{
  "annotation_id": "824e26f6-b55c-4f1e-8dcd-cf4a6e895184",
  "date_created": "2026-03-02T18:02:30.979000Z",
  "date_modified": "2026-03-02T18:02:30.979000Z",
  "file_hash": "ed89e8b84954a1bf4a609353cea7550dee2b9a2b484897648494f00da9f3f641",
  "private": false,
  "record": {
    "abstract": "Since Grover\u0027s seminal work, quantum search has been studied in great detail.\nIn the usual search problem, we have a collection of n items and we would like\nto find a marked item. We consider a new variant of this problem in which\nevaluating the i-th item may take a different number of time steps for\ndifferent i.\n  Let t_i be the number of time steps required to evaluate the i-th item. If\nthe numbers t_i are known in advance, we give an algorithm that solves the\nproblem in O(\\sqrt{t_1^2+t_2^2+...+t_n^2}) steps. This is optimal, as we also\nshow a matching lower bound. The case, when t_i are not known in advance, can\nbe solved with a polylogarithmic overhead. We also give an application of our\nnew search algorithm to computing read-once functions.",
    "arxiv_id": "quant-ph/0609168",
    "authors": [
      "Andris Ambainis"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Quantum search with variable times",
    "url": "https://arxiv.org/abs/quant-ph/0609168"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fbb37fcd-6783-4916-ac85-d27dd8eec4f1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}