We show how to combine the light-cone and matrix product algorithms to simulate quantum systems far from equilibrium for long times. For the case of the XXZ spin chain at Δ=0.5, we simulate to a time of ≈22.5. While part of the long simulation time is due to the use of the light-cone method, we also describe a modification of the infinite time-evolving bond decimation algorithm with improved numerical stability, and we describe how to incorporate symmetry into this algorithm. While statistical sampling error means that we are not yet able to make a definite statement, the behavior of the simulation at long times indicates the appearance of either “revivals” in the order parameter as predicted by Hastings and Levitov (e-print arXiv:0806.4283) or of a distinct shoulder in the decay of the order parameter.