{
  "annotation_id": "1ac41384-01bf-46b7-b070-3988c5e2afcc",
  "date_created": "2026-03-02T18:02:06.978000Z",
  "date_modified": "2026-03-02T18:02:06.978000Z",
  "file_hash": "c4a6432e60947a74236908cd8fc9b4c24e6dc5b1ff2adb26030121fb6dcd3356",
  "private": false,
  "record": {
    "abstract": "We consider a model of quantum computation in which the set of elementary\noperations is limited to Clifford unitaries, the creation of the state\n$|0\\rangle$ computational basis. In addition, we allow the creation of a\none-qubit ancilla in a mixed state $\\rho$, which should be regarded as a\nparameter of the model. Our goal is to determine for which $\\rho$ universal\nquantum computation (UQC) can be efficiently simulated. To answer this\nquestion, we construct purification protocols that consume several copies of\n$\\rho$ and produce a single output qubit with higher polarization. The\nprotocols allow one to increase the polarization only along certain \"magic\"\ndirections. If the polarization of $\\rho$ along a magic direction exceeds a\nthreshold value (about 65%), the purification asymptotically yields a pure\nstate, which we call a magic state. We show that the Clifford group operations\ncombined with magic states preparation are sufficient for UQC. The connection\nof our results with the Gottesman-Knill theorem is discussed.",
    "arxiv_id": "quant-ph/0403025",
    "authors": [
      "Sergei Bravyi",
      "Alexei Kitaev"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.71.022316",
    "journal_ref": "Phys. Rev. A 71, 022316 (2005)",
    "title": "Universal Quantum Computation with ideal Clifford gates and noisy   ancillas",
    "url": "https://arxiv.org/abs/quant-ph/0403025"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8d0ea9f6-e945-46fe-b09d-b73264e7ac1e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}