A Method of Determining Excited-States for Quantum Computation

TL;DR

This paper introduces a novel method to compute excited-state energies in quantum systems by projecting out the ground state, enabling the use of existing variational algorithms to find low-lying excited states.

Contribution

The paper presents a new approach that constructs an effective Hamiltonian whose ground state corresponds to an excited state of the original Hamiltonian, validated on the H2 molecule.

Findings

Method successfully applied to H2 molecule

Conditions for method's success discussed

Enables use of variational algorithms for excited states

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 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.