Related papers: Using aromas to search for preserved measures and …

Quantum algorithms are built enabling to find Poincar\'e recurrence times and periodic orbits of classical dynamical systems. It is shown that exponential gain compared to classical algorithms can be reached for a restricted class of…

Variational quantum metrology represents a powerful tool for optimizing generic estimation strategies, combining the principles of variational optimization with the techniques of quantum metrology. Such optimization procedures result…

We show, in full generality, that the staircase method provides integrals for mappings, and correspondences, obtained as traveling wave reductions of (systems of) integrable partial difference equations. We apply the staircase method to a…

We study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which…

We present an approach to higher dimensional Darboux transformations suitable for application to quantum integrable systems and based on the bispectral property of partial differential operators. Specifically, working with the…

We present an algorithm for determining the minimal order differential equations associated to a given Feynman integral in dimensional or analytic regularisation. The algorithm is an extension of the Griffiths-Dwork pole reduction adapted…

We show that measurement can recover the quantum coherence of a qubit in a non-Markovian environment. The experimental demonstration in an optical system is provided by comparing the visibilities (and fidelities) of the final states with…

Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…

Here we present a new approach to search for first order invariants (first integrals) of rational second order ordinary differential equations. This method is an alternative to the Darbouxian and symmetry approaches. Our procedure can…

Algorithms for embedding certain types of nilpotent subalgebras in maximal subalgebras of the same type are developed, using methods of real algebraic groups. These algorithms are applied to determine non-conjugate subalgebras of the…

In many applications, the information about the number of eigenvalues inside a given region is required. In this paper, we propose a contour-integral based method for this purpose. The new method is motivated by two findings. There exist…

We introduce a new path integral Monte Carlo method for investigating nonadiabatic systems in thermal equilibrium and demonstrate an approach to reducing stochastic error. We derive a general path integral expression for the partition…

We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…

Reasoning based on causality, instead of association has been considered as a key ingredient towards real machine intelligence. However, it is a challenging task to infer causal relationship/structure among variables. In recent years, an…

With the development of low order scaling methods for performing Kohn-Sham Density Functional Theory, it is now possible to perform fully quantum mechanical calculations of systems containing tens of thousands of atoms. However, with an…

The presented method of investigating the solutions to differential equations is not new. Such an approach was developed by Cartan in his analysis of the integrability of differential equations. Here this approach is outlined to demonstrate…

In this paper, we investigate a trade-off between the number of radar observations (or measurements) and their resolution in the context of radar range estimation. To this end, we introduce a novel estimation scheme that can deal with…

Variational quantum algorithms are promising tools for near-term quantum computers as their shallow circuits are robust to experimental imperfections. Their practical applicability, however, strongly depends on how many times their circuits…

Differential equations are one of the main approaches to evaluate multi-loop Feynman integrals. The construction of a canonical or $\varepsilon$-factorised basis for multi-loop integrals remains a key bottleneck for this approach,…

Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…