A Method of Determining Excited-States for Quantum Computation

The calculation of molecular ground-state and excited-state energies, or more generally the energy spectra of chemical and material systems, is an application of great interest in a gate-based quantum computational model. In this contribution, we propose a phenomenological approach to the calculation of low-lying excited-states of a given problem Hamiltonian. Specifically, 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 is shown to be fully valid for the H2 molecule. In addition, conditions for the method’s success are discussed in terms of classes of Hamiltonians. A discussion on the broad impact of this method in the era of NISQ devices will also be presented.