Performance analysis of classical adiabatic annealing on Ising machines

Ising machines are a promising approach to solve optimization problems. They map them onto the Ising model and search for low-energy configurations. However, navigating the rugged energy landscapes remains difficult. To improve this navigation, classical adiabatic annealing has been proposed as a heuristic optimization method for classical Ising machines. Using this technique, the Hamiltonian of the Ising machine is gradually transformed from an easily solvable Hamiltonian to the target Hamiltonian. However, its claimed effectiveness is primarily motivated by an analogy to quantum adiabatic annealing, and systematic benchmarking has remained limited. In this work, we investigate the potential of classical adiabatic annealing as an optimization strategy for analog Ising machines. Using continuation methods, we analyze its dynamics and identify saddle node bifurcations as a key mechanism limiting performance. Motivated by this insight, we develop an optimized annealing strategy we refer to as hybrid classical adiabatic annealing, designed to circumvent these bifurcations and assess its performance. Although the proposed approach can improve convergence to optimal solutions, numerical simulations show only marginal performance gains compared to other optimization strategies. We therefore conclude that, while the hybrid strategy can offer occasional benefits, it does not provide a sufficient practical advantage over simpler, existing techniques.