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arXiv · 2610.17204

Quantum integration in Besov spaces with mixed smoothness

Bernd Käßemodel·Tino Ullrich
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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.

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Bernd Käßemodel, Tino Ullrich. 2026-10-12. Quantum integration in Besov spaces with mixed smoothness. https://arxiv.org/abs/2610.17204

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