Abstract

We propose an annealing scheme usable on modern Ising machines for crystal structure prediction by taking into account general n-body atomic interactions, in particular three-body interactions needed for covalent bonds. The crystal structure is represented by discretizing a unit cell and placing binary variables on grid points to encode atomic occupancy, leading to QUBO or HUBO formulations solvable using simulated and quantum annealing. Using Lennard-Jones clusters, we show that the target atom number need not be fixed a priori, enabling simultaneous optimization of particle density and configuration. We also present a physically motivated reduction scheme for higher-order interaction terms. For a covalently bonded monolayer MoS₂ crystal modeled by a Stillinger-Weber potential, we demonstrate simultaneous optimization of particle density and crystal structure using simulated annealing and show recovery of ground states not represented on the initial discretization.

Abstract

We propose an annealing scheme usable on modern Ising machines for crystal structure prediction by taking into account general n-body atomic interactions, in particular three-body interactions needed for covalent bonds. The crystal structure is represented by discretizing a unit cell and placing binary variables on grid points to encode atomic occupancy, leading to QUBO or HUBO formulations solvable using simulated and quantum annealing. Using Lennard-Jones clusters, we show that the target atom number need not be fixed a priori, enabling simultaneous optimization of particle density and configuration. We also present a physically motivated reduction scheme for higher-order interaction terms. For a covalently bonded monolayer MoS₂ crystal modeled by a Stillinger-Weber potential, we demonstrate simultaneous optimization of particle density and crystal structure using simulated annealing and show recovery of ground states not represented on the initial discretization.

Abstract

We propose an annealing scheme usable on modern Ising machines for crystal structure prediction by taking into account general n-body atomic interactions, in particular three-body interactions needed for covalent bonds. The crystal structure is represented by discretizing a unit cell and placing binary variables on grid points to encode atomic occupancy, leading to QUBO or HUBO formulations solvable using simulated and quantum annealing. Using Lennard-Jones clusters, we show that the target atom number need not be fixed a priori, enabling simultaneous optimization of particle density and configuration. We also present a physically motivated reduction scheme for higher-order interaction terms. For a covalently bonded monolayer MoS₂ crystal modeled by a Stillinger-Weber potential, we demonstrate simultaneous optimization of particle density and crystal structure using simulated annealing and show recovery of ground states not represented on the initial discretization.

Abstract

We propose an annealing scheme usable on modern Ising machines for crystal structure prediction by taking into account general n-body atomic interactions, in particular three-body interactions needed for covalent bonds. The crystal structure is represented by discretizing a unit cell and placing binary variables on grid points to encode atomic occupancy, leading to QUBO or HUBO formulations solvable using simulated and quantum annealing. Using Lennard-Jones clusters, we show that the target atom number need not be fixed a priori, enabling simultaneous optimization of particle density and configuration. We also present a physically motivated reduction scheme for higher-order interaction terms. For a covalently bonded monolayer MoS₂ crystal modeled by a Stillinger-Weber potential, we demonstrate simultaneous optimization of particle density and crystal structure using simulated annealing and show recovery of ground states not represented on the initial discretization.