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A cellular automaton collider is a finite state machine build of rings of one-dimensional cellular automata. We show how a computation can be performed on the collider by exploiting interactions between gliders (particles, localisations).…
This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…
We compute explicitly the group of connected components $\pi_0G(\mathbb{R})$ of the real Lie group $G(\mathbb{R})$ for an arbitrary (not necessarily linear) connected algebraic group $G$ defined over the field $\mathbb{R}$ of real numbers.…
The Cellular Potts Model (CPM) is a lattice based modeling technique which is widely used for simulating cellular patterns such as foams or biological tissues. Despite its realism and generality, the standard Monte Carlo algorithm used in…
The use of high-dimensional data for targeted therapeutic interventions requires new ways to characterize the heterogeneity observed across subgroups of a specific population. In particular, models for partially exchangeable data are needed…
We show how to perform universal quantum computation with atoms confined in optical lattices which works both in the presence of defects and without individual addressing. The method is based on using the defects in the lattice, wherever…
Quantum algorithms use the principles of quantum mechanics, as for example quantum superposition, in order to solve particular problems outperforming standard computation. They are developed for cryptography, searching, optimisation,…
The calculation time for the energy of atoms and molecules scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chemical…
A geometrical approach to quantum computation is presented, where a non-abelian connection is introduced in order to rewrite the evolution operator of an energy degenerate system as a holonomic unitary. For a simple geometrical model we…
This work presents an abstract model for the computations performed by analytic column stores or columnar query processors. The model is based on circuits whose wires carry columns rather than scalar values, and whose nodes apply operators…
Studying the response of quantum systems is essential for gaining deeper insights into the fundamental nature of matter and its behavior in diverse physical contexts. Computation of nuclear response is critical for many applications, but…
We present quantum algorithms, for Hamiltonians of linear combinations of local unitary operators, for Hamiltonian matrix-vector products and for preconditioning with the inverse of shifted reduced Hamiltonian operator that contributes to…
The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) is generalized to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules.…
Constructing appropriate unitary matrix operators for new quantum algorithms and finding the minimum cost gate sequences for the implementation of these unitary operators is of fundamental importance in the field of quantum information and…
In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As…
A new parallelized simulation code is presented, which uses a Monte Carlo method to determine particle spectra in the KATRIN source. Reaction chains are generated from the decay of tritium within the source. The code includes all relevant…
In this paper, we study the relationship between algebraic manipulation detection (AMD) codes and highly nonlinear functions. As applications, on one hand, a generic construction for systematic AMD codes is introduced based on highly…
The problem of computing modulo prime-power sums is investigated in distributed source coding as well as computation over Multiple-Access Channel (MAC). We build upon group codes and present a new class of codes called Quasi Group Codes…
An analytical-numeric calculation method of extremely complicated integrals is presented. These integrals appear often in magnet soliton theory. The appropriate analytical continuation and a corresponding integration contour allow to reduce…
The Coupled Cluster (CC) method is used to compute the electronic correlation energy in atoms and molecules and often leads to highly accurate results. However, due to its single-reference nature, standard CC in its projected form fails to…