Quantum Approximation II. Sobolev Embeddings

Details Quantum Approximation II. Sobolev Embeddings Quantum Approximation II. Sobolev Embeddings

2003-05-06

arxiv.org/abs/quant-ph/0305031v1

Physics

Quantum Physics

23 pages, paper submitted to the Journal of Complexity

Scientific paper

A basic problem of approximation theory, the approximation of functions from the Sobolev space W_p^r([0,1]^d) in the norm of L_q([0,1]^d), is considered from the point of view of quantum computation. We determine the quantum query complexity of this problem (up to logarithmic factors). It turns out that in certain regions of the domain of parameters p,q,r,d quantum computation can reach a speedup of roughly squaring the rate of convergence of classical deterministic or randomized approximation methods. There are other regions were the best possible rates coincide for all three settings.

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