In the present work, we propose a scheme for digital formulation of lattice
gauge theories with dynamical fermions in 3+1 dimensions. All interactions are
obtained as a stroboscopic sequence of two-body interactions with an auxiliary
system. This enables quantum simulations of lattice gauge theories where the
magnetic four-body interactions arising in two and more spatial dimensions are
obtained without the use of perturbation theory, thus resulting in stronger
interactions compared with analogue approaches. The simulation scheme is
applicable to lattice gauge theories with either compact or finite gauge
groups. The required bounds on the digitization errors in lattice gauge
theories, due to the sequential nature of the stroboscopic time evolution, are
provided. Furthermore, an implementation of a lattice gauge theory with a
non-abelian gauge group, the dihedral group D3, is proposed employing the
aforementioned simulation scheme using ultracold atoms in optical lattices.Comment: 38 pages, 5 figure