{
  "abstract": "The Minimum Birkhoff Decomposition (MBD) seeks a sparse weighted sum of matchings and is a challenging optimization problem with applications in network scheduling and energy trading. We scale a quantum-assisted decomposition method by combining single-layer QAOA sampling with Extended Fully-Corrective Frank-Wolfe (E-FCFW) optimization, spectral graph partitioning, and greedy feasibility repair. We demonstrate the pipeline on the 1,354-node PEGASE bus test case (representing a 1,354-bus transmission grid with 1,710 transmission lines), whose 1,710 edges define a native 1,710-variable matching optimization problem requiring 1,710 qubits in the unpartitioned encoding. Partitioning enables distributed execution on IBM superconducting quantum processors. The best reported hardware result uses a 50-qubit partition bound, while reducing partitions to 20 qubits degrades convergence in the partition-size comparison. Larger partitions are more demanding for matrix product state (MPS) simulation, and bond-dimension tests show that truncating quantum correlations reduces candidate quality. The results therefore motivate retaining a substantive quantum sampling task within each partition as the overall problem scales. On the PEGASE-1354 benchmark, repaired QAOA samples achieve lower residual decomposition error than both simulated annealing and uniform random sampling baselines, while spatial circuit packing reduces hardware execution time by approximately a factor of three. These results demonstrate that combining spectral partitioning, spatial circuit packing, and classical feasibility repair provides an executable path for deploying gate-based quantum sampling on thousand-variable constrained optimization problems on current hardware.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10772",
  "author_total": 9,
  "authors": [
    {
      "name": "Amana Liaqat"
    },
    {
      "name": "Ahmed Darwish"
    },
    {
      "name": "Stephen DiAdamo"
    },
    {
      "name": "Dan Holme"
    },
    {
      "name": "Kieran McDowall"
    },
    {
      "name": "Emre Sahin"
    },
    {
      "name": "Naeimeh Mohseni"
    },
    {
      "name": "Giorgio Cortiana"
    },
    {
      "name": "Corey O'Meara"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6c46hssc7p4ct.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10772",
  "fulltext_url": null,
  "id": "6c46hssc7p4ct",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10772",
  "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",
      "cs.ET"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7221179558",
  "pdf_url": "https://arxiv.org/pdf/2610.10772",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6c46hssc7p4ct.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2610.10772",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10772"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Scaling Quantum Optimization to the Thousand-Qubit Scale with Distributed Quantum Sampling",
  "title_text": "Scaling Quantum Optimization to the Thousand-Qubit Scale with Distributed Quantum Sampling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/6c46hssc7p4ct",
  "venue": "arXiv",
  "versions": []
}