{
  "annotation_id": "f978d306-c25f-4184-b523-c9ace01215a4",
  "date_created": "2026-03-02T18:01:49.217000Z",
  "date_modified": "2026-03-02T18:01:49.217000Z",
  "file_hash": "6255b9517743d1ae2de898df56eff379b007b94fad55516419e8bae92e119506",
  "private": false,
  "record": {
    "abstract": "We analyze the complexity of the quantum optimization algorithm based on\nadiabatic evolution for the set partition problem. We introduce a cost function\ndefined on a logarithmic scale of the partition residues so that the total\nnumber of values of the cost function is of the order of the problem size. We\nsimulate the behavior of the algorithm by numerical solution of the\ntime-dependent Schroedinger equation as well as the stationary equation for the\nadiabatic eigenvalues. The numerical results for the time-dependent quantum\nevolution indicate that the complexity of the algorithm scales exponentially\nwith the problem size.This result appears to contradict the recent numerical\nresults for complexity of quantum adiabatic algorithm applied to a different\nNP-complete problem (Farhi et al, Science 292, p.472 (2001)).",
    "arxiv_id": "quant-ph/0112143",
    "authors": [
      "V. N. Smelyanskiy",
      "U. V. Toussaint",
      "D. A. Timucin"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Simulations of the adiabatic quantum optimization for the Set Partition   Problem",
    "url": "https://arxiv.org/abs/quant-ph/0112143"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6fd83f60-be2c-4aca-ade2-55edeb50e123",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}