International Conference on Natural Computation (ICNC)

Quantum Approximation Error on Some Sobolev Classes

Peixin Ye

Published Jan 1, 2007• 0 citations

Abstract

We study the approximation of functions from anisotropic and generalized Sobolev classes under Lq([0, 1]d) norm in the quantum model of computation. Based on the quantum algorithm for approximation of finite imbedding from LNPto LiNQ, we develop a quantum algorithm for approximating the imbedding from anisotropic Sobolev classes B(Wpr(|0, 1|d)) to Lq(|0, 1|d) space for all 1 les q,p les infin and prove their optimality. Our results show that for p < q the quantum model of computation can bring a speedup of roughly squaring the rate of classical deterministic and randomized settings.

DOI: 10.1109/icnc.2007.588

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