{
  "abstract": "Every 3-regular graph of girth at least $g$ has a cut containing at least a fraction $M_g$ of its edges, and the best rigorous bounds at large girth are $0.912\\le \\lim_{g\\to\\infty}M_g \\le 0.92386$. Lower bounds on $M_g$ follow from the performance of local algorithms: on a graph of girth $g \\ge 2p+2$ a depth-$p$ local algorithm sees the same tree around every edge, so its expected cut fraction on that tree bounds $M_g$ from below. We apply this strategy to the Variational Iterative Rotation Algorithm (VIRAL), a classical local algorithm, and evaluate it on the depth-$p$ tree for every even depth up to $p=32$. The resulting bounds exceed those recently obtained from the Quantum Approximate Optimization Algorithm (QAOA) for every $p\\ge 4$, by $0.005$ to $0.011$, and they extend the range of girths covered from $g=36$ to $g=66$. Notably, at $g=66$ we obtain $M_{66} \\ge 0.9127$ at $99.99999\\%$ confidence level, which raises the asymptotic lower bound from $0.912$ to $0.9127$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17236",
  "author_total": 3,
  "authors": [
    {
      "name": "Flaviano Morone"
    },
    {
      "name": "Shivang Rawat"
    },
    {
      "name": "Dries Sels"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/55qn49sg9bba3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17236",
  "fulltext_url": null,
  "id": "55qn49sg9bba3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17236",
  "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",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7221829193",
  "pdf_url": "https://arxiv.org/pdf/2610.17236",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/55qn49sg9bba3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.17236",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17236"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Whither quantum advantage? New classical lower bounds for Max-Cut on large-girth 3-regular graphs",
  "title_text": "Whither quantum advantage? New classical lower bounds for Max-Cut on large-girth 3-regular graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/55qn49sg9bba3",
  "venue": "arXiv",
  "versions": []
}