Quantum Approximation on Anisotropic Sobolev and Hölder-Nikolskii Classes

Abstract

We estimate the quantum query error of approximation to functions from the anisotropic Sobolev classwhen p < q, the quantum algorithms can essentially improve the rate of convergence of classical deterministic and randomized algorithms; while for the class B(H r p ([0, 1] d )) and, when p ≥ q, the optimal convergence rate is the same for all three settings.