{
  "annotation_id": "05d2023d-2139-4f71-afa3-ed50a4138f5f",
  "date_created": "2026-03-02T18:01:51.785000Z",
  "date_modified": "2026-03-02T18:01:51.785000Z",
  "file_hash": "cb1bc08e4a997206283887cb8570678048d2322e5297bacdeea84f55188a012d",
  "private": false,
  "record": {
    "abstract": "What additional gates are needed for a set of classical universal gates to do\nuniversal quantum computation? We answer this question by proving that any\nsingle-qubit real gate suffices, except those that preserve the computational\nbasis.\n  The result of Gottesman and Knill[quant-ph/9807006] implies that any quantum\ncircuit involving only the Controlled-NOT and Hadamard gates can be efficiently\nsimulated by a classical circuit. In contrast, we prove that Controlled-NOT\nplus any single-qubit real gate that does not preserve the computational basis\nand is not Hadamard (or its alike) are universal for quantum computing.\n  Previously only a ``generic\u0027\u0027 gate, namely a rotation by an angle\nincommensurate with pi, is known to be sufficient in both problems, if only one\nsingle-qubit gate is added.",
    "arxiv_id": "quant-ph/0205115",
    "authors": [
      "Yaoyun Shi"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Both Toffoli and Controlled-NOT need little help to do universal quantum   computation",
    "url": "https://arxiv.org/abs/quant-ph/0205115"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3d29fc1c-a633-4446-b4ac-9097dc25d8f0",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}