Excited state preparation of molecular systems through variance minimization based methods

Simulating excited states is important in chemistry, physics, and material science applications. Minimizing variance is a common way to get general excited states in some cases, while recently there has been interest in using the folded spectra method to get a specific target state near a target energy. These methods could be potentially executed using quantum-classical hybrid algorithms similar to variational quantum eigensolvers. Here we explore these methods for small molecular systems by considering the UCCSD ansatz. We investigate numerically how the folded spectrum behaves upon changing the reference energy and how the optimization behaves for finite shots of quantum measurements. We also describe measurement strategies for implementing such methods.