{
  "abstract": "Product formulas are a basic tool for simulating quantum many-body dynamics, but a fundamental degree of freedom in their application---the ordering of Hamiltonian terms---has remained largely unexplored. Here we systematically study such ordering effects, quantifying their impact on simulation accuracy and exploiting them to design more accurate product-formula simulations. We develop an efficiently computable, ordering-sensitive bound on the finite-step-size Trotter error for geometrically local Hamiltonians for arbitrarily high-order product formulas. For translation-invariant one-dimensional chains, our bounds are close to exact second-, fourth-, and sixth-order Trotter errors in small-system tests, while on large-scale systems they improve on previous higher-order analytical bounds by orders of magnitude. We further use the local structure of the error bounds and estimates to optimize ordering efficiently, reducing the long-chain problem to a minimum-mean-weight-cycle problem on a weighted de Bruijn graph. For random translation-invariant chains, sequential (staircase-like) orderings consistently outperform standard brickwall circuits; when circuit depth is restricted, the optimizer instead favors wave-like parallel-sequential orderings, which preserve much of the accuracy advantage over brickwall circuits. These results establish ordering as a useful degree of freedom for both understanding and improving product-formula simulation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03672",
  "author_total": 5,
  "authors": [
    {
      "name": "Zhenning Liu"
    },
    {
      "name": "Zhi-Yuan Wei"
    },
    {
      "name": "Michael Foss-Feig"
    },
    {
      "name": "Alexey V. Gorshkov"
    },
    {
      "name": "Andrew M. Childs"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8thsj5m3feds5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03672",
  "fulltext_url": null,
  "id": "8thsj5m3feds5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03672",
  "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": "W7220403102",
  "pdf_url": "https://arxiv.org/pdf/2610.03672",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8thsj5m3feds5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.03672",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03672"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Ordering-Aware Theory of Trotter Error",
  "title_text": "Ordering-Aware Theory of Trotter Error",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:45Z",
  "url": "https://research.draconitic.com/paper/8thsj5m3feds5",
  "venue": "arXiv",
  "versions": []
}