  We show how to implement a Rydberg-atom quantum simulator to study the
non-equilibrium dynamics of an Abelian (1+1)-D lattice gauge theory. The
implementation locally codifies the degrees of freedom of a $\mathbf{Z}_3$
gauge field, once the matter field is integrated out by means of the Gauss'
local symmetries. The quantum simulator scheme is based on current available
technology and scalable to considerable lattice sizes. It allows, within
experimentally reachable regimes, to explore different string dynamics and to
infer information about the Schwinger $U(1)$ model.
