Determination of stable proton configurations by black-box optimization using an Ising machine

Stable proton configurations in solid-state materials are a prerequisite for the theoretical microscopic investigation of solid-state proton-conductive materials. However, a large number of initial atomistic configurations should be considered to find stable proton configurations, and relaxation calculations using the density functional theory approach are required for each initial configuration. Consequently, the determination of stable configurations is a difficult and time-consuming task. Furthermore, when the size of the simulation cells or the number of doped atoms increases, the number of initial configurations leads to a combinatorial explosion, rendering the computation infeasible. In this study, black-box optimization was combined with an Ising machine and density functional calculations to perform an efficient search for stable proton configurations. Scandium-doped barium zirconate, a typical high-proton conductive oxide, was selected as the model system. The Ising machine was able to rapidly select the initial atomistic configuration, ultimately leading to stable proton configurations after subsequent relaxation calculations. This optimization strategy should be able to solve various issues related to configuration optimization in solid-state materials, thereby promoting novel scientific discoveries.