Test of the unitary coupled-cluster variational quantum eigensolver for a simple strongly correlated condensed-matter system

The variational quantum eigensolver has been proposed as a low-depth quantum circuit that can be employed to examine strongly correlated systems on today's noisy intermediate-scale quantum computers. We examine details associated with the factorized form of the unitary coupled-cluster variant of this algorithm. We apply it to a simple strongly correlated condensed-matter system with nontrivial behavior - the four-site Hubbard model at half-filling. This work shows some of the subtle issues one needs to take into account when applying this algorithm in practice, especially to condensed-matter systems.