{
  "abstract": "Quantum linear-system algorithms access the coefficient matrix through a block-encoding oracle $U_A$ and the right-hand side through a state-preparation oracle $U_b$. The optimal query complexities of these two oracles are known separately: $O(κ\\log(1/\\varepsilon))$ queries to $U_A$ and $O(κ/s)$ queries to $U_b$, where $s=α\\|A^{-1}b\\|$. Whether a single algorithm can achieve both bounds simultaneously has remained open. We resolve this question affirmatively. Given a constant-factor estimate of $s$, we give a quantum linear-system algorithm that prepares the normalized solution to error $\\varepsilon$ using simultaneously $ O\\left(κ\\log\\frac1\\varepsilon\\right)$ queries to $U_A$ and $O\\left(κ/{s}\\right)$ queries to $U_b$. The algorithm separates state preparation from precision refinement, so only the matrix-query count depends on the target accuracy. We also prove a matching same-instance worst-case lower bound: for every quantum linear-system algorithm and every solution-norm scale, there exists a single Hermitian instance on which that algorithm requires both $Ω(κ\\log(1/\\varepsilon))$ matrix queries and $Ω(κ/s)$ state-preparation queries. Thus the two oracle complexities can be optimized simultaneously, and the resulting bounds are jointly optimal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33686",
  "author_total": 3,
  "authors": [
    {
      "name": "Minbo Gao"
    },
    {
      "name": "Zhengfeng Ji"
    },
    {
      "name": "Chenghua Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6ca0mm6htxyav.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33686",
  "fulltext_url": null,
  "id": "6ca0mm6htxyav",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33686",
  "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": "W7214754214",
  "pdf_url": "https://arxiv.org/pdf/2609.33686",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6ca0mm6htxyav.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.33686",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33686"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Simultaneously Query-Optimal Quantum Linear-System Algorithm",
  "title_text": "Simultaneously Query-Optimal Quantum Linear-System Algorithm",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/6ca0mm6htxyav",
  "venue": "arXiv",
  "versions": []
}