  We propose a scheme for digital quantum simulation of lattice gauge theories
with dynamical fermions. Using a layered optical lattice with ancilla atoms
that can move and interact with the other atoms (simulating the physical
degrees of freedom), we obtain a stroboscopic dynamics which yields the
four-body plaquette interactions, arising in models with $2+1$ and higher
dimensions, without the use of perturbation theory. As an example we show how
to simulate a $\mathbb{Z}_2$ model in $2+1$ dimensions.
