Excited-state search by quantum annealing toward quantum chemistry calculations

We report two methods to obtain an excited state of a spin-1/2 system using quantum annealing (QA) and adiabatic quantum computation (AQC), and evaluate their performance based on the fidelity of the output states. Although QA and AQC has been developed to search ground states of Ising Hamiltonians, excited state is also required when we analyze quantum systems such as electrons in molecules. We propose two methods to obtain the excited states: methods using non-adiabatic transition and adiabatic transition. It is unclear which method is better under noisy environment. In order to compare the methods, we numerically solved the Lindblad master equation for a certain simple model, and compared their fidelity of output states. As a result, we found that the output of method using adiabatic transition was as high fidelity as the other even when the problem seemed to be difficult for the adiabatic method.