PreprintCC BY 4.0arXiv
Quantum integration in Besov spaces with mixed smoothness
Abstract
We study the complexity of high-dimensional integration of periodic functions from Besov spaces Srp,qB(𝕋d) 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.
Related
- Prevalent smoothness in inhomogeneous Besov spaces
- Triebel - Lizorkin spaces of dominating mixed smoothness are algebras with respect to pointwise multiplication
- Limits of Besov Norms on Quantum Euclidean Spaces
- Besov and Triebel--Lizorkin Spaces on Filtered Lie Groups, III: the Spaces F∞,qα
- Besov and Triebel--Lizorkin Spaces on Filtered Lie Groups, II: Pointwise Multiplication, Localization, Differences
BibTeX
@misc{kaßemodel2026quantum,
title = {{Quantum integration in Besov spaces with mixed smoothness}},
author = {Bernd Käßemodel and Tino Ullrich},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17204},
eprint = {2610.17204},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17204},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum integration in Besov spaces with mixed smoothness
AU - Bernd Käßemodel
AU - Tino Ullrich
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17204
UR - https://arxiv.org/abs/2610.17204
AB - We study the complexity of high-dimensional integration of periodic functions from Besov spaces S^r_p,qB(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.
ER -