{
  "annotation_id": "d19930ed-dfa6-4511-a6d1-54fe48d5a7f1",
  "date_created": "2026-03-02T18:02:44.488000Z",
  "date_modified": "2026-03-02T18:02:44.488000Z",
  "file_hash": "97bd2bfeb5ff3cfaca7121f90b4d6b91859fb064704fa077a15654b3c8532c3a",
  "private": false,
  "record": {
    "abstract": "Let ${\\cal H}$ be the state-space of a quantum computer coupled with the\nenvironment by a set of error operators spanning a Lie algebra ${\\cal L}.$\nSuppose ${\\cal L}$ admits a noiseless quantum code i.e., a subspace ${\\cal\nC}\\subset{\\cal H}$ annihilated by ${\\cal L}.$ We show that a universal set of\ngates over $\\cal C$ is obtained by any generic pair of ${\\cal L}$-invariant\ngates. Such gates - if not available from the outset - can be obtained by\nresorting to a symmetrization with respect to the group generated by ${\\cal\nL}.$ Any computation can then be performed completely within the coding\ndecoherence-free subspace.",
    "arxiv_id": "quant-ph/9901047",
    "authors": [
      "Paolo Zanardi"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.60.R729",
    "journal_ref": "Phys. Rev. A 60 (1999) R729",
    "title": "Computation on a Noiseless Quantum Code and Symmetrization",
    "url": "https://arxiv.org/abs/quant-ph/9901047"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "300fda95-3767-4389-8156-34f1ed20af68",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}