{
  "annotation_id": "33cbe3ac-3670-4ea0-984c-f12e4f947558",
  "date_created": "2026-03-02T18:02:03.478000Z",
  "date_modified": "2026-03-02T18:02:03.478000Z",
  "file_hash": "3ebb87d75528d858ea2012a2ee3ec25086664c65a47dd32231d7cb5565a9096b",
  "private": false,
  "record": {
    "abstract": "The Grover walk, which is related to the Grover\u0027s search algorithm on a\nquantum computer, is one of the typical discrete time quantum walks. However, a\nlocalization of the two-dimensional Grover walk starting from a fixed point is\nstriking different from other types of quantum walks. The present paper\nexplains the reason why the walker who moves according to the degree-four\nGrover\u0027s operator can remain at the starting point with a high probability. It\nis shown that the key factor for the localization is due to the degeneration of\neigenvalues of the time evolution operator. In fact, the global time evolution\nof the quantum walk on a large lattice is mainly determined by the degree of\ndegeneration. The dependence of the localization on the initial state is also\nconsidered by calculating the wave function analytically.",
    "arxiv_id": "quant-ph/0311118",
    "authors": [
      "Norio Inui",
      "Yoshinao Konishi",
      "Norio Konno"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.69.052323",
    "title": "Localization of Two-Dimensional Quantum Walks",
    "url": "https://arxiv.org/abs/quant-ph/0311118"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "623880da-f680-41e9-94ff-f1742be5e31e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}