{
  "abstract": "We study the quantum evolution induced by graph-indexed Ising Hamiltonians as a source of structural signal for graph learning. Graph automorphisms preserve symmetries of the Hamiltonian, and these symmetries constrain the quantum evolution in a way that turns time-dependent local measurements into informative probes of graph structure. Leveraging this idea, we introduce QDAGer, a quantum-inspired graph-pair Transformer that injects quantum-dynamical features from time series of node occupations and connected two-point correlators directly into the attention mechanism. We apply QDAGer to learning Graph Edit Distance (GED), an NP-hard similarity measure, using either a direct permutation-invariant embedding discrepancy or an alignment-based surrogate loss. Experiments on multiple GED benchmarks under different edit cost settings show that the proposed dynamical features provide a stronger inductive bias than classical structural alternatives under the same training protocol. In addition, we report ablations where the dynamical signal is replaced by standard random-walk and heat-kernel features while keeping the architecture fixed, highlighting that the gain comes from the injected dynamics rather than model capacity alone.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.17750",
  "author_total": 2,
  "authors": [
    {
      "name": "Mehdi Djellabi"
    },
    {
      "name": "Louis-Paul Henry"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6jv074r9aajgp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.17750",
  "fulltext_url": null,
  "id": "6jv074r9aajgp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.17750",
  "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": "W7203775983",
  "pdf_url": "https://arxiv.org/pdf/2608.17750",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6jv074r9aajgp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2608.17750",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.17750"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "On the Expressive Power of the Transverse-Field Ising Model for Graph Learning",
  "title_text": "On the Expressive Power of the Transverse-Field Ising Model for Graph Learning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:19Z",
  "url": "https://research.draconitic.com/paper/6jv074r9aajgp",
  "venue": "arXiv",
  "versions": []
}