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We propose an annealing scheme usable on modern Ising machines for crystalstructures prediction (CSP) by taking into account the general n-body atomicinteractions, and in particular three-body interactions which are necessary tosimulate covalent bonds. The crystal structure is represented by discretizing aunit cell and placing binary variables which express the existence ornon-existence of an atom on every grid point. The resulting quadraticunconstrained binary optimization (QUBO) or higher-order unconstrained binaryoptimization (HUBO) problems implement the CSP problem and is solved usingsimulated and quantum annealing. Using the example of Lennard-Jones clusters weshow that it is not necessary to include the target atom number in theformulation allowing for simultaneous optimization of both the particle densityand the configuration and argue that this is advantageous for use on annealingmachines as it reduces the total amount of interactions. We further provide ascheme that allows for reduction of higher-order interaction terms that isinspired by the underlying physics. We show for a covalently bonded monolayerMoS2 crystal that we can simultaneously optimize for the particle density aswell as the crystal structure using simulated annealing. We also show that wereproduce ground states of the interatomic potential with high probability thatare not represented on the initial discretization of the unit cell.

Annealing for prediction of grand canonical crystal structures: Efficient implementation of n-body atomic interactions