Digital Quantum Simulation of Z2 Lattice Gauge Theories with Dynamical Fermionic Matter

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 fourbody 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 Z(2) model in (2 + 1) dimensions.