  We discuss efficient simulation and certification of the dynamics induced by
a quantum many-body Hamiltonian with short-ranged interactions, extending prior
results for one-dimensional systems [Osborne, Phys. Rev. Lett. 97, 157202
(2006) and Lanyon, Maier et al, Nat. Phys. 13, 1158 (2017)] to lattices in
arbitrary spatial dimensions.
