  Lattice gauge theories are fundamental to such distinct fields as particle
physics, condensed matter or quantum information theory. The recent progress in
the control of artificial quantum systems already allows for studying Abelian
lattice gauge theories in table-top experiments. However, the realization of
non-Abelian models remains challenging. Here, we employ a coherent quantum
control scheme to enforce non-Abelian gauge invariance, and discuss this idea
in detail for a one dimensional SU(2) lattice gauge system. Finally, we comment
on how to extend our scheme to other non-Abelian gauge symmetries and higher
spatial dimensions, which summarized, provides a promising route for the
quantum simulation of non-Abelian lattice gauge theories.
