{
  "annotation_id": "1f7d7e21-d925-440e-9377-60c079cb1f51",
  "date_created": "2026-03-02T18:02:00.267000Z",
  "date_modified": "2026-03-02T18:02:00.267000Z",
  "file_hash": "22000e653f880c3dec49da31f72012b1e9ad9fe7dfcc14381aa5decf84706a6b",
  "private": false,
  "record": {
    "abstract": "We consider asymptotic behaviour of a Hadamard walk on a cycle. For a walk\nwhich starts with a state in which all the probability is concentrated on one\nnode, we find the explicit formula for the limiting distribution and discuss\nits asymptotic behaviour when the length of the cycle tends to infinity. We\nalso demonstrate that for a carefully chosen initial state, the limiting\ndistribution of a quantum walk on cycle can lie further away from the uniform\ndistribution than its initial state.",
    "arxiv_id": "quant-ph/0304113",
    "authors": [
      "Malgorzata Bednarska",
      "Andrzej Grudka",
      "Pawel Kurzynski",
      "Tomasz Luczak",
      "Antoni Wojcik"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1016/j.physleta.2003.08.023",
    "journal_ref": "Phys. Lett. A 317 (2003) 21",
    "title": "Quantum walks on cycles",
    "url": "https://arxiv.org/abs/quant-ph/0304113"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3c35a124-ee0a-40ca-8e8a-f5545f12ba63",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}