Quantum annealing for lattice models with competing long-range interactions

Abstract Predicting ordered states in long-range interacting lattice models constitutes a challenging task relevant to condensed matter physics, statistical mechanics, quantum many-body theory, materials science, and computational physics. Energy landscapes often contain many competing states with similar energies, while finite-size simulations can depend sensitively on geometry. Here, we use superconducting qubit quantum annealing devices to determine ground states of Ising models with algebraically decaying competing long-range interactions in the thermodynamic limit from finite system optimizations. This is enabled by a unit-cell-based optimization scheme. We demonstrate the approach on three paradigmatic problems: the calculation of devil’s staircases of magnetization plateaux of the long-range Ising model in a longitudinal field on the triangular lattice, motivated by atomic quantum simulators; the ground state of the same model on the Kagomé lattice without a field, motivated by artificial spin ice metamaterials; and models with additional few-nearest-neighbor interactions relevant for frustrated Ising compounds. Our work provides a realistic application of existing quantum annealing technology across many research areas.