Related papers: A multigrid accelerated eigensolver for the Hermit…
Close to the continuum the lattice spacing affects the smallest eigenvalues of the Wilson Dirac operator in a very specific manner determined by the way in which the discretization breaks chiral symmetry. These effects can be computed…
We compute the low lying eigenvalues of the Hermitian Dirac operator in lattice QCD with $N_{\rm f} = 2+1+1$ twisted mass fermions. We discuss whether these eigenvalues are in the $\epsilon$-regime or the $p$-regime of Wilson chiral…
The simulation of lattice QCD on massively parallel computers stimulated the development of scalable algorithms for the solution of sparse linear systems. We tackle the problem of the Wilson-Dirac operator inversion by combining a Schwarz…
The overlap Dirac operator, which satisfies the Ginsparg-Wilson relation, realizes exact chiral symmetry on the lattice without any unphysical doubler modes. To perform the path integrals, one should, however, note that the overlap fermion…
Establishing an exact relation for the derivative we show that the eigenvalue flows of the hermitean Wilson-Dirac operator obey a differential equation. We obtain a complete overview of the characteristic features of its solutions. The…
Hybrid quantum-classical variational algorithms such as the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA) are promising applications for noisy, intermediate-scale quantum (NISQ) computers.…
This paper introduces and analyses the new grid-based tensor approach for approximate solution of the eigenvalue problem for linearized Hartree-Fock equation applied to the 3D lattice-structured and periodic systems. The set of localized…
Here is presented an original program based on molecular Schrodinger equations. It is dedicated to target specific states of infrared vibrational spectrum in a very precise way with a minimal usage of memory. An eigensolver combined with a…
Considering Ginsparg-Wilson type fermions dynamically in lattice QCD simulations is a challenging task. The hope is to be able to approach smaller pion masses and to eventually reach physical situations. The price to pay is substantially…
We investigate the distribution of low-lying eigenmodes of hermitian Wilson-Dirac operator, $H_W$, with the gauge action whose form is designed to avoid topology change, as well as with the standard plaquette action. On the quenched…
We compute Neuberger's overlap operator by the Lanczos algorithm applied to the Wilson-Dirac operator. Locality of the operator for quenched QCD data and its eigenvalue spectrum in an instanton background are studied.
We describe an algebraic algorithm which allows to express every one-loop lattice integral with gluon or Wilson-fermion propagators in terms of a small number of basic constants which can be computed with arbitrary high precision. Although…
We consider the solution of large-scale nonlinear algebraic Hermitian eigenproblems of the form $T(\lambda)v=0$ that admit a variational characterization of eigenvalues. These problems arise in a variety of applications and are…
Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper…
Dynamical Mean Field Theory (DMFT) is one of the powerful computational approaches to study electron correlation effects in solid-state materials and molecules. Its practical applicability is, however, limited by the quantity of numerical…
We describe and test a method to compute Euclidean meson two-point functions in lattice QCD. The contribution from the low-lying eigenmodes of the Dirac operator is averaged over all positions of the quark sources. The contribution from the…
We test a method for computing the static quark-antiquark potential in lattice QCD, which is not based on Wilson loops, but where the trial states are formed by eigenvector components of the covariant lattice Laplace operator. The runtime…
We report on the first successful QCD multigrid algorithm which demonstrates constant convergence rates independent of quark mass and lattice volume for the Wilson Dirac operator. The new ingredient is the adaptive method for constructing…
Diffusion models have emerged as a promising class of generative models that map noisy inputs to realistic images. More recently, they have been employed to generate solutions to partial differential equations (PDEs). However, they still…
The accelerated progress in manufacturing noisy intermediate-scale quantum (NISQ) computing hardware has opened the possibility of exploring its application in transforming approaches to solving computationally challenging problems. The…