{
  "annotation_id": "978a68f2-6843-42cf-8101-d97ff08ba323",
  "date_created": "2026-03-02T18:02:37.775000Z",
  "date_modified": "2026-03-02T18:02:37.775000Z",
  "file_hash": "3dee6a00ec7a3e93ce50988d6e3da6899189e1c6e79e25f1543570296396be97",
  "private": false,
  "record": {
    "abstract": "We show how to carry out quantum logical operations (controlled-not and\nToffoli gates) on encoded qubits for several encodings which protect against\nvarious 1-bit errors. This improves the reliability of these operations by\nallowing one to correct for one bit errors which either preexisted or occurred\nin course of operation. The logical operations we consider allow one to cary\nout the vast majority of the steps in the quantum factoring algorithm. Thus,\nour results help bring quantum factoring and other quantum computations closer\nto reality",
    "arxiv_id": "quant-ph/9605013",
    "authors": [
      "Wojciech Hubert Zurek",
      "Raymond Laflamme"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevLett.77.4683",
    "title": "Quantum Logical Operations on Encoded Qubits",
    "url": "https://arxiv.org/abs/quant-ph/9605013"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "57f72c77-da99-4e25-83de-38f9fc9ad630",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}