  The recently proposed Clifford Circuits Augmented Matrix Product States
(CA-MPS) (arXiv:2405.09217) seamlessly augments Density Matrix Renormalization
Group with Clifford circuits. In CA-MPS, the entanglement from stabilizers is
transferred to the Clifford circuits which can be easily handled according to
the Gottesman-Knill theorem. As a result, MPS needs only to deal with the
non-stabilizer entanglement, which largely reduce the bond dimension and the
resource required for the accurate simulation of many-body systems. In this
work, we generalize CA-MPS to the framework of Time-Dependent Variational
Principle (TDVP) for time evolution simulations. In this method, we apply
Clifford circuits to the resulting MPS in each TDVP step with a two-site
sweeping process similar as in DMRG, aiming at reducing the entanglement
entropy in the MPS, and the Hamiltonian is transformed accordingly using the
chosen Clifford circuits. Similar as in CA-MPS, the Clifford circuits doesn't
increase the number of terms in the Hamiltonian which makes the overhead very
small in the new method. We test this method in both XXZ chain and two
dimensional Heisenberg model. The results show that the Clifford circuits
augmented TDVP method can reduce the entanglement entropy in the time evolution
process and hence makes the simulation reliable for longer time. The Clifford
circuits augmented Time-Dependent Variational Principle provides a useful tool
for the simulation of time evolution process of many-body systems in the
future.
