{
  "annotation_id": "0fdfc218-19b2-4ef5-af61-c81acc0e68b7",
  "date_created": "2026-03-02T18:02:20.591000Z",
  "date_modified": "2026-03-02T18:02:20.591000Z",
  "file_hash": "473f08d610950d0604997b7334588d31f90948b048fb8866e7876d09abab2b2b",
  "private": false,
  "record": {
    "abstract": "We study a reduced quantum circuit computation paradigm in which the only\nallowable gates either permute the computational basis states or else apply a\n\"global Hadamard operation\", i.e. apply a Hadamard operation to every qubit\nsimultaneously. In this model, we discuss complexity bounds (lower-bounding the\nnumber of global Hadamard operations) for common quantum algorithms : we\nillustrate upper bounds for Shor\u0027s Algorithm, and prove lower bounds for\nGrover\u0027s Algorithm. We also use our formalism to display a gate that is neither\nquantum-universal nor classically simulable, on the assumption that Integer\nFactoring is not in BPP.",
    "arxiv_id": "quant-ph/0508153",
    "authors": [
      "Dan Shepherd"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "On the Role of Hadamard Gates in Quantum Circuits",
    "url": "https://arxiv.org/abs/quant-ph/0508153"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "16e8841c-44ec-44f1-a1bb-fd65e761d659",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}