  This research demonstrates that Ising machines can effectively solve optimal
elemental configuration searches in crystals, with Au-Cu alloys serving as an
example. The energy function is derived using the cluster expansion method in
the form of a QUBO function, enabling efficient problem-solving via Ising
machines. We have successfully obtained reasonable solutions for crystal
structures consisting of over 10,000 atoms. Notably, we have also obtained
plausible solutions for optimization problems with constrained solutions, such
as situations where the composition ratio of atomic species is predetermined.
These findings suggest that Ising machines can be valuable tools for addressing
materials science challenges.
