Digital quantum simulation of $\mathbb{Z}_2$ 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 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. 
Erez Zohar, Alessandro Farace, Benni Reznik, J. Ignacio Cirac
quant-ph cond-mat.quant-gas hep-lat hep-th