{
  "abstract": "Two-stage stochastic combinatorial optimisation concerns discrete decisions made before all relevant information is known. An initial decision is made; once uncertainty is resolved, it can be adapted to the realised scenario, at a cost. The aim is to find the initial decision that minimises the upfront cost plus the expected cost of optimal adaptation. The first-stage decision problem is often NP-hard, and computing the expected minimum recourse cost can be $\\#\\mathrm{P}$-hard for a single first-stage candidate. We introduce Quantum Approximate Stochastic Combinatorial Optimisation (QASCO), a variational quantum-walk ansatz that coherently incorporates scenario-dependent recourse into its dynamics to search over first-stage decisions without explicitly evaluating expected minimum recourse costs. We demonstrate QASCO for MaxCut with stochastic edge weights, obtain a circuit with polynomial per-layer gate complexity, and study the ansatz via exact state-vector simulation. Across the instances considered, QASCO concentrates amplitude more effectively on stochastic-optimal first-stage decisions than a previously proposed two-stage QAOA construction. We further show that the ansatz can be calibrated using a depth-independent number of parameters and applied to unseen instances without further circuit-parameter optimisation, including joint decision--scenario--recourse spaces spanning more than $2^{32}$ configurations. Under a query-cost model, comparison with the tested classical heuristics using sample-average approximations of the expected minimum recourse cost shows that QASCO more reliably reaches globally optimal first-stage solutions while requiring fewer cut evaluations. These results show how to incorporate scenario-dependent recourse into the ansatz dynamics, providing a general framework for variational quantum walks in two-stage stochastic combinatorial optimisation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22876",
  "author_total": 4,
  "authors": [
    {
      "name": "Edric Matwiejew"
    },
    {
      "name": "Paulo E. Santos"
    },
    {
      "name": "Jingbo B. Wang"
    },
    {
      "name": "Ugo Varetto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dpk7tbkkehzb8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22876",
  "fulltext_url": null,
  "id": "dpk7tbkkehzb8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22876",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7222972768",
  "pdf_url": "https://arxiv.org/pdf/2610.22876",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dpk7tbkkehzb8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:32Z",
      "native_id": "2610.22876",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22876"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum approximate stochastic combinatorial optimisation",
  "title_text": "Quantum approximate stochastic combinatorial optimisation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:28Z",
  "url": "https://research.draconitic.com/paper/dpk7tbkkehzb8",
  "venue": "arXiv",
  "versions": []
}