{
  "abstract": "Simulating nonlinear dynamics with quantum computers has gained increasing attention. In general, such simulations require additional quantum resources because unitary quantum evolution is linear. A fundamental question is how nonlinear dynamics can be embedded into fully coherent, ancilla-free unitary circuits and how the complexity of the dynamics governs the required quantum resources. In this work, we generalize the ancilla-free double-bracket quantum algorithm for imaginary-time evolution by replacing its state-independent Hamiltonian with a state-dependent Hermitian operator. Our framework recursively calls an initial state preparation oracle and its inverse, and prepares the target solution to any prescribed accuracy using a fully coherent, ancilla-free unitary embedding. We relate the query cost to the complexity of the nonlinear dynamics, specifically their sensitivity to initial conditions. We obtain query upper bounds of $\\exp(O(T))$, $\\exp(O(T^2))$, and $\\exp(\\exp(O(T)))$ when the distance between solutions contracts at least exponentially (contractive), does not increase (nonexpansive), or grows at most exponentially (expansive), respectively, where $T$ is the target evolution time. For the discrete Gross--Pitaevskii equation, our ancilla-free double-bracket circuit achieves optimal worst-case query complexity $Θ(e^{gT/2})$ over a specified family of single-qubit initial states, where $g>0$ is the nonlinearity strength. These results connect the complexity of nonlinear dynamics to the query cost of coherent quantum simulation and provide a foundation for designing ancilla-free unitary embeddings with optimal query complexity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37802",
  "author_total": 3,
  "authors": [
    {
      "name": "Yuki Ito"
    },
    {
      "name": "Hideaki Hakoshima"
    },
    {
      "name": "Keisuke Fujii"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d74fys0m0kc51.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37802",
  "fulltext_url": null,
  "id": "d74fys0m0kc51",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37802",
  "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": "W7214973452",
  "pdf_url": "https://arxiv.org/pdf/2609.37802",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d74fys0m0kc51.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.37802",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37802"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Complexity of Ancilla-Free Unitary Embeddings for Nonlinear Dynamics via Generalized State-Dependent Double-Bracket Flows",
  "title_text": "Quantum Complexity of Ancilla-Free Unitary Embeddings for Nonlinear Dynamics via Generalized State-Dependent Double-Bracket Flows",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/d74fys0m0kc51",
  "venue": "arXiv",
  "versions": []
}