Related papers: Geometric Algorithm for Abelian-Gauge Models
A high fidelity fluid-structure interaction simulation may require many days to run, on hundreds of cores. This poses a serious burden, both in terms of time and economic considerations, when repetitions of such simulations may be required…
Alexandrov proved that any simplicial complex homeomorphic to a sphere with strictly non-negative Gaussian curvature at each vertex can be isometrically embedded uniquely in $\mathbb{R}^3$ as a convex polyhedron. Due to the nonconstructive…
Nielsen, et al. [1, 2] proposed a view of quantum computation where determining optimal algorithms is equivalent to extremizing a geodesic length or cost functional. This view of optimization is highly suggestive of an action principle of…
We present an efficient algorithm for calculating the properties of Ising models in two dimensions, directly in the spin basis, without the need for mapping to fermion or dimer models. The algorithm gives numerically exact results for the…
We introduce an effective algorithmic method for the computation of a lower bound for uniform expansion in one-dimensional dynamics. The approach employs interval arithmetic and thus provides a rigorous numerical result (computer-assisted…
We consider the problem of multiple change-point estimation in the mean of a Gaussian AR(1) process. Taking into account the dependence structure does not allow us to use the dynamic programming algorithm, which is the only algorithm giving…
We present in detail three different quasi-Newton isogeometric algorithms for the treatment of free boundary problems. Two algorithms are based on standard Galerkin formulations, while the third is a fully-collocated scheme. With respect to…
Paraxial diffraction modeling based on the Fourier transform has seen widespread implementation for simulating the response of a diffraction-limited optical system. For systems where the paraxial assumption is not sufficient, a class of…
Ising and Potts models are an important class of discrete probability distributions which originated from statistical physics and since then have found applications in several disciplines. Simulation from these models is a well known…
The framework of geometric extremes is based on the convergence of scaled sample clouds onto a limit set, characterized by a gauge function, with the shape of the limit set determining extremal dependence structures. While it is known that…
Quantum simulation of synthetic dynamic gauge field has attracted much attentions in recent years. There are two traditional ways to simulate gauge theories. One is to directly simulate the full Hamiltonian of gauge theories with local…
Simple algorithm of dynamics of Ising magnetic is described. The algorithm can be implemented on conventional digital computer and can be used for construction of specialized processor for simulation of ferromagnetic systems. The algorithm…
The adiabatic quantum algorithm has drawn intense interest as a potential approach to accelerating optimization tasks using quantum computation. The algorithm is most naturally realised in systems which support Hamiltonian evolution, rather…
Global optimization heuristics are popular to optimize hard non-convex problems. Despite their irrefutably large cost-to-solution, in the lack of other working greedy or convex approaches, global optimization algorithms remain the…
We present a new numerical method for the isometric embedding of 2-geometries specified by their 2-metrics in three dimensional Euclidean space. Our approach is to directly solve the fundamental embedding equation supplemented by six…
The random current representation of the Ising model, along with a related path expansion, has been a source of insight on the stochastic geometric underpinning of the ferromagnetic model's phase structure and critical behavior in different…
We introduce a new update scheme to systematically improve the efficiency of parallel tempering simulations. We show that by adapting the number of sweeps between replica exchanges to the canonical autocorrelation time, the average…
Simulations of lattice gauge theories on noisy quantum hardware inherently suffer from violations of the gauge symmetry due to coherent and incoherent errors of the underlying physical system that implements the simulation. These gauge…
At fine lattice spacings, Markov chain Monte Carlo simulations of QCD and other gauge theories with or without fermions are plagued by slow modes that give rise to large autocorrelation times. This can lead to simulation runs that are…
A major driver of quantum-simulator technology is the prospect of probing high-energy phenomena in synthetic quantum matter setups at a high level of control and tunability. Here, we propose an experimentally feasible realization of a…