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When lattice QCD is formulated in sectors of fixed quark numbers, the canonical fermion determinants can be expressed explicitly in terms of transfer matrices. This in turn provides a complete factorization of the fermion determinants in…
We present variants of the Conjugate Gradient (CG), Conjugate Residual (CR), and Generalized Minimal Residual (GMRES) methods which are both pipelined and flexible. These allow computation of inner products and norms to be overlapped with…
We have reported elsewhere in this conference on our continuing project to determine non-perturbative Wilson coefficients on the lattice, as a step towards a completely non-perturbative determination of the nucleon structure. In this talk…
We construct a number of lattice fermions, which fulfill the Ginsparg-Wilson relation either exactly or approximately, and test them in the framework of the 2-flavor Schwinger model. We start from explicit approximations within a short…
Nowadays, many fields of study are have to deal with large and sparse data matrixes, but the most important issue is finding the inverse of these matrixes. Thankfully, Krylov subspace methods can be used in solving these types of problem.…
In this article, we review some of the recent developments towards the future goal of quantum computing or quantum simulating lattice QCD. This includes a novel theoretical framework developed for non-Abelian gauge theories that is the…
We introduce an approach to expand gauge-invariant Wilson operators on lattice. This approach is based on non-abelian Stokes theorem and overcomes some shortage of some former methods. It is also suitable for expanding any Wilson operators…
A new computational idea for continuum quantum field theories is outlined. This approach is based on the lattice source Galerkin methods developed by Garcia, Guralnik and Lawson. The method has many promising features including treating…
We present a comparison of a number of iterative solvers of linear systems of equations for obtaining the fermion propagator in lattice QCD. In particular, we consider chirally invariant overlap and chirally improved Wilson (maximally)…
We present a performance comparison of the Kramers equation and the boson algorithms for simulations of QCD with two flavors of dynamical Wilson fermions and gauge group $SU(2)$. Results are obtained on $6^312$, $8^312$ and $16^4$ lattices.…
Despite the successful enhancement to the Harrow-Hassidim-Lloyd algorithm by Childs et al., who introduced the Fourier approach leveraging linear combinations of unitary operators, our research has identified non-trivial redundancies within…
A new deterministic, numerical method to solve fermion field theories is presented. This approach is based on finding solutions $Z[J]$ to the lattice functional equations for field theories in the presence of an external source $J$. Using…
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…
Efficient algorithms for the solution of partial differential equations on parallel computers are often based on domain decomposition methods. Schwarz preconditioners combined with standard Krylov space solvers are widely used in this…
GMRES is a popular Krylov subspace method for solving linear systems of equations involving a general non-Hermitian coefficient matrix. The conventional bounds on GMRES convergence involve polynomial approximation problems in the complex…
Far-from-equilibrium dynamics of SU(2) gauge theory with Wilson fermions is studied in 1+1 space-time dimensions using a real-time lattice approach. Lattice improved Hamiltonians are shown to be very efficient in simulating Schwinger pair…
Inverse problems arise in various scientific and engineering applications, necessitating robust numerical methods for their solution. In this work, we consider the effectiveness of Krylov subspace iterative methods, including GMRES, QMR,…
Nonlocal quark bilinear operators connected by link paths are used for studying parton distribution functions (PDFs) and transverse momentum-dependent PDFs of hadrons using lattice QCD. The nonlocality makes it difficult to understand the…
In a series of recent papers we have shown how the dynamical behavior of certain classical systems can be analyzed using operators evolving according to Heisenberg-like equations of motions. In particular, we have shown that raising and…
A method of numerically solving the Maxwell equations is considered for modeling harmonic electromagnetic fields. The vector finite element method makes it possible to obtain a physically consistent discretization of the differential…