{
  "abstract": "In this work, we analyze the average-case hardness of approximation for the Quantum Hypergraph Max-Cut problem using the theoretical framework of the Quantum Overlap Gap Property (QOGP). We establish two main results. Our first result applies to a wide class of stable quantum algorithms, satisfying a Lipschitz property with respect to the quantum Wasserstein distance of order $2$. We show a weak hardness result, demonstrating that for any Lipschitz constant $L$, there is some $k$ such that $L$-stable algorithms cannot approximate the optimal solution to Quantum Hypergraph Max-Cut on $k$-uniform hypergraphs in the average case. Additionally, we establish a strong hardness result where $k$ is independent of $L$, but only for a more restricted class of local quantum algorithms defined using the quantum Wasserstein distance of order $\\infty$. We apply these results to establish concrete depth lower bounds for popular quantum algorithms for preparing near-optimal states for this problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10838",
  "author_total": 2,
  "authors": [
    {
      "name": "Mikhail Mints"
    },
    {
      "name": "Eric R. Anschuetz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8xy497z38psxr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10838",
  "fulltext_url": null,
  "id": "8xy497z38psxr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10838",
  "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",
      "cs.CC"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7212225413",
  "pdf_url": "https://arxiv.org/pdf/2609.10838",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8xy497z38psxr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:26Z",
      "native_id": "2609.10838",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10838"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "The Quantum Overlap Gap Property and Algorithmic Hardness for the Quantum Hypergraph Max-Cut Problem",
  "title_text": "The Quantum Overlap Gap Property and Algorithmic Hardness for the Quantum Hypergraph Max-Cut Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:26Z",
  "url": "https://research.draconitic.com/paper/8xy497z38psxr",
  "venue": "arXiv",
  "versions": []
}