Abstract
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 Z₂ model in 2+1 dimensions.