{
  "abstract": "We develop Multivariate Quantum Signal Processing for designing matrix-valued transformations of multiple noncommuting nonnormal block-encoded matrices. Our framework equips quantum transducers with the analytic structure of multiport Infinite-Impulse-Response (IIR) filters and establishes a transfer-function methodology for designing quantum query algorithms. Efficiently computable analytic bounds that hold uniformly across the oracle promise yield efficient quantum circuits with logarithmic error dependence and near-unity success probability, paralleling the approximation-theoretic guarantees of univariate QSP/QSVT. We provide a complete characterization of achievable transfer functions and a principled library of analytic IIR components. Our modular designs greatly improve or resolve the per-oracle query complexity of open multi-oracle problems: (1) Hamiltonian simulation under $H=\\sum_j H_j$ with weighted quasinorm cost $\\approx t\\langle\\vecλ,\\vec C\\rangle_{1/2}+\\mathcal{O}(\\|\\vec C\\|_1\\log(1/ε))$ for block-encoding normalizations $\\vecλ$ and costs $\\vec C$; (2) sparse simulation with optimal time--norm $Θ(\\sqrt{d}\\|H\\|_{\\rm 1\\to2}t)$ and additive error dependence; (3) solving linear systems and (4) differential equations under minimal matrix assumptions with optimal weighted state-preparation and multi-term cost; (5) ground-state preparation and energy estimation; (6) generalized eigenvalue problems. We apply these to exactly simulate downfolded Hamiltonians with leading cost $t\\langle\\vecλ_{\\rm eff},\\vec C_{\\rm eff}\\rangle_{1/2}$ further reduced by fractional dynamic correlation energy contributions from coarse-grained Hamiltonians, and show similar classical-data-input-reduction results for multiscale graph classification via Kron reduction. We also show the online generalization with anisotropic Kalman filtering of streaming quantum data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01125",
  "author_total": 1,
  "authors": [
    {
      "name": "Guang Hao Low"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9jkc35whffbez.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01125",
  "fulltext_url": null,
  "id": "9jkc35whffbez",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01125",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.01125",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9jkc35whffbez.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.01125",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01125"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Multivariate Quantum Signal Processing",
  "title_text": "Multivariate Quantum Signal Processing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/9jkc35whffbez",
  "venue": "arXiv",
  "versions": []
}