{
  "annotation_id": "68858ba2-25e7-4088-9a5b-09317158b5bb",
  "date_created": "2026-03-02T18:02:03.421000Z",
  "date_modified": "2026-03-02T18:02:03.421000Z",
  "file_hash": "8d30c6891de1d8dbe129d3bdf434535e3f1153b6e55a69c78621ee8ca81cece4",
  "private": false,
  "record": {
    "abstract": "The complexity class NP is quintessential and ubiquitous in theoretical\ncomputer science. Two different approaches have been made to define \"Quantum\nNP,\" the quantum analogue of NP: NQP by Adleman, DeMarrais, and Huang, and QMA\nby Knill, Kitaev, and Watrous. From an operator point of view, NP can be viewed\nas the result of the exists-operator applied to P. Recently, Green, Homer,\nMoore, and Pollett proposed its quantum version, called the N-operator, which\nis an abstraction of NQP. This paper introduces the exists^{Q}-operator, which\nis an abstraction of QMA, and its complement, the forall^{Q}-operator. These\noperators not only define Quantum NP but also build a quantum hierarchy,\nsimilar to the Meyer-Stockmeyer polynomial hierarchy, based on two-sided\nbounded-error quantum computation.",
    "arxiv_id": "quant-ph/0308125",
    "authors": [
      "Tomoyuki Yamakami"
    ],
    "categories": [
      "quant-ph",
      "cs.CC"
    ],
    "title": "Quantum NP and a Quantum Hierarchy",
    "url": "https://arxiv.org/abs/quant-ph/0308125"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "06ef0677-4a5f-480d-90f2-5b02a1129cb1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}