{
  "annotation_id": "2dbee84a-14af-44e4-9bdb-35de3f97daa2",
  "date_created": "2026-03-02T18:01:59.613000Z",
  "date_modified": "2026-03-02T18:01:59.613000Z",
  "file_hash": "a3854244f317d04a39f400fad0e436c06b6d4ee36c1a3b3135a287f846c0b77f",
  "private": false,
  "record": {
    "abstract": "A basic problem of approximation theory, the approximation of functions from\nthe Sobolev space W_p^r([0,1]^d) in the norm of L_q([0,1]^d), is considered\nfrom the point of view of quantum computation. We determine the quantum query\ncomplexity of this problem (up to logarithmic factors). It turns out that in\ncertain regions of the domain of parameters p,q,r,d quantum computation can\nreach a speedup of roughly squaring the rate of convergence of classical\ndeterministic or randomized approximation methods. There are other regions were\nthe best possible rates coincide for all three settings.",
    "arxiv_id": "quant-ph/0305031",
    "authors": [
      "Stefan Heinrich"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Quantum Approximation II. Sobolev Embeddings",
    "url": "https://arxiv.org/abs/quant-ph/0305031"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b478d562-277c-426c-a3f7-8f82d51e80ac",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}