{
  "annotation_id": "720634ab-471b-490d-b840-9250d7d82f0d",
  "date_created": "2026-03-02T18:02:23.619000Z",
  "date_modified": "2026-03-02T18:02:23.619000Z",
  "file_hash": "f7dae4fe8cc92b672eb0591c66d259c70a25eb75b390d0274e97c5cf8432ed98",
  "private": false,
  "record": {
    "abstract": "We introduce a continuous-time quantum walk on an ultrametric space\ncorresponding to the set of p-adic integers and compute its time-averaged\nprobability distribution. It is shown that localization occurs for any location\nof the ultrametric space for the walk. This result presents a striking contrast\nto the classical random walk case. Moreover we clarify a difference between the\nultrametric space and other graphs, such as cycle graph, line, hypercube and\ncomplete graph, for the localization of the quantum case. Our quantum walk may\nbe useful for a quantum search algorithm on a tree-like hierarchical structure.",
    "arxiv_id": "quant-ph/0602070",
    "authors": [
      "Norio Konno"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "International Journal of Quantum Information, Vol.4, No.6,\n  pp.1023-1035 (2006)",
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Continuous-time quantum walks on ultrametric spaces",
    "url": "https://arxiv.org/abs/quant-ph/0602070"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "350896e8-e8b8-40d2-bdf6-477af0eb37d8",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}