{
  "annotation_id": "30b6eecc-4c6c-4465-8dda-356b677411ba",
  "date_created": "2026-03-02T18:02:10.048000Z",
  "date_modified": "2026-03-02T18:02:10.048000Z",
  "file_hash": "d88d931c34a1bd9fd271df72de1c4bb9a133d4c2fa45e70819cc5157953023c5",
  "private": false,
  "record": {
    "abstract": "We describe generalizations of the Pauli group, the Clifford group and\nstabilizer states for qudits in a Hilbert space of arbitrary dimension d. We\nexamine a link with modular arithmetic, which yields an efficient way of\nrepresenting the Pauli group and the Clifford group with matrices over the\nintegers modulo d. We further show how a Clifford operation can be efficiently\ndecomposed into one and two-qudit operations. We also focus in detail on\nstandard basis expansions of stabilizer states.",
    "arxiv_id": "quant-ph/0408190",
    "authors": [
      "Erik Hostens",
      "Jeroen Dehaene",
      "Bart De Moor"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.71.042315",
    "journal_ref": "Phys. Rev. A 71, 042315 (2005)",
    "title": "Stabilizer states and Clifford operations for systems of arbitrary   dimensions, and modular arithmetic",
    "url": "https://arxiv.org/abs/quant-ph/0408190"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "199ed651-70f2-4ac5-967d-357038d73db4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}