  The variational quantum eigensolver (VQE) algorithm, designed to calculate
the energy of molecular ground states on near-term quantum computers, requires
specification of symmetries that describe the system, e.g. spin state and
number of electrons. This opens the possibility of using VQE to obtain excited
states as the lowest energy solutions of a given set of symmetries. In this
paper, the performances of various unitary coupled cluster (UCC) ans\"atze
applied to VQE calculations on excited states are investigated, using quantum
circuits designed to represent single reference and multireference
wavefunctions to calculate energy curves with respect to variations in the
molecular geometry. These ans\"atze include standard UCCSD, as well as modified
versions of UCCGSD and k-UpCCGSD which are engineered to tackle excited states
without undesired spin symmetry cross-over to lower states during VQE
optimization. These studies are carried out on a range of systems including
H$_2$, H$_3$, H$_4$, NH, and OH$^{+}$, CH$_2$, NH$^{+}_{2}$, covering examples
of spin singlet, doublet and triplet molecular ground states with single and
multireference excited states. In most cases, our calculations are in excellent
agreement with results from full configuration interaction calculations on
classical machines, thus showing that the VQE algorithm is capable of
calculating the lowest excited state at a certain symmetry, including
multireference closed and open shell states, by setting appropriate
restrictions on the excitations considered in the cluster operator, and
appropriate constraints in the qubit register encoding the starting mean field
state.
