{
  "abstract": "The Heisenberg picture can make quantum many-body simulation efficient when evolved observables admit compact operator representation within low-dimensional structures. Conventional Pauli-string propagation and truncation techniques exploit this structure, but in coherent Hamiltonian dynamics their error control is often heuristic and their stability can be poor. We introduce a state-adapted Krylov framework based on geometric generalized mean-field projections of many-body observables onto low-body operator subspaces. The resulting dynamics approximate expectation values, do not extend spatial support beyond that prescribed by Lieb-Robinson bounds, and compress high-body correlations onto their state-relevant low-body representatives rather than simply discarding them. We derive necessary operator-entanglement obstructions to low-body representation and conditional sufficient bounds on representation and dynamical errors involving nonstabilizerness and controlled high-body tails. Numerical benchmarks show improved, stable finite-$m$ hierarchies and simulations on large three-dimensional lattices, establishing a scalable state-adapted alternative to conventional Heisenberg-picture weight-truncation of Pauli strings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12840",
  "author_total": 3,
  "authors": [
    {
      "name": "Federico Tomás B. Pérez"
    },
    {
      "name": "Gabriela Wójtowicz"
    },
    {
      "name": "Martin B. Plenio"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/at7ydwt049gfb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12840",
  "fulltext_url": null,
  "id": "at7ydwt049gfb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12840",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7212496409",
  "pdf_url": "https://arxiv.org/pdf/2609.12840",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/at7ydwt049gfb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:07Z",
      "native_id": "2609.12840",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12840"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "State-adapted generalized mean-field projections for Pauli propagation of Heisenberg dynamics",
  "title_text": "State-adapted generalized mean-field projections for Pauli propagation of Heisenberg dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/at7ydwt049gfb",
  "venue": "arXiv",
  "versions": []
}