Related papers: Tractability of Approximation for Weighted Korobov…
In the theory of tractability of multivariate problems one usually studies problems with finite smoothness. Then we want to know which $s$-variate problems can be approximated to within $\varepsilon$ by using, say, polynomially many in $s$…
We consider approximation problems for a special space of d variate functions. We show that the problems have small number of active variables, as it has been postulated in the past using concentration of measure arguments. We also show…
In this paper, we study tractability of $L_2$-approximation of one-periodic functions from weighted Korobov spaces in the worst-case setting. The considered weights are of product form. For the algorithms we allow information from the class…
We study multivariate integration and approximation for functions belonging to a weighted reproducing kernel Hilbert space based on half-period cosine functions in the worst-case setting. The weights in the norm of the function space depend…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
In this paper, we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences ${\bf a}=\{a_j\}_{j\geq1}$ and ${\bf b}=\{b_j\}_{j\geq1}$ of positive numbers. We obtain strong equivalences…
In this paper we consider $L_p$-approximation, $p \in \{2,\infty\}$, of periodic functions from weighted Korobov spaces. In particular, we discuss tractability properties of such problems, which means that we aim to relate the dependence of…
We study multivariate approximation defined over tensor product Hilbert spaces. The domain space is a weighted tensor product Hilbert space with exponential weights which depend on two sequences $\boldsymbol{a}=\{a_j\}_{j\in\mathbb{N}}$ and…
This paper is a study of weighted counting of the solutions of acyclic conjunctive queries ($\ACQ$). The unweighted quantifier free version of this problem is known to be tractable (for combined complexity), but it is also known that…
Quantum computers are believed to bring computational advantages in simulating quantum many body systems. However, recent works have shown that classical machine learning algorithms are able to predict numerous properties of quantum systems…
We study the $L_{\infty}$-approximation of $d$-variate functions from Hilbert spaces via linear functionals as information. It is a common phenomenon in tractability studies that unweighted problems (with each dimension being equally…
Significant advances in the development of computing devices based on quantum effects and the demonstration of their use to solve various problems have rekindled interest in the nature of the "quantum computational advantage." Although…
Quantum algorithms can potentially solve a handful of problems more efficiently than their classical counterparts. In that context, it has been discussed that Markov chains problems could be solved significantly faster using quantum…
Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…
It is well-known that the problem of sampling recovery in the $L_2$-norm on unweighted Korobov spaces (Sobolev spaces with mixed smoothness) as well as classical smoothness classes such as H\"older classes suffers from the curse of…
We consider multivariate $\mathbb{L}_2$-approximation in reproducing kernel Hilbert spaces which are tensor products of weighted Walsh spaces and weighted Korobov spaces. We study the minimal worst-case error…
This paper studies the multivariate approximation of functions in weighted Korobov spaces using multiple rank-1 lattice rules. It has been shown by K\"{a}mmerer and Volkmer (2019) that algorithms based on multiple rank-1 lattices achieve…
Although quantum machine learning has shown great promise, the practical application of quantum computers remains constrained in the noisy intermediate-scale quantum era. To take advantage of quantum machine learning, we investigate the…
Insofar as quantum computation is faster than classical, it appears to be irreversible. In all quantum algorithms found so far the speed-up depends on the extra-dynamical irreversible projection representing quantum measurement. Quantum…
This note is devoted to discussing multivariate approximation of continuous functions on $[0,1]^d$ with analytic Korobov kernels in the worst and average case settings. We only consider algorithms that use finitely many evaluations of…