Effectiveness of Combinatorial Optimization for Stable-Structure Search in Solid Solutions and Disordered Systems

Improving materials properties often involves introducing cation/anion substitutions and vacancies, which are widely practiced. Ab initio studies of the resulting solid solutions and disordered systems typically employ the supercell method, and portions of the host structure are replaced with dopants to generate candidate configurations. Each configuration is then evaluated individually to identify energetically stable structures and their properties.

Because the number of configurations grows rapidly, exhaustive ab initio calculations are infeasible. A common remedy is prescreening by electrostatic energy, which is relatively inexpensive in small problems. However, as the number of candidate configurations grows, evaluating the electrostatic energy itself becomes challenging.

We formulate the stable-structure search as a combinatorial optimization problem and design an Ising-type Hamiltonian with future deployment on quantum-annealing hardware in mind.We apply this Hamiltonian to various inorganic materials and validate the stable-structure search using both simulated and quantum annealing. The presentation will first describe the Hamiltonian design and then discuss the effectiveness of the annealing methods for this problem on the basis of optimization performance and computational time.