{
  "annotation_id": "9070c6b1-cd97-425d-af2b-c9a9e319d340",
  "date_created": "2026-03-02T18:02:48.046000Z",
  "date_modified": "2026-03-02T18:02:48.046000Z",
  "file_hash": "0d85d244c7769beee97be7a6c8be961d3e24db72d20752ab113395aaf5f9f290",
  "private": false,
  "record": {
    "abstract": "A novel universal and fault-tolerant basis (set of gates) for quantum\ncomputation is described. Such a set is necessary to perform quantum\ncomputation in a realistic noisy environment. The new basis consists of two\nsingle-qubit gates (Hadamard and ${\\sigma_z}^{1/4}$), and one double-qubit gate\n(Controlled-NOT). Since the set consisting of Controlled-NOT and Hadamard gates\nis not universal, the new basis achieves universality by including only one\nadditional elementary (in the sense that it does not include angles that are\nirrational multiples of $\\pi$) single-qubit gate, and hence, is potentially the\nsimplest universal basis that one can construct. We also provide an alternative\nproof of universality for the only other known class of universal and\nfault-tolerant basis proposed by Shor and by Kitaev.",
    "arxiv_id": "quant-ph/9906054",
    "authors": [
      "P. Oscar Boykin",
      "Tal Mor",
      "Matthew Pulver",
      "Vwani Roychowdhury",
      "Farrokh Vatan"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "On Universal and Fault-Tolerant Quantum Computing",
    "url": "https://arxiv.org/abs/quant-ph/9906054"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9d25fa1f-4822-4684-aa03-a7034003acbc",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}