{
  "abstract": "Randomized Hamiltonian simulation methods are often governed by a trade-off between systematic bias and sampling overhead. We study how classical variance-reduction techniques can be applied to such methods without changing their mean channel, and therefore without introducing additional bias. As a motivating unbiased estimator, we formulate continuous time-evolution probabilistic angle interpolation (continuous TE-PAI), a quasiprobabilistic random-circuit protocol whose remaining Monte Carlo error is purely statistical. Continuous TE-PAI removes Trotter discretization error with finite-depth random circuits, whereas deterministic Trotterization does so only in the infinite-depth limit. Further, in tensor-network simulations, we demonstrate that discretization error can cause an unphysical exponential growth in the bond dimension required for Trotterized simulations, whereas comparable-depth continuous TE-PAI circuits avoid this growth. We then show that the variance of randomized product-formula-based estimators admits a canonical decomposition into a classical counting component and a quantum ordering component such that the dominant simulation overhead results from the non-commutative parts of the Hamiltonian dynamics. Motivated by this decomposition, we achieve an $\\approx70\\%$ error-reduction using the counting-component for small systems whereas our tensor-network simulations of $n=30$ spin-chain dynamics use coarser statistics tailored to the observable and estimator attaining a negligible bias and a reduction of $\\approx 80\\%$ leading to $\\approx91\\%$ and $\\approx96\\%$ sampling-cost reductions, respectively.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.23544",
  "author_total": 3,
  "authors": [
    {
      "name": "Joshua W. Dai"
    },
    {
      "name": "Fredrik Hasselgren"
    },
    {
      "name": "Chusei Kiumi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bax4n8s6w4h04.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.23544",
  "fulltext_url": null,
  "id": "bax4n8s6w4h04",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.23544",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7165689343",
  "pdf_url": "https://arxiv.org/pdf/2606.23544",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bax4n8s6w4h04.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:03Z",
      "native_id": "2606.23544",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.23544"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Structure-Aware Variance Reduction for Unbiased Randomized Hamiltonian Simulation",
  "title_text": "Structure-Aware Variance Reduction for Unbiased Randomized Hamiltonian Simulation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:03Z",
  "url": "https://research.draconitic.com/paper/bax4n8s6w4h04",
  "venue": "arXiv",
  "versions": []
}