How Physical Dynamics Shape the Properties of Ising Machines: Evaluating Oscillators vs. Bistable Latches as Ising Spins

Abstract: Ising machines exploit the natural dynamics of physical systems to minimize the Ising Hamiltonian and thereby address computationally hard combinatorial optimization problems. This paradigm has motivated a range of physical implementations. In the electronic domain, coupled networks of oscillators and bistable latches have emerged as two prominent realizations of Ising machines and are the focus of the present work. Despite this common abstraction, we demonstrate that differences in the underlying physical dynamics of oscillators and latches lead to fundamentally different stability properties and computational behavior of the resulting dynamical systems. Specifically, we show analytically that in Bistable Latch Ising Machines (BLIMs) all discrete Ising configurations possess identical linear stability, whereas in Oscillator Ising Machines (OIMs) the Jacobian spectrum depends explicitly on the spin configuration, enabling selective destabilization of higher-energy states. Evaluating the performance of both models on MaxCut instances of varying sizes, we find that this difference in stability structure yields consistently higher-quality solutions with OIMs. These results highlight how the characteristics of the device nonlinearity directly shape the dynamical and functional properties of Ising machine implementations.