{
  "annotation_id": "c7a37bf1-d853-4f7e-826c-88cae5b94860",
  "date_created": "2026-03-02T18:02:03.422000Z",
  "date_modified": "2026-03-02T18:02:03.422000Z",
  "file_hash": "b08993c51b0d9bfd5ec44232dba3b51d96191b1be502368eb44b364eafcaec5b",
  "private": false,
  "record": {
    "abstract": "Unitary operations are expressed in the quantum circuit model as a finite\nsequence of elementary gates, such as controlled-not gates and single qubit\ngates. We prove that the simplified Toffoli gate by Margolus, which coincides\nwith the Toffoli gate up to a single change of sign, cannot be realized with\nless than three controlled-not gates. If the circuit is implemented with three\ncontrolled-not gates, then at least four additional single qubit gates are\nnecessary. This proves that the implementation suggested by Margolus is\noptimal.",
    "arxiv_id": "quant-ph/0312225",
    "authors": [
      "Guang Song",
      "Andreas Klappenecker"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "The simplified Toffoli gate implementation by Margolus is optimal",
    "url": "https://arxiv.org/abs/quant-ph/0312225"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5280822b-b9f6-4065-bff4-d1df88afc4f4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}