{
  "annotation_id": "a5399b6b-7ae5-4eb8-8806-b9240c589717",
  "date_created": "2026-03-02T18:02:45.191000Z",
  "date_modified": "2026-03-02T18:02:45.191000Z",
  "file_hash": "63f4ba06ba1fb556e7c7de37c6eef4b9d54259db409cddddfc18215832c9a5d4",
  "private": false,
  "record": {
    "abstract": "We propose definitions of QAC^0, the quantum analog of the classical class\nAC^0 of constant-depth circuits with AND and OR gates of arbitrary fan-in, and\nQACC^0[q], where n-ary Mod-q gates are also allowed. We show that it is\npossible to make a `cat\u0027 state on n qubits in constant depth if and only if we\ncan construct a parity or Mod-2 gate in constant depth; therefore, any circuit\nclass that can fan out a qubit to n copies in constant depth also includes\nQACC^0[2]. In addition, we prove the somewhat surprising result that parity or\nfanout allows us to construct Mod-q gates in constant depth for any q, so\nQACC^0[2] = QACC^0. Since ACC^0[p] != ACC^0[q] whenever p and q are mutually\nprime, QACC^0[2] is strictly more powerful than its classical counterpart, as\nis QAC^0 when fanout is allowed.",
    "arxiv_id": "quant-ph/9903046",
    "authors": [
      "Cristopher Moore"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Quantum Circuits: Fanout, Parity, and Counting",
    "url": "https://arxiv.org/abs/quant-ph/9903046"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7f74543e-905c-442d-a576-0572f3569fb0",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}