  Despite the advantage quantum computers are expected to deliver when
performing simulations compared to their classical counterparts, the current
noisy intermediate-scale quantum (NISQ) devices remain limited in their
capabilities. The training of parameterized quantum circuits (PQCs) remains a
significant practical challenge, exacerbated by the requirement of shallow
circuit depth necessary for their hardware implementation. Hybrid methods
employing classical computers alongside quantum devices, such as the
Variational Quantum Eigensolver (VQE), have proven useful for analyzing the
capabilities of NISQ devices to solve relevant optimization problems. Still, in
the simulation of complex structures involving the many-body problem in quantum
mechanics, major issues remain about the representation of the system and
obtaining results which clearly outperform classical computational devices. In
this research contribution we propose the use of parameterized Tensor Networks
(TNs) to attempt an improved performance of the VQE algorithm. A joint approach
is presented where the Hamiltonian of a system is encapsulated into a Matrix
Product Operator (MPO) within a parameterized unitary TN hereby splitting up
the optimization task between the TN and the VQE. We show that the hybrid
TN-VQE implementation improves the convergence of the algorithm in comparison
to optimizing randomly-initialized quantum circuits via VQE.
