Solving a 3-spin Combinatorial Optimization Model Using Macrospin-Based LLG Dynamics

Physical dynamics have long inspired new ways of computing. Recent progress in Ising machines—physical systems that solve optimization problems by evolving toward minima of Ising-like Hamiltonians—motivates studying how different non-classical computing models derive their computational advantages from underlying physical dynamics. In our previous work, we showed that a bit encoded in a macrospin evolving under Landau–Lifshitz–Gilbert (LLG) dynamics can efficiently find the ground state of the Sherrington–Kirkpatrick (SK) model and approach the Parisi value asymptotically [1]. However, the SK model is not sufficient for a thorough comparison between classical binary bits and the LLG driven macrospins, as it does not demonstrate the overlap gap property (OGP), a topological indicator of algorithmic hardness. In this study, we use the same LLG framework to solve the 3-spin model that exhibits the OGP. We benchmark the performance of LLG dynamics against other classical and non-classical computing models. Our results offer physical insight into what properties make certain physical structures advantageous in solving optimization problems, and how they may inform the design of future Ising-based computing architectures.