{
  "abstract": "Dissipation has been recently demonstrated as a powerful primitive for designing quantum algorithms. We apply this viewpoint directly to linear-system solving, $Ax=b$. We construct a simple purely dissipative Lindbladian whose unique fixed point encodes the linear-system solution. We prove dimension-independent trace-distance mixing in $Θ(κ^2\\log(1/\\eps))$ time. We then show how to run this Lindbladian on digital quantum computers via collective block encoding and Lindbladian simulation, resulting in an $O\\!\\left(κ^2\\log(1/\\eps) \\frac{\\log(κ/\\eps)}{\\log\\log(κ/\\eps)}\\right)$ query complexity for both $U_A$, the block encoding of $A$, and $U_b$, the $|b\\rangle$ state preparation unitary.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12284",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhong-Xia Shang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8bjqpv2n0r08v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12284",
  "fulltext_url": null,
  "id": "8bjqpv2n0r08v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12284",
  "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": "W7212899484",
  "pdf_url": "https://arxiv.org/pdf/2609.12284",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8bjqpv2n0r08v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:07Z",
      "native_id": "2609.12284",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12284"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A Simple Quantum Linear-System Solver via Dissipation",
  "title_text": "A Simple Quantum Linear-System Solver via Dissipation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:07Z",
  "url": "https://research.draconitic.com/paper/8bjqpv2n0r08v",
  "venue": "arXiv",
  "versions": []
}