{
  "annotation_id": "6e63ab96-e28c-4ba6-910a-76dccde2e213",
  "date_created": "2026-03-02T18:02:38.209000Z",
  "date_modified": "2026-03-02T18:02:38.209000Z",
  "file_hash": "9eb864851d04afa6b9541d4e9d0bafd2aed5e91c0e757a017dc4614cc5bd4a20",
  "private": false,
  "record": {
    "abstract": "Recently, it was realized that use of the properties of quantum mechanics\nmight speed up certain computations dramatically. Interest in quantum\ncomputation has since been growing. One of the main difficulties of realizing\nquantum computation is that decoherence tends to destroy the information in a\nsuperposition of states in a quantum computer, thus making long computations\nimpossible. A futher difficulty is that inaccuracies in quantum state\ntransformations throughout the computation accumulate, rendering the output of\nlong computations unreliable. It was previously known that a quantum circuit\nwith t gates could tolerate O(1/t) amounts of inaccuracy and decoherence per\ngate. We show, for any quantum computation with t gates, how to build a\npolynomial size quantum circuit that can tolerate O(1/(log t)^c) amounts of\ninaccuracy and decoherence per gate, for some constant c. We do this by showing\nhow to compute using quantum error correcting codes. These codes were\npreviously known to provide resistance to errors while storing and transmitting\nquantum data.",
    "arxiv_id": "quant-ph/9605011",
    "authors": [
      "Peter W. Shor"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Fault-tolerant quantum computation",
    "url": "https://arxiv.org/abs/quant-ph/9605011"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c36b2a6a-444a-45e6-9b7d-baea39e7c373",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}