{
  "abstract": "Nonlinear stochastic differential equations describe dynamics under uncertainty, but their nonlinear coefficients and noise averaging complicate quantum representations. We develop a Kolmogorov--Lindblad mapping that encodes their probability laws as the position diagonals of trace-one quantum density operators. For each Brownian realisation, a stochastic flow transports the initial ensemble; the square-root Jacobian makes its action on half-densities unitary. Averaging the resulting pure-state projectors gives a Lindblad equation with Hermitian jump operators. Its diagonal reproduces the Fokker--Planck density, while forward and backward intertwining identities recover bounded observables and time correlations independently of the initial coherences. A Galerkin approximation obtained by projecting the Stratonovich generators preserves the Lindblad structure. We give a residual-based error estimate and conditional quantum costs that display the dimension dependence of approximation constants, operator normalisations, state preparation and readout. Numerical experiments for double-well Langevin dynamics and noisy Lorenz--63 show rapid convergence of selected statistics at fixed dimension. The construction provides an exact bridge from flow-regular nonlinear diffusions to quantum channels; any computational advantage additionally requires controlled approximation and coherent access for the chosen problem family.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.09903",
  "author_total": 2,
  "authors": [
    {
      "name": "Hsuan-Cheng Wu"
    },
    {
      "name": "Xiantao Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dqjbnxdvykwye.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.09903",
  "fulltext_url": null,
  "id": "dqjbnxdvykwye",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.09903",
  "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": "W7202204068",
  "pdf_url": "https://arxiv.org/pdf/2608.09903",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dqjbnxdvykwye.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2608.09903",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.09903"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "From Nonlinear Stochastic Differential Equations to Quantum Channels: The Kolmogorov--Lindblad Mapping",
  "title_text": "From Nonlinear Stochastic Differential Equations to Quantum Channels: The Kolmogorov--Lindblad Mapping",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:22Z",
  "url": "https://research.draconitic.com/paper/dqjbnxdvykwye",
  "venue": "arXiv",
  "versions": []
}