Semiclassical approach to finite temperature quantum annealing with trapped ions

Recently it has been demonstrated that an ensemble of trapped ions may serve as a quantum annealer for the number-partitioning problem [Nature Comm. DOI: 10.1038/ncomms11524]. This hard computational problem may be addressed employing a tunable spin glass architecture. Following the proposal of the trapped ions annealer, we study here its robustness against thermal effects, that is, we investigate the role played by thermal phonons. For the efficient description of the system, we use a semiclassical approach, and benchmark it against the exact quantum evolution. The aim is to understand better and characterize how the quantum device approaches a solution of, an otherwise, difficult to solve NP-hard problem.