{
  "abstract": "This paper studies the cluster-assignment layer of a cluster-first-route-second decomposition for the capacitated pickup-and-delivery problem with time windows (CPDPTW), instead of a direct route-ordering quadratic unconstrained binary optimization (QUBO). Sample-based subspace diagonalization (SQD) degenerates to best-of-shots for any diagonal optimization Hamiltonian, so a useful transfer to routing requires non-diagonal relaxation. Quantum random access optimization (QRAO) provides this non-diagonality by encoding binary variables through non-commuting quantum random access code (QRAC) observables. CPDPTW-derived conflict graphs expose a routing-specific obstruction because dense objectives and penalty-encoded constraints destroy QRAO compression. We keep the Hamiltonian sparse by encoding only the sparsified objective and enforcing one-hot, capacity, and cluster time-budget feasibility by repair after rounding. We make no quantum-advantage claim. Under strong repair the classical pass alone reaches near-optimal cost at the tested sizes. The result is a regime map linking sparsification, achieved compression, linear-combination-of-unitaries (LCU) 1-norm, heavy-hex two-qubit depth, sampling drift, and final routing quality on Qiskit Aer, calibrated FakeTorino, and IBM Heron ibm_quebec. Across a 108-row ideal-calibrated-hardware evaluation grid spanning four to twelve pickup-delivery request pairs, the hardware slice has mean gap 0.0016 and mean device-vs-ideal total variation distance (TVD) 0.279; a decoder ablation at sizes six through twelve isolates the non-diagonal signal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: In the proceeding of IEEE Quantum Artificial Intelligence 2026",
  "arxiv": "2609.19575",
  "author_total": 2,
  "authors": [
    {
      "name": "Farzan Moosavi"
    },
    {
      "name": "Bilal Farooq"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/54b1nhjyzf6r0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19575",
  "fulltext_url": null,
  "id": "54b1nhjyzf6r0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19575",
  "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": "W7213604375",
  "pdf_url": "https://arxiv.org/pdf/2609.19575",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/54b1nhjyzf6r0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.19575",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19575"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Vehicle-Routing Clustering by Sparse Quantum Relaxation",
  "title_text": "Vehicle-Routing Clustering by Sparse Quantum Relaxation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:19Z",
  "url": "https://research.draconitic.com/paper/54b1nhjyzf6r0",
  "venue": "arXiv",
  "versions": []
}