Quantum Integration Error on Some Classes of Multivariate Functions

Abstract. We study the approximation of the integration of multivariate functions classes in the quantum model of computation. We first obtain a lower bound of the n-th minimal query error for integration on anisotropic Sobolev-Slobodezkii classes. Then combining our previous results we determine the optimal bound of n-th minimal query error for anisotropic H¨older-Nikolskii class and Sobolev class. The results show that for these two type of classes the quantum algorithms give significant speed up over classical deterministic and randomized algorithms.

• Type: Conference
• Year: 2007
• Where: ICIC
• Authors: Peixin Ye, Qing He
• Keywords: Anisotropic Sobolev-slobodezkii Classes, ICIC 2007, Minimal Query Error, N-th Minimal Query