{
  "annotation_id": "5b0ffc0e-5cf8-45cd-a1b4-47dfa5a3e58f",
  "date_created": "2026-03-02T18:02:03.468000Z",
  "date_modified": "2026-03-02T18:02:03.468000Z",
  "file_hash": "ae086fccf30610f61de069ee22c864a55f1bab8673e6d4278b91ab81698564ba",
  "private": false,
  "record": {
    "abstract": "This note introduces some examples of quantum random walks in d-dimensional\nEucilidean space and proves the weak convergence of their rescaled n-step\ndensities. One of the examples is called the Plancherel quantum walk because\nthe \"quantum coin flip\" is the Fourier Integral (or Plancherel) Transform. The\nother examples are the Birkhoff quantum walks, so named because the coin flips\nare effected by means of measure preserving transformations to which the\nBirkhoff\u0027s Ergodic Theorem is applied.",
    "arxiv_id": "quant-ph/0310026",
    "authors": [
      "Alex D. Gottlieb"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Two examples of discrete-time quantum walks taking continuous steps",
    "url": "https://arxiv.org/abs/quant-ph/0310026"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f5fd8640-080f-44b0-ae59-1f8e45d53a86",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}