Algorithmic Developments for Calculating Excited States on Quantum Hardware*

Calculating ground state energies has been the focus of many quantum algorithms due to their importance in chemistry, physics, and material science applications. Near-term strategies include quantum-classical hybrid algorithms such as variational quantum eigensolver. Excited states are generally harder to prepare than ground states with classical algorithms and evidence suggests that the same holds true for quantum algorithms. There have been various methods to prepare the excited states in quantum computers such as variance minimization or subspace diagonalization methods.  Here we build off recent classical innovations in orbital optimization to propose a new method for calculating excited states on quantum hardware.