{
  "abstract": "Quantum annealers can sample degenerate optima unevenly, so the composition of finite-read output matters when multiple solutions are sought. We investigate whether problem structure can steer this output through node-dependent anneal offsets for Minimum Vertex Cover (MVC). In MVC, vertex degree equals the number of incident edge-cover constraints and therefore measures local constraint participation. We use this relation to define degree-conditioned offset-scheduled quantum annealing (DC-OSQA), a static rule assigning more negative offsets to vertices with larger max-normalized degree. Experiments used a D-Wave Advantage2 system1 quantum processing unit (QPU). For each graph, DC-OSQA was compared with a zero-offset baseline using the same MVC encoding, fixed physical embedding, majority-vote chain decoding, and 1000-read budget. A sampled bitstring was counted as a certified candidate only if it represented a feasible vertex cover and its cardinality matched the minimum independently certified by integer linear programming. Across 120 paired comparisons on sparse Barabasi-Albert graphs with two attachments per added vertex and graph sizes N = 70-150, DC-OSQA increased the mean number of distinct certified candidates from 171.7 to 455.8 and the mean number of complete-linkage Hamming-distance families from 22.5 to 80.0; paired gains were positive at every tested size. These shifts, together with lower empirical concentration, indicate a change in the composition of the observed certified support. At N = 150, the degree-aligned assignment exceeded the within-instance mean over 20 random reassignments of the same offset values in 19 of 20 graphs for certified-support size and all 20 graphs for Hamming families. Within the tested ensemble, these results show that an MVC-specific degree rule changes the certified optima observed within a fixed QPU read budget.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03379",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiwan Kang"
    },
    {
      "name": "Namshik Han"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aa3rzy5sv5qcp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03379",
  "fulltext_url": null,
  "id": "aa3rzy5sv5qcp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03379",
  "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": "W7220448212",
  "pdf_url": "https://arxiv.org/pdf/2610.03379",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aa3rzy5sv5qcp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.03379",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03379"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Degree-conditioned anneal offsets reshape certified-optimum sampling for minimum vertex cover",
  "title_text": "Degree-conditioned anneal offsets reshape certified-optimum sampling for minimum vertex cover",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:45Z",
  "url": "https://research.draconitic.com/paper/aa3rzy5sv5qcp",
  "venue": "arXiv",
  "versions": []
}