{
  "annotation_id": "a4311a25-4c96-4eed-a71f-a9eb3289f0af",
  "date_created": "2026-03-02T18:02:20.017000Z",
  "date_modified": "2026-03-02T18:02:20.017000Z",
  "file_hash": "e3a325139584a7f7aa49c49befedf5bb7d74b1437346bbadf735cca7ef492c07",
  "private": false,
  "record": {
    "abstract": "Grover\u0027s search algorithm can be applied to a wide range of problems; even\nproblems not generally regarded as searching problems, can be reformulated to\ntake advantage of quantum parallelism and entanglement, and lead to algorithms\nwhich show a square root speedup over their classical counterparts.\n  In this paper, we discuss a systematic way to formulate such problems and\ngive as an example a quantum scheduling algorithm for an $R||C_{max}$ problem.\n$R||C_{max}$ is representative for a class of scheduling problems whose goal is\nto find a schedule with the shortest completion time in an unrelated parallel\nmachine environment.\n  Given a deadline, or a range of deadlines, the algorithm presented in this\npaper allows us to determine if a solution to an $R||C_{max}$ problem with $N$\njobs and $M$ machines exists, and if so, it provides the schedule. The time\ncomplexity of the quantum scheduling algorithm is $\\mathcal{O}(\\sqrt{M^N})$\nwhile the complexity of its classical counterpart is $\\mathcal{O}(M^N)$.",
    "arxiv_id": "quant-ph/0511028",
    "authors": [
      "Feng Lu",
      "Dan C. Marinescu"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "An R||C_{max} Quantum Scheduling Algorithm",
    "url": "https://arxiv.org/abs/quant-ph/0511028"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e568db4c-b86f-49fb-9129-76ae374d2cc5",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}