New paths in Lattice gauge theories

The theory of Quantum Chromodynamics (QCD) is a crucial element in our current understanding of the laws that govern the universe. It describes the Strong Interaction, the force that governs the behavior of quarks and gluons and confines them at low energies into hadrons, such as protons, neutrons and pions.Lattice QCD (LQCD) is a numerical approach that allows non-perturbative studies of the strong interaction at hadronic energy scales, where other theoretical methods fail. It works by discretizing space-time on a lattice of points, fixing the fermion field to the lattice sites and representing the gluon field as the links between them.Our current numerical approach to Lattice QCD is based upon Markov Chain Monte Carlo (MCMC) methods, from which statistical ensembles of lattice gauge field configurations are generated using a discrete version of the QCD action when evaluating the path-integrals. These calculations require the world's largest supercomputing facilities and possible improvements or new ideas are actively being researched. In this dissertation we present three such attempts.First, we propose a new strategy to employ the recent advances in Machine Learning into LQCD. In particular, we present a method to use Neural Networks to accelerate the calculations of hadron two-point correlation functions and discuss its applicability.The second effort we present is part of new collaborative undertaking by the OPEN LATtice Initiative (OPENLAT) to generate new state-of-the-art LQCD ensembles using the recently proposed Stabilized Wilson Fermions (SWF) package, which also includes a modified lattice action. The first results for the light hadron spectrum, obtained by Bayesian model averaging, are presented indicating the excellent scaling behavior of SWF towards the continuum.Finally, the tentative new approach of Quantum Computing for Lattice Field Theories is introduced as a possible radical solution to the sign problem. We compare three algorithms for quantum state preparation in the case of the Schwinger model, a toy model for QCD, and discuss their applicability to Noisy Intermediate-Scale Quantum (NISQ) systems.