{
  "annotation_id": "b6b971cb-5e62-4421-80af-2995ec0577c1",
  "date_created": "2026-03-02T18:02:31.102000Z",
  "date_modified": "2026-03-02T18:02:31.102000Z",
  "file_hash": "72224af5cab831efb31d0cd5ffdb51c44c9cdaca84045c7d05bf30ba9add4254",
  "private": false,
  "record": {
    "abstract": "A quantum walk, \\emph{i.e.}, the quantum evolution of a particle on a graph,\nis termed \\emph{scalar} if the internal space of the moving particle (often\ncalled the coin) has a dimension one. Here, we study the existence of scalar\nquantum walks on Cayley graphs, which are built from the generators of a group.\nAfter deriving a necessary condition on these generators for the existence of a\nscalar quantum walk, we present a general method to express the evolution\noperator of the walk, assuming homogeneity of the evolution. We use this\nnecessary condition and the subsequent constructive method to investigate the\nexistence of scalar quantum walks on Cayley graphs of various groups presented\nwith two or three generators. In this restricted framework, we classify all\ngroups -- in terms of relations between their generators -- that admit scalar\nquantum walks, and we also derive the form of the most general evolution\noperator. Finally, we point out some interesting special cases, and extend our\nstudy to a few examples of Cayley graphs built with more than three generators.",
    "arxiv_id": "quant-ph/0609234",
    "authors": [
      "Olga Lopez Acevedo",
      "J\u00e9r\u00e9mie Roland",
      "Nicolas J. Cerf"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "Quantum Information \u0026 Computation, 8(1\u00262):68-81, 2008.",
    "title": "Exploring scalar quantum walks on Cayley graphs",
    "url": "https://arxiv.org/abs/quant-ph/0609234"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "15bc5cdd-bccc-47c5-8e26-d51e167db3ae",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}