{
  "abstract": "Quantum Max-Cut is a well-studied local Hamiltonian problem for which the classical complexity of the bipartite case remains open. We give a polynomial-time classical randomized algorithm for the spin-$\\tfrac12$ antiferromagnetic Heisenberg model, equivalently Quantum Max-Cut, on dense balanced bipartite expanders. This class includes $G(n,n,p)$ with high probability for every fixed $p>0$. The algorithm estimates the ground energy and any ground state edge correlation to additive error $\\varepsilon$ in time polynomial in $n$ and $1/\\varepsilon$. We construct a Markov chain on perfect matchings of the complete bipartite graph, each matching representing a product of singlets, that converges to the ground state, and use the expansion of the graph to show that polynomially many steps and samples of this chain suffice.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03670",
  "author_total": 3,
  "authors": [
    {
      "name": "Stuart Wayland"
    },
    {
      "name": "Zackary Jorquera"
    },
    {
      "name": "Alexandra Kolla"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dj4ssf2jq42dy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03670",
  "fulltext_url": null,
  "id": "dj4ssf2jq42dy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03670",
  "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": "W7220466733",
  "pdf_url": "https://arxiv.org/pdf/2610.03670",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dj4ssf2jq42dy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.03670",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03670"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Classical Algorithms for Bipartite Quantum Max-Cut on Dense Expanders",
  "title_text": "Classical Algorithms for Bipartite Quantum Max-Cut on Dense Expanders",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:45Z",
  "url": "https://research.draconitic.com/paper/dj4ssf2jq42dy",
  "venue": "arXiv",
  "versions": []
}