  The variational quantum eigensolver (VQE) algorithm combines the ability of
quantum computers to efficiently compute expectation values with a classical
optimization routine in order to approximate ground state energies of quantum
systems. In this paper, we study the application of VQE to the simulation of
molecular energies using the unitary coupled cluster (UCC) ansatz. We introduce
new strategies to reduce the circuit depth for the implementation of UCC and
improve the optimization of the wavefunction based on efficient classical
approximations of the cluster amplitudes. Additionally, we propose an
analytical method to compute the energy gradient that reduces the sampling cost
for gradient estimation by several orders of magnitude compared to numerical
gradients. We illustrate our methodology with numerical simulations for a
system of four hydrogen atoms that exhibit strong correlation and show that the
circuit depth of VQE using a UCC ansatz can be reduced without introducing
significant loss of accuracy in the final wavefunctions and energies.
