{
  "abstract": "Quantum linear systems algorithms (QLSAs) aim to solve linear systems $A\\bb{x}=\\bb{b}$ exponentially faster than classical methods under certain conditions. In this work, we develop quantum algorithms for solving linear algebraic equations from an ODE-based perspective. Inspired by the linear combination of Hamiltonian simulation (LCHS) representation in the Fourier approach \\cite{Childs2017QLSA}, we express the solution $\\bb{x}$ as a linear combination of solutions to a system of linear convection equations, which become Schrödinger-type equations with unitary evolutions in the Fourier domain. We refer to this representation as LC-Schrödingerization. Based on this result, we construct an LCHS-based quantum algorithm with two LCHS instances: one for time-marching and one for numerical integration. The key construction uses the derivative of a Gaussian-smoothed hat function and recovers the solution over a fixed auxiliary interval. This permits a truncation time independent of the target accuracy and avoids the loss in success probability from selecting a single grid point. Periodization and explicit Fourier coefficients provide the corresponding projection error bounds. Under the stated oracle assumptions and given a constant-factor estimate of the solution norm, direct simulation of the select operators and block preconditioning achieve the optimal matrix-query complexity $\\mathcal{O}(κ_A\\log\\frac1\\varepsilon)$ without using variable-time amplitude amplification (VTAA). The same upper bound holds for queries to the right-hand-side preparation oracle.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19676",
  "author_total": 3,
  "authors": [
    {
      "name": "Yin Yang"
    },
    {
      "name": "Yue Yu"
    },
    {
      "name": "Long Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e65qmdm5h46g8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19676",
  "fulltext_url": null,
  "id": "e65qmdm5h46g8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19676",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.19676",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e65qmdm5h46g8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.19676",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19676"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Linear combination of Schrödingerization for quantum linear systems with optimal matrix-query complexity",
  "title_text": "Linear combination of Schrödingerization for quantum linear systems with optimal matrix-query complexity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:19Z",
  "url": "https://research.draconitic.com/paper/e65qmdm5h46g8",
  "venue": "arXiv",
  "versions": []
}