A method of determining molecular excited-states using quantum computation

Abstract

A method is presented in which the ground-state subspace is projected out of a Hamiltonian representation. As a result of this projection, an effective Hamiltonian is constructed where its ground-state coincides with an excited-state of the original problem. Thus, low-lying excited-state energies can be calculated using existing hybrid quantum classical techniques and variational algorithm(s) for determining ground-state. The method as formulated is shown to be fully valid for the $$\\hbox{H}_2$$\n and LiH molecules. The primary restriction with our technique is the number of terms required in the projection operator, therefore we explore arguments to reduce the number of terms and discuss applicability to different classes of Hamiltonians.