  Ab-initio calculations of real-time evolution for lattice gauge theory have
very interesting potential applications but present challenging computational
aspects. We show that tensor renormalization group methods developed in the
context of Euclidean-time lattice field theory can be applied to calculation of
Trotterized evolution operators at real time. We discuss the optimization of
truncation procedures for various observables. We apply the numerical methods
to the 1D Quantum Ising Model with an external transverse field in the ordered
phase and compare with universal quantum computing for $N_{s}=4$ and 8 sites.
