{
  "annotation_id": "f1d1ef48-a499-4526-9477-c50b3f2d5fae",
  "date_created": "2026-03-02T18:02:16.422000Z",
  "date_modified": "2026-03-02T18:02:16.422000Z",
  "file_hash": "1adb04de5069e4a2a383184f460adb3621e0ccd4451ef5ae8772c09f9a3f2ce1",
  "private": false,
  "record": {
    "abstract": "We show how a number of NP-complete as well as NP-hard problems can be\nreduced to the Sturm-Liouville eigenvalue problem in the quantum setting with\nqueries. We consider power queries which are derived from the propagator of a\nsystem evolving with a Hamiltonian obtained from the discretization of the\nSturm-Liouville operator. We show that the number of power queries as well the\nnumber of qubits needed to solve the problems studied in this paper is a low\ndegree polynomial. The implementation of power queries by a polynomial number\nof elementary quantum gates is an open issue. If this problem is solved\npositively for the power queries used for the Sturm-Liouville eigenvalue\nproblem then a quantum computer would be a very powerful computation device\nallowing us to solve NP-complete problems in polynomial time.",
    "arxiv_id": "quant-ph/0504194",
    "authors": [
      "A. Papageorgiou",
      "H. Wozniakowski"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "The Sturm-Liouville eigenvalue problem and NP-complete problems in the   quantum setting with queries",
    "url": "https://arxiv.org/abs/quant-ph/0504194"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d108f497-36f4-4d02-848b-2a7e8568a1b3",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}