{
  "abstract": "The Minimum Vertex Cover (MVC) problem is a fundamental NP-hard combinatorial optimization problem with applications in network analysis and resource allocation. Grover's algorithm provides a quadratic reduction in query complexity for unstructured search, but existing Grover-based MVC formulations can incur substantial quantum resource overhead due to costly vertex-counting circuits and complex oracle constructions. We develop and evaluate several encoding and oracle-design strategies for reducing the qubit count, circuit depth, and gate complexity of Grover-based MVC search. First, we construct a Dicke-Parallel formulation that restricts the search to fixed-cardinality subsets, eliminating explicit vertex counting, together with a parallel edge-verification oracle that reduces feasibility-checking overhead. We then develop an Edge-Counting formulation that replaces per-edge auxiliary storage with a logarithmic-size counting register, substantially reducing ancillary-qubit requirements. Finally, we propose an Edge-Centric encoding that represents endpoint selections directly and derives vertex-selection states through incident-edge Boolean operations, enabling more depth-efficient oracle construction. Our resource analysis reveals complementary trade-offs among qubit width, circuit depth, gate count, and Grover iteration count. Edge-Counting is particularly attractive under tight qubit constraints, while Edge-Centric can reduce both circuit depth and Grover iteration count when the graph has a moderate edge count and sufficient representation multiplicity. Dicke-Parallel provides a more robust choice when such multiplicity is limited or graph density makes the edge-based search space large. These results provide practical guidance for selecting Grover-based MVC formulations according to hardware constraints and graph structure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07252",
  "author_total": 6,
  "authors": [
    {
      "name": "Beilei Jiang"
    },
    {
      "name": "Harry Fu"
    },
    {
      "name": "Pavan Krishna Yarlagadda"
    },
    {
      "name": "Alexander Shan"
    },
    {
      "name": "Yunhe Feng"
    },
    {
      "name": "Song Fu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5vj7jwe00qshp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07252",
  "fulltext_url": null,
  "id": "5vj7jwe00qshp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07252",
  "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",
      "cs.ET"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7220897034",
  "pdf_url": "https://arxiv.org/pdf/2610.07252",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5vj7jwe00qshp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2610.07252",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07252"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Resource-Aware Grover Search for Minimum Vertex Cover",
  "title_text": "Resource-Aware Grover Search for Minimum Vertex Cover",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:22Z",
  "url": "https://research.draconitic.com/paper/5vj7jwe00qshp",
  "venue": "arXiv",
  "versions": []
}