{
  "annotation_id": "d8189e46-60fb-4589-ab47-5023501eff76",
  "date_created": "2026-03-02T18:02:44.591000Z",
  "date_modified": "2026-03-02T18:02:44.591000Z",
  "file_hash": "c592a131525181f66bc9b8685c428f2c4d083c16b72da222f0985ef834d9c141",
  "private": false,
  "record": {
    "abstract": "Since Shor\u0027s discovery of an algorithm to factor numbers on a quantum\ncomputer in polynomial time, quantum computation has become a subject of\nimmense interest. Unfortunately, one of the key features of quantum computers -\nthe difficulty of describing them on classical computers - also makes it\ndifficult to describe and understand precisely what can be done with them. A\nformalism describing the evolution of operators rather than states has proven\nextremely fruitful in understanding an important class of quantum operations.\nStates used in error correction and certain communication protocols can be\ndescribed by their stabilizer, a group of tensor products of Pauli matrices.\nEven this simple group structure is sufficient to allow a rich range of quantum\neffects, although it falls short of the full power of quantum computation.",
    "arxiv_id": "quant-ph/9807006",
    "authors": [
      "Daniel Gottesman"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "Group22: Proceedings of the XXII International Colloquium on Group\n  Theoretical Methods in Physics, eds. S. P. Corney, R. Delbourgo, and P. D.\n  Jarvis, pp. 32-43 (Cambridge, MA, International Press, 1999)",
    "title": "The Heisenberg Representation of Quantum Computers",
    "url": "https://arxiv.org/abs/quant-ph/9807006"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a84aad81-cdc3-4fa6-b805-0a2b5f90449e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}