Exploring Molecular Excited States with a Contracted Quantum Eigensolver

An important focus of quantum computing approaches for molecular systems is in accurately characterizing ground states. However, many interesting phenomena require access to higher energy states, which are more difficult to obtain in an accurate and efficient manner. In this work we introduce a contraction of a projected Schrödinger equation, which provides a necessary and sufficient condition for excited state solutions. From this, we introduce a contracted quantum eigensolver which can be used to find a solution of the contracted equation using a quantum computer. We then present applications to molecular systems demonstrating the approach.