{
  "abstract": "We introduce \"matrix product belief propagation\" (MP-BP) as a controlled method for the approximate contraction of two-dimensional tensor networks and graphical models, which generically leads to a quadratic reduction of errors relative to existing methods: at similar computational effort, the number of accurate digits is asymptotically doubled. For infinite systems, MP-BP can be understood as a practical implementation of Baxter's corner-transfer-matrix method; for reflection-symmetric networks, it further coincides with the boundary matrix-product-state and corner-transfer-matrix renormalization group algorithms as conventionally implemented. In the limit of unit matrix-product rank, MP-BP is equivalent to belief propagation, and more generally, can be understood as a generalization of BP in which the \"messages\" live on surfaces and are assumed to have a matrix-product factorization. We further extend the quadratic improvement to the computation of expectation values, and numerically demonstrate the qualitatively improved convergence for a variety of classical and quantum 2D tensor network problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05598",
  "author_total": 6,
  "authors": [
    {
      "name": "Gabriel Woolls"
    },
    {
      "name": "Shahin Jahanbani"
    },
    {
      "name": "Adarsh Pashikanti"
    },
    {
      "name": "Matthew T. Fishman"
    },
    {
      "name": "Joseph Tindall"
    },
    {
      "name": "Michael P. Zaletel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dwym3hnb375vz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05598",
  "fulltext_url": null,
  "id": "dwym3hnb375vz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05598",
  "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",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7211997902",
  "pdf_url": "https://arxiv.org/pdf/2609.05598",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dwym3hnb375vz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.05598",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05598"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Matrix Product Belief Propagation",
  "title_text": "Matrix Product Belief Propagation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:48Z",
  "url": "https://research.draconitic.com/paper/dwym3hnb375vz",
  "venue": "arXiv",
  "versions": []
}