{
  "abstract": "Linear combination of Hamiltonian simulation (LCHS) provides an asymptotically optimal framework for the quantum simulation of linear non-unitary dynamics. The LCHS approach approximately implements the Peano--Baker propagator through an integral representation determined by a kernel function. We establish an LCHS approximation theorem for a broadened class of admissible kernel functions, defined by natural complex-analytic conditions. In the standard time-independent block-encoding access model, we explicitly construct, for each target error $\\varepsilon$, the unique kernel function in this class minimizing the query-cost functional and show that the minimum of this functional has the asymptotic expansion $\\tfrac{2\\mathrm{e}}π\\big(\\log\\frac{1}{\\varepsilon}-\\log\\log\\frac{1}{\\varepsilon}+o(1)\\big)$ as ${\\varepsilon\\downarrow0}$. The provably optimal leading coefficient $2\\mathrm{e}/π$ improves by a factor of approximately 2.1 on the coefficient obtained empirically by Low and Somma through numerical minimization over their family of optimally scaling kernel functions. We construct a spectrally convergent quadrature with explicit bounds on operator error and linear combination of unitaries (LCU) subnormalization, proving that this asymptotic improvement persists after discretization into a finite linear combination of unitaries suitable for implementation. Our results are based on Hardy space theory and convex analysis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03669",
  "author_total": 2,
  "authors": [
    {
      "name": "Harriet Apel"
    },
    {
      "name": "Bjorn K. Berntson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7egrznh5tb4bp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03669",
  "fulltext_url": null,
  "id": "7egrznh5tb4bp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03669",
  "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": "W7220375989",
  "pdf_url": "https://arxiv.org/pdf/2610.03669",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7egrznh5tb4bp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.03669",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03669"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Optimal kernel functions for linear combination of Hamiltonian simulation",
  "title_text": "Optimal kernel functions for linear combination of Hamiltonian simulation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:45Z",
  "url": "https://research.draconitic.com/paper/7egrznh5tb4bp",
  "venue": "arXiv",
  "versions": []
}