{
  "annotation_id": "59ffb708-d12e-4341-8988-38e624c75fdc",
  "date_created": "2026-03-02T18:02:23.827000Z",
  "date_modified": "2026-03-02T18:02:23.827000Z",
  "file_hash": "4c4c45a539a0388628b1d44c6b5168b42f865be3e6134e89186f7e56a4bd9b9e",
  "private": false,
  "record": {
    "abstract": "The standard setting of quantum computation for continuous problems uses\ndeterministic queries and the only source of randomness for quantum algorithms\nis through measurement. This setting is related to the worst case setting on a\nclassical computer in the sense that the number of qubits needed to solve a\ncontinuous problem must be at least equal to the logarithm of the worst case\ninformation complexity of this problem. Since the number of qubits must be\nfinite, we cannot solve continuous problems on a quantum computer with infinite\nworst case information complexity. This can even happen for continuous problems\nwith small randomized complexity on a classical computer. A simple example is\nintegration of bounded continuous functions. To overcome this bad property that\nlimits the power of quantum computation for continuous problems, we study the\nquantum setting in which randomized queries are allowed. This type of query is\nused in Shor\u0027s algorithm. The quantum setting with randomized queries is\nrelated to the randomized classical setting in the sense that the number of\nqubits needed to solve a continuous problem must be at least equal to the\nlogarithm of the randomized information complexity of this problem.",
    "arxiv_id": "quant-ph/0601196",
    "authors": [
      "H. Wozniakowski"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "The Quantum Setting with Randomized Queries for Continuous Problems",
    "url": "https://arxiv.org/abs/quant-ph/0601196"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "aaeb875d-d7a1-4263-88b3-22e435e466ee",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}