Complexity for the Approximation of Sobolev Imbeddings in the Quantum Computation Model

【摘要】：正Using a new and elegant reduction approach we derive a lower bound of quantum complexity for the approximation of imbeddings from anisotropic Sobolev classes B(W_p~r([0,l]~d)) to anisotropic Sobolev space W_ ~s([0,1]~d) for all 1≤p,q≤∞. When p≥q this bound is optimal.In this case the quantum algorithms are not significantly better than the classical deterministic or randomized algorithms.When p≥q we conjecture that quantum algorithms bring speed-up over the classical deterministic and randomized ones.This conjecture was confirmed in the situation s=0.

【基金】：supported by National Nature Science Foundation under Grant 10971251
【分类号】：O413