{
  "annotation_id": "cf235e8c-d6af-44c0-ab15-837f28c7fa33",
  "date_created": "2026-03-02T18:02:34.416000Z",
  "date_modified": "2026-03-02T18:02:34.416000Z",
  "file_hash": "76949692e604d920568903234a7cc9efc8e6930ff4889a859f562007437f2a14",
  "private": false,
  "record": {
    "abstract": "Recently, Nielsen et al have proposed a geometric approach to quantum\ncomputation. They\u0027ve shown that the size of the minimum quantum circuits\nimplementing a unitary U, up to polynomial factors, equals to the length of\nminimal geodesic from identity I through U. They\u0027ve investigated a large class\nof solutions to the geodesic equation, called Pauli geodesics. They\u0027ve raised a\nnatural question whether we can explicitly construct a family of unitaries U\nthat have exponentially long minimal length Pauli geodesics? We give a positive\nanswer to this question.",
    "arxiv_id": "quant-ph/0701202",
    "authors": [
      "Wei Huang"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "An explicit family of unitaries with exponentially minimal length Pauli   geodesics",
    "url": "https://arxiv.org/abs/quant-ph/0701202"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "34b6542c-4b47-433e-b838-e989159c7991",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}