{
  "abstract": "Topological phases of matter are characterized by global properties of quantum states beyond conventional local order parameters. The Chern number is a central invariant in this characterization, linking the geometry of quantum states to robust physical observables and making its determination key to understanding quantum matter. We construct a nearly optimal quantum algorithm for estimating the Chern number of a smooth Hamiltonian family over a two-dimensional parameter torus with a unique, gapped ground state, including interacting many-body systems. The algorithm transports and reuses two ground-state copies prepared at a single reference point and uses generalized quantum signal processing to coherently accumulate geometric phases. It achieves a Hamiltonian-oracle evolution time of $\\tilde{O}(L_xL_y/Δ_{\\min}^3)$, where $L_x,L_y$ bound the parameter derivatives of the Hamiltonian and $Δ_{\\min}$ is a known spectral-gap lower bound. We prove a matching worst-case oracle lower bound, even when the Chern number is promised to be zero or one, establishing optimality up to polylogarithmic factors. For local Hamiltonian families with an inverse-polynomial gap and a supplied guiding state, exact Chern-number computation is in $\\mathsf{FBQP}$ and is $\\mathsf{BQP}$-hard, and merely deciding whether the Chern number is zero or one is already $\\mathsf{BQP}$-complete. These results establish how efficiently quantum computers can estimate a quantized topological invariant and provide evidence for quantum advantage in characterizing topological phases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35978",
  "author_total": 5,
  "authors": [
    {
      "name": "Soichiro Imamura"
    },
    {
      "name": "Shintaro Ae"
    },
    {
      "name": "Kazuki Sakamoto"
    },
    {
      "name": "Ryu Hayakawa"
    },
    {
      "name": "Chusei Kiumi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ah7tz8mac7h3d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35978",
  "fulltext_url": null,
  "id": "ah7tz8mac7h3d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35978",
  "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": "W7214973920",
  "pdf_url": "https://arxiv.org/pdf/2609.35978",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ah7tz8mac7h3d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.35978",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35978"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Chern-number estimation: nearly optimal quantum algorithm and provable quantum speedup",
  "title_text": "Chern-number estimation: nearly optimal quantum algorithm and provable quantum speedup",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/ah7tz8mac7h3d",
  "venue": "arXiv",
  "versions": []
}