Pseudo-Hermitian Ising machines from magnetic systems

Ising machines are hardware solvers that attempt to solve challenging combinatorial problems by encoding them in complex physical systems. We identify instances of pseudo-Hermitian physics in classical macrospin dynamics and study their nonequilibirum behavior as described by the Landau-Lifshitz-Gilbert equation. We then discuss scaling to large system sizes with long range dissipative coupling. We then propose a scheme which utilizes unique features offered by pseudo-Hermitian physics to construct dynamical Ising machines. Using analytic methods, we identify mappings onto NP-complete and NP-hard problems, which we then simulate numerically for small sizes. Finally, we discuss applications in the broader field of neuromorphic computing.