{
  "annotation_id": "b19f3a62-0919-456b-8e60-6686b43e3c44",
  "date_created": "2026-03-02T18:01:45.902000Z",
  "date_modified": "2026-03-02T18:01:45.902000Z",
  "file_hash": "85d12ee2872ca1124739f15bd692349a4ccf6cde64a893b4eea1306d53ad2768",
  "private": false,
  "record": {
    "abstract": "We analyze the quantum walk in higher spatial dimensions and compare\nclassical and quantum spreading as a function of time. Tensor products of\nHadamard transformations and the discrete Fourier transform arise as natural\nextensions of the quantum coin toss in the one-dimensional walk simulation, and\nother illustrative transformations are also investigated. We find that\nentanglement between the dimensions serves to reduce the rate of spread of the\nquantum walk. The classical limit is obtained by introducing a random phase\nvariable.",
    "arxiv_id": "quant-ph/0108004",
    "authors": [
      "Troy D. Mackay",
      "Stephen D. Bartlett",
      "Leigh T. Stephenson",
      "Barry C. Sanders"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/35/12/304",
    "journal_ref": "J. Phys. A: Math. Gen. 35, 2745 (2002)",
    "title": "Quantum walks in higher dimensions",
    "url": "https://arxiv.org/abs/quant-ph/0108004"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "35dfadea-2331-4b45-b40d-e542a463e52d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}