{
  "annotation_id": "557cb050-56af-4508-b6fe-8dff4a66df85",
  "date_created": "2026-03-02T18:02:23.900000Z",
  "date_modified": "2026-03-02T18:02:23.900000Z",
  "file_hash": "e8dec067fd9d774bf7e3ce33e5ac2e8c926196c627c1464b7f3382eb3635e92d",
  "private": false,
  "record": {
    "abstract": "We prove upper and lower bounds relating the quantum gate complexity of a\nunitary operation, U, to the optimal control cost associated to the synthesis\nof U. These bounds apply for any optimal control problem, and can be used to\nshow that the quantum gate complexity is essentially equivalent to the optimal\ncontrol cost for a wide range of problems, including time-optimal control and\nfinding minimal distances on certain Riemannian, subriemannian, and Finslerian\nmanifolds. These results generalize the results of Nielsen, Dowling, Gu, and\nDoherty, Science 311, 1133-1135 (2006), which showed that the gate complexity\ncan be related to distances on a Riemannian manifold",
    "arxiv_id": "quant-ph/0603160",
    "authors": [
      "Michael A. Nielsen",
      "Mark R. Dowling",
      "Mile Gu",
      "Andrew C. Doherty"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.73.062323",
    "title": "Optimal control, geometry, and quantum computing",
    "url": "https://arxiv.org/abs/quant-ph/0603160"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "98f1fd47-3d02-42bf-889a-a26fddf7dd1b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}