  Gauge theories form the basis of our understanding of modern physics -
ranging from the description of quarks and gluons to effective models in
condensed matter physics. In the non-perturbative regime, gauge theories are
conventionally treated discretely as lattice gauge theories. The resulting
systems are evaluated with path-integral based Monte Carlo methods. These
methods, however, can suffer from the sign problem and do not allow for a
direct evaluation of real-time dynamics. In this work, we present a unified and
comprehensive framework for gauged Gaussian Projected Entangled Pair States
(PEPS), a variational ansatz based on tensor networks. We review the
construction of Hamiltonian lattice gauge theories, explain their similarities
with PEPS, and detail the construction of the state. The estimation of ground
states is based on a variational Monte Carlo procedure with the PEPS as an
ansatz state. This sign-problem-free ansatz can be efficiently evaluated in any
dimension with arbitrary gauge groups, and can include dynamical fermionic
matter, suggesting new options for the simulation of non-perturbative regimes
of gauge theories, including QCD.
