  We describe an algorithm to simulate time evolution using the Multi-scale
Entanglement Renormalization Ansatz (MERA) and test it by studying a critical
Ising chain with periodic boundary conditions and with up to L ~ 10^6 quantum
spins. The cost of a simulation, which scales as L log(L), is reduced to log(L)
when the system is invariant under translations. By simulating an evolution in
imaginary time, we compute the ground state of the system. The errors in the
ground state energy display no evident dependence on the system size. The
algorithm can be extended to lattice systems in higher spatial dimensions.
