{
  "abstract": "We give a quantum algorithm for simulating a $d$-sparse Hermitian Hamiltonian $H$, assuming a known upper bound $Λ$ on its maximum column Euclidean norm $\\|H\\|_{1\\to2}$. For $tΛ\\ge1/2$, simulation with operator-norm error $ε$ uses \\[ O\\!\\left(tΛ\\sqrt d+\\sqrt d\\log(2/ε)\\right) \\] sparse-oracle queries. This removes the subpolynomial overhead in Low's algorithm [STOC 2019], replacing it with an additive logarithmic precision term. For $d>1$ and $tΛ\\ge\\log(2/ε)$, the bound matches the worst-case lower bound. A known spectral-norm upper bound may also be used in place of $Λ$. The number of 1- and 2-qubit gates is linear in the query scale, up to oracle costs and polynomial overhead in the input bit lengths and logarithmic precision parameters. As applications, we obtain $O(κ\\sqrt d\\,\\mathrm{polylog}(κ/ε))$ queries for solving $d$-sparse quantum linear systems with $\\|A\\|\\le1$ and $\\|A^{-1}\\|\\leκ$, under standard sparse and state-preparation access. We also give a gate-efficient implementation of black-box unitaries with at most $d$ nonzero entries per row and column using $O(\\sqrt d\\log(2/ε))$ queries, given sparse access to the unitary and its adjoint. At constant error, the query bound is optimal and yields $Θ(\\sqrt N)$ queries for arbitrary $N\\times N$ unitaries, resolving the open question on black-box unitary implementation posed by Berry and Childs [QIC 2012].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02030",
  "author_total": 2,
  "authors": [
    {
      "name": "Zecheng Li"
    },
    {
      "name": "Chunhao Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6zzsda1xjjc6a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02030",
  "fulltext_url": null,
  "id": "6zzsda1xjjc6a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02030",
  "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": "W7216401923",
  "pdf_url": "https://arxiv.org/pdf/2610.02030",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6zzsda1xjjc6a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.02030",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02030"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Sparse Hamiltonian simulation with optimal dependence on the maximum column Euclidean norm",
  "title_text": "Sparse Hamiltonian simulation with optimal dependence on the maximum column Euclidean norm",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/6zzsda1xjjc6a",
  "venue": "arXiv",
  "versions": []
}