{
  "annotation_id": "ea7b6388-5d32-42c9-a5f4-70a2670907b3",
  "date_created": "2026-03-02T18:02:24.002000Z",
  "date_modified": "2026-03-02T18:02:24.002000Z",
  "file_hash": "3465db6027112f7bf566baec6788b9c6a0a1bae0060b11e0e86e823f493a8b4e",
  "private": false,
  "record": {
    "abstract": "Geometric phases are important in quantum physics and now central to fault\ntolerant quantum computation. For spin-1/2 and SU(2), the Bloch sphere $S^2$,\ntogether with a U(1) phase, provides a complete SU(2) description. We\ngeneralize to $N$-level systems and SU($N$) in terms of a $2(N-1)$-dimensional\nbase space and reduction to a ($N$-1)-level problem, paralleling closely the\ntwo-dimensional case. This iteratively solves the time evolution of an\n$N$-level system and gives ($N$-1) geometric phases explicitly. A complete\nanalytical construction of a S^4 Bloch-like sphere for two qubits is given for\nthe Spin(5) or SO(5) subgroup of SU(4).",
    "arxiv_id": "quant-ph/0511192",
    "authors": [
      "D. B. Uskov",
      "A. R. P. Rau"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.74.030304",
    "journal_ref": "Phys.Rev.A74:030304,2006",
    "title": "Geometric phase for SU(N) through fiber bundles and unitary integration",
    "url": "https://arxiv.org/abs/quant-ph/0511192"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "39f6ee93-4061-4a3b-bc2b-cf663b4feea9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}