Related papers: Fast Algorithm for Quasi-2D Coulomb Systems
We report a novel hybrid method of simultaneous atomistic simulation of solids in critical regions (contacts surfaces, cracks areas, etc.), along with continuum modeling of other parts. The continuum is treated in terms of quasi-atoms of…
Ewald summation is widely used to calculate electrostatic interactions in computer simulations of condensed-matter systems. We present an analysis of the errors arising from truncating the infinite real- and Fourier-space lattice sums in…
Variational quantum algorithms constitute one of the most widespread methods for using current noisy quantum computers. However, it is unknown if these heuristic algorithms provide any quantum-computational speedup, although we cannot…
We present a new reciprocal space analytical method to cutoff the long range interactions in supercell calculations for systems that are infinite and periodic in 1 or 2 dimensions, extending previous works for finite systems. The proposed…
We show that finite-range alternatives to the standard long-range BKS pair potential for silica might be used in molecular dynamics simulations. We study two such models that can be efficiently simulated since no Ewald summation is…
Change-point problems have appeared in a great many applications for example cancer genetics, econometrics and climate change. Modern multiscale type segmentation methods are considered to be a statistically efficient approach for multiple…
We present two randomised approximate counting algorithms with $\widetilde{O}(n^{2-c}/\varepsilon^2)$ running time for some constant $c>0$ and accuracy $\varepsilon$: (1) for the hard-core model with fugacity $\lambda$ on graphs with…
We present a novel, highly efficient algorithm to parallelize O(N^2) direct summation method for N-body problems with individual timesteps on distributed-memory parallel machines such as Beowulf clusters. Previously known algorithms, in…
Kernel methods augmented with random features give scalable algorithms for learning from big data. But it has been computationally hard to sample random features according to a probability distribution that is optimized for the data, so as…
Simulating long-range interacting systems is a challenging task due to its computational complexity that the computational effort for each local update is of order $\cal{O}$$(N)$, where $N$ is the size of system. Recently, a technique,…
Calculating interactions or correlations between pairs of particles is typically the most time-consuming task in particle simulation or correlation analysis. Straightforward implementations using a double loop over particle pairs have…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
Recent results suggest that quantum computers possess the potential to speed up nonconvex optimization problems. However, a crucial factor for the implementation of quantum optimization algorithms is their robustness against experimental…
Simulation of quantum systems is challenging due to the exponential size of the state space. Tensor networks provide a systematically improvable approximation for quantum states. 2D tensor networks such as Projected Entangled Pair States…
Quantum algorithms require accurate representations of electronic states on a quantum device, yet the approximation of electronic wave functions for strongly correlated systems remains a profound theoretical challenge, with existing methods…
To simulate plasma phenomena, large-scale computational resources have been employed in developing high-precision and high-resolution plasma simulations. One of the main obstacles in plasma simulations is the requirement of computational…
Fast Ewald summation efficiently evaluates Coulomb interactions and is widely used in molecular dynamics simulations. It is based on a split into a short-range and a long-range part, where evaluation of the latter is accelerated using the…
Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum…
The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum…
Quantum computers are known for their potential to achieve up-to-exponential speedup compared to classical computers for certain problems. To exploit the advantages of quantum computers, we propose quantum algorithms for linear stochastic…