  Tensor network representations of quantum many-body states provide powerful
tools for strongly correlated systems, tailored to capture local correlations
such as ground states exhibiting entanglement area laws. When applying tensor
network states to interacting fermionic systems, a proper choice of basis or
orbitals can greatly reduce the bond dimension of tensors and speed up
calculations. We introduce such a change of basis with unitary gates obtained
via compressing fermionic Gaussian states into quantum circuits corresponding
to various tensor networks. These circuits can reduce the ground state
entanglement entropy and improve the performance of algorithms such as the
density matrix renormalization group. We study the 1D single impurity Anderson
model to show the power of the method in improving computational efficiency and
interpreting impurity physics. Furthermore, fermionic Gaussian circuits also
show potential for suppressing entanglement during the time evolution of a
low-lying excited state that is used to compute the impurity Green's function.
Lastly, we consider Gaussian multi-scale entanglement renormalization ansatz
(GMERA) circuits which compress fermionic Gaussian states hierarchically. The
emergent coarse-grained physical models from these GMERA circuits are studied
in terms of their entanglement properties and suitability for performing time
evolution.
