Year: 2026
Type: preprint
Abstract: We study the complexity of high-dimensional integration of periodic functions from Besov spaces $S^r_{p,q}B(\mathbb{T}^d)$ with mixed smoothness in the quantum model of computation. We construct new quantum algorithms based on the multivariate Faber-Schauder decomposition of such functions and analyze their convergence rates. We show a gain of one convergence order compared to the well-known deterministic rates of convergence. We additionally obtain lower bounds showing the optimality of our results up to logarithms.
Source: arXiv (Cornell University)
Authors: Käßemodel, Bernd, Ullrich, Tino
Institutions: Chemnitz University of Technology, Leipzig University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G7922932005
OpenAlex ID: W7221801578