  We propose and test an algorithm to simulate a lattice system of interacting
fermions in two spatial dimensions. The approach is an extension of the
entanglement renormalization technique [Phys. Rev. Lett. 99, 220405 (2007)] and
the related multi-scale entanglement renormalization ansatz. Benchmark
calculations for free and interacting fermions on a lattice of $6\times 6$
sites and periodic boundary conditions confirm the validity of this proposal.
