{
  "abstract": "We give a quantum algorithm for Lindbladian simulation given a block encoding of the Hamiltonian $H$ and a projected unitary encoding of the stacked jump operator $B=\\sum_{k=1}^m \\lvert k\\rangle\\otimes L_k$, with normalization factors $α_H$ and $α_B$, respectively. For evolution time $t$, set $τ=(α_H+α_B^2)t$. The algorithm approximates the evolution channel to diamond-norm error $\\varepsilon$ using $O\\!\\left(τ+\\frac{\\log(1/\\varepsilon)}{\\log\\!\\left(e+\\log(1/\\varepsilon)/τ\\right)}\\right)$ oracle queries, matching the query lower bound for Hamiltonian simulation. The number of additional one- and two-qubit gates is linear in the query complexity up to polylogarithmic factors. The query- and gate-complexity bounds extend to Lipschitz-continuous time-dependent Lindbladians under coherent time-indexed oracle access. Our construction uses a one-query transducer that implements a product of rational approximations to short-time evolution when supplied with a catalyst. We bound the error from omitting the catalyst by exploiting orthogonality between different sequences of Kraus labels. The gate implementation combines a compressed Kraus-label representation, which stores only the positions and values of the nonzero labels, with the rotation factorization of Chen et al.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18757",
  "author_total": 4,
  "authors": [
    {
      "name": "Boyang Chen"
    },
    {
      "name": "Minbo Gao"
    },
    {
      "name": "Xinzhao Wang"
    },
    {
      "name": "Shuo Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2q5dch1zq4sbv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18757",
  "fulltext_url": null,
  "id": "2q5dch1zq4sbv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18757",
  "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.DS"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7213524672",
  "pdf_url": "https://arxiv.org/pdf/2609.18757",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2q5dch1zq4sbv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:01Z",
      "native_id": "2609.18757",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18757"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Query-Optimal and Gate-Efficient Lindbladian Simulation",
  "title_text": "Query-Optimal and Gate-Efficient Lindbladian Simulation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:01Z",
  "url": "https://research.draconitic.com/paper/2q5dch1zq4sbv",
  "venue": "arXiv",
  "versions": []
}