  The "folding algorithm"\cite{fold1} is a matrix product state algorithm for
simulating quantum systems that involves a spatial evolution of a matrix
product state. Hence, the computational effort of this algorithm is controlled
by the temporal entanglement. We show that this temporal entanglement is, in
many cases, equal to the spatial entanglement of a modified Hamiltonian. This
inspires a modification to the folding algorithm, that we call the "hybrid
algorithm". We find that this leads to improved accuracy for the same numerical
effort. We then use these algorithms to study relaxation in a transverse plus
parallel field Ising model, finding persistent quasi-periodic oscillations for
certain choices of initial conditions.
