{
  "annotation_id": "890ab81d-54a0-4d4d-b885-3900d04050fa",
  "date_created": "2026-03-02T18:02:03.471000Z",
  "date_modified": "2026-03-02T18:02:03.471000Z",
  "file_hash": "fde3040542d195f4d277412131cf8b2ea713fcb565507995c21600b505091100",
  "private": false,
  "record": {
    "abstract": "Temporal fluctuations in the Hadamard walk on circles are studied. A temporal\nstandard deviation of probability that a quantum random walker is positive at a\ngiven site is introduced to manifest striking differences between quantum and\nclassical random walks. An analytical expression of the temporal standard\ndeviation on a circle with odd sites is shown and its asymptotic behavior is\nconsidered for large system size. In contrast with classical random walks, the\ntemporal fluctuation of quantum random walks depends on the position and\ninitial conditions, since temporal standard deviation of the classical case is\nzero for any site. It indicates that the temporal fluctuation of the Hadamard\nwalk can be controlled.",
    "arxiv_id": "quant-ph/0309204",
    "authors": [
      "Norio Inui",
      "Yoshinao Konishi",
      "Norio Konno",
      "Takahiro Soshi"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Fluctuations of Quantum Random Walks on Circles",
    "url": "https://arxiv.org/abs/quant-ph/0309204"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d950d1bd-82fb-4de2-89c5-37b22d5c07f2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}