{
  "abstract": "Low-energy estimation and state preparation for general $k$-local Hamiltonians are fundamental challenges in quantum complexity theory. Buhrman et al.~ [BGLGST, PRL 2025] recently broke the natural Grover bound $O^\\ast(2^{n/2})$ for both problems, with the improvement depending on the relative accuracy $\\varepsilon$ and the locality $k$. In this work, we present faster exponential quantum algorithms for these problems, where the binary entropy function governs the runtime exponent. For sufficiently small $\\varepsilon/k$, our algorithms improve the exponent by a factor of $\\log(k/\\varepsilon)$ over [BGLGST, PRL 2025]. Our main technical result is an entropy-governed lower bound on the dimension of the Hamiltonian's low-energy subspace, obtained by depolarizing its ground state. For fixed $k$, this bound is optimal up to constant factors in the exponent. The same framework yields tighter bounds for Heisenberg, $XY$, and Ising models on arbitrary interaction graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34532",
  "author_total": 4,
  "authors": [
    {
      "name": "Sevag Gharibian"
    },
    {
      "name": "François Le Gall"
    },
    {
      "name": "Ranitha Mataraarachchi"
    },
    {
      "name": "Suguru Tamaki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dg4aq7dbnp6za.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34532",
  "fulltext_url": null,
  "id": "dg4aq7dbnp6za",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34532",
  "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",
      "cs.CC"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7214739086",
  "pdf_url": "https://arxiv.org/pdf/2609.34532",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dg4aq7dbnp6za.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.34532",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34532"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Near-Optimal Bounds on the Density of Low-Energy States of $k$-Local Hamiltonians and Faster Quantum Algorithms",
  "title_text": "Near-Optimal Bounds on the Density of Low-Energy States of k-Local Hamiltonians and Faster Quantum Algorithms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/dg4aq7dbnp6za",
  "venue": "arXiv",
  "versions": []
}