Excited state search using quantum annealing

Synopsis

Quantum annealing (QA) is one of the ways of finding ground states of problem Hamiltonians. We initially apply transverse fields corresponding to a driver Hamiltonian and adiabatically change the Hamiltonian to the problem Hamiltonian to obtain the target ground state. However, for some purposes such as quantum chemistry, both ground and excited states are needed to understand the properties of the molecules. Here, we describe a scheme based on QA to search arbitrary excited states of problem Hamiltonians. By splitting the degeneracy of the driver Hamiltonian with inhomogeneous transverse fields, we can prepare a nondegenerate excited state as the initial state, and an adiabatic change of the Hamiltonian provides a target excited state as long as the adiabatic condition holds. We also show that our scheme enables us to find a desired excited state by designing the driver Hamiltonian suitably even in the presence of weak decoherence. As possible applications, we discuss post-quantum cryptograph and measurements of the energy relaxation time of quantum states.