Tensor Train Optimization of Parameterized Quantum Circuits

We examine a particular realization of derivative-free method as implemented on tensor train based optimization to the variational quantum eigensolver. As an example, we consider parameterized quantum circuits composed of a low-depth hardware-efficient ansatz and Hamiltonian variational ansatz for addressing the ground state of the transverse field Ising model. We further make a comparison with gradient-based optimization techniques and discuss on the advantage of using tensor train based optimization, especially in the presence of noise.