Around the same time, other groups have developed similar approaches in which quantum information plays a predominant role as, for example, in DMRG implementations for periodic boundary conditions [3], and for studying mixed-state dynamics in one-dimensional quantum lattice systems,. Those last approaches actually provide a formalism that is more general than the original TEBD approach, as it also allows to deal with evolutions with matrix product operators; this enables the simulation of nontrivial non-infinitesimal evolutions as opposed to the TEBD case, and is a crucial ingredient to deal with higher-dimensional analogues of matrix product states.