Least Action Principle for the Real-Time Density Matrix Renormalization   Group
  A kind of least action principle is introduced for the discrete time evolution of one-dimensional quantum lattice models. Based on this principle, we obtain an optimal condition for the matrix product states on succeeding time slices generated by the real-time density matrix renormalization group method. This optimization can also be applied to classical simulations of quantum circuits. We discuss the time reversal symmetry in the fully optimized MPS. 
Kouji Ueda, Chenglong Jin, Naokazu Shibata, Yasuhiro Hieida, and   Tomotoshi Nishino