Finding excited states on a quantum computer using unitary block optimization with VQE

The variational quantum eigensolver (VQE) is a well studied quantum algorithm for finding ground states of quantum systems. Significantly less work has been dedicated to finding excited states. In this presentation we describe a DMRG inspired framework called the unitary block optimization scheme to optimize and find excited states on a quantum computer. We describe our algorithm and benchmark and compare it against other approaches in finding low lying excited states of spin models.