algorithm for characters of the symmetric group",
  "title_text": "An efficient Hamiltonian-based quantum algorithm for characters of the symmetric group",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/bxpspfad08jkk",
  "venue": "arXiv",
  "versions": []
}