{
  "abstract": "We study discrete-time quantum walks on weighted graphs, where every edge in an edge cut set is assigned a small weight $ε>0$. The parameter $ε$ represents the strength of the connections through the cut edges: as $ε\\to 0$, these connections vanish, and the graph decomposes into the connected components obtained by removing the cut edges. We refer to these weighted cut edges as {\\it weak edges}. We show that, for sufficiently small $ε$ and on the time scale $t=Θ(ε^{-1/2})$, the finding probabilities between the connected components are asymptotically described by a continuous-time wave equation on a reduced graph, whose vertices represent the connected components and whose edges represent the weak edges connecting them. The wave equation is governed by a symmetric weighted Laplacian determined by the reduced graph and the number of arcs contained in the components. Consequently, finding probabilities of leading-term are independent of the detailed internal structures of the components. We further show that this wave equation has the same form as Newton's equation of motion for a classical spring-mass system on the reduced graph.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07768",
  "author_total": 2,
  "authors": [
    {
      "name": "Taisuke Hosaka"
    },
    {
      "name": "Etsuo Segawa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b09tegq37sp8r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07768",
  "fulltext_url": null,
  "id": "b09tegq37sp8r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07768",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7220901488",
  "pdf_url": "https://arxiv.org/pdf/2610.07768",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b09tegq37sp8r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2610.07768",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07768"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Pulsation of quantum walk on finite graph",
  "title_text": "Pulsation of quantum walk on finite graph",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/b09tegq37sp8r",
  "venue": "arXiv",
  "versions": []
}