{
  "annotation_id": "5530e457-7aa2-4ce6-9997-aff553785c8e",
  "date_created": "2026-03-02T18:02:03.199000Z",
  "date_modified": "2026-03-02T18:02:03.199000Z",
  "file_hash": "0ecd3add7413d853a15b2feedea84571b0dd4317584fd724de83b89446e0ae2a",
  "private": false,
  "record": {
    "abstract": "Fault-tolerant logical operations for qubits encoded by CSS codes are\ndiscussed, with emphasis on methods that apply to codes of high rate, encoding\nk qubits per block with k\u003e1. It is shown that the logical qubits within a given\nblock can be prepared by a single recovery operation in any state whose\nstabilizer generator separates into X and Z parts. Optimized methods to move\nlogical qubits around and to achieve controlled-not and Toffoli gates are\ndiscussed. It is found that the number of time-steps required to complete a\nfault-tolerant quantum computation is the same when k\u003e1 as when k=1.",
    "arxiv_id": "quant-ph/0311014",
    "authors": [
      "Andrew M. Steane",
      "Ben Ibinson"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.72.052335",
    "title": "Fault-Tolerant Logical Gate Networks for CSS Codes",
    "url": "https://arxiv.org/abs/quant-ph/0311014"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "63a8f3d0-3dd9-4160-8270-c4a53b87d49e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}