  Tensor network methods have evolved from solving optimization problems in
quantum many-body spin systems. While the tensor network is now regarded as a
powerful tool in quantum computer simulation, there still exists a complexity
issue in updating the tensors. This work studies the tensor updates
simplification in the context of the tensor network based quantum computer
simulation. According to the numerical simulations, a method called simple
update, also originated in quantum many-body spin systems, shows a good balance
of the fidelity and the computational complexity.
