{
  "abstract": "Comparing solvers for quadratic unconstrained binary optimization (QUBO) requires distinguishing solution quality from optimality certification. We compare classical, tensor-network, and fixed-schedule quantum approaches on 180 benchmark instances from ten families with 14-48 variables, supplemented by harder synthetic instances with known optimal solutions, extending to 128 variables. On the main benchmark, a general-purpose branch-and-cut solver matches all reference energies and certifies 176 instances within a 600,s cap. When the known optima are moved to randomly chosen bitstrings, the search comparison changes: at n = 48 the branch-and-cut solver finds only four of ten optima and certifies none, whereas parallel tempering reaches every optimum in every tested run at a 60,s budget. Structural and trajectory diagnostics explain aspects of tensor-network performance. A treewidth bound ranks trajectory bond-dimension demand at Spearman $ρ= 0.78$ in sample and $0.73$ out of sample, but provides only a coarse runtime estimate. Controlled experiments identify excited-state trapping during warm-started density-matrix renormalization group (DMRG) sweeps and demonstrate mitigation by restarting the variational search. These diagnostics do not yield a validated solver-selection rule. The tested linear-ramp quantum approximate optimization algorithm (LR-QAOA) runs offer no solution-quality improvement over the classical comparators. In the separate Wishart scaling study, on the harder setting, none of the classical methods tested reaches the optimum at the sampled sizes from n = 72 onward within the tested budgets. While this does not provide evidence for quantum advantage, it identifies a domain for further investigation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35126",
  "author_total": 3,
  "authors": [
    {
      "name": "Gerhard Hellstern"
    },
    {
      "name": "Cedric Schacht"
    },
    {
      "name": "Martin Zaefferer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1g0f9z8v4b5s3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35126",
  "fulltext_url": null,
  "id": "1g0f9z8v4b5s3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35126",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7223888756",
  "pdf_url": "https://arxiv.org/pdf/2610.35126",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1g0f9z8v4b5s3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.35126",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35126"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Comparing classical and quantum QUBO solvers: optimality, trajectory diagnostics, and limits of solver selection",
  "title_text": "Comparing classical and quantum QUBO solvers: optimality, trajectory diagnostics, and limits of solver selection",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:35Z",
  "url": "https://research.draconitic.com/paper/1g0f9z8v4b5s3",
  "venue": "arXiv",
  "versions": []
}