arXiv subjects

E. M. H. E. B. Ekanayake

Publications and source records attributed to E. M. H. E. B. Ekanayake.

3 recordsLinked to original sources

arXiv2025

Analyzing Parametric Oscillator Ising Machines through the Kuramoto Lens

Networks of coupled nonlinear oscillators are emerging as powerful physical platforms for implementing Ising machines. Yet the relationship between parametric-oscillator implementations and traditional oscillator-based Ising machines remains underexplored. In this work, we develop a Kuramoto-style, canonical phase description of parametric oscillator Ising machines by starting from the Stuart-Landau oscillator model -- the canonical normal form near a Hopf bifurcation, and a natural reduced description for many parametric oscillator implementations such as the degenerate optical parametric oscillator (DOPO) among others. The resulting phase dynamics combine the usual phase-difference coupling observed in the standard Kuramoto model along with an intrinsic phase sum term that is generated when conjugate coupling is considered. Moreover, our formulation helps explain why explicit second-harmonic driving is unnecessary in parametric oscillators and also reveals how quasi-steady amplitude heterogeneity scales the original strength of the spin interaction with potentially adverse impacts on the solution quality. Our work helps develop a unifying view of the oscillator-based approach to designing Ising machines.

eess.SY↗

arXiv2025

Spin Freezing in Oscillator Ising Machines: When Second Harmonic Injection Impedes Computation

Second harmonic injection (SHI) has emerged as a critical mechanism in enabling networks of coupled oscillators to function as Oscillator Ising Machines (OIMs), capable of minimizing the Ising Hamiltonian. While SHI facilitates phase binarization essential for mapping oscillator phases to spin states, we demonstrate that it can also induce a previously unreported phenomenon -- spin freezing -- where oscillator spins are unable to transition between spin states, even when such a transition can reduce the Ising energy. This freezing effect can impair the analog dynamics of the OIM, preventing it from reaching lower-energy spin configurations. Through theoretical analysis and numerical simulations, we show that the onset of spin freezing is highly sensitive to the initial phase configuration of the oscillators. Contrary to conventional practice, which favors random initialization, we find that initializing all oscillators at specific phase values ($ϕ= π$ or $ϕ= \fracπ{2}$) delays the onset of spin freezing and consistently yields higher-quality solutions. These findings point to the need to carefully engineer the SHI for optimal performance.

physics.comp-ph↗

arXiv2025

Different Paths, Same Destination: Designing New Physics-Inspired Dynamical Systems with Engineered Stability to Minimize the Ising Hamiltonian

Oscillator Ising machines (OIMs) represent an exemplar case of using physics-inspired non-linear dynamical systems to solve computationally challenging combinatorial optimization problems (COPs). The computational performance of such systems is highly sensitive to the underlying dynamical properties, the topology of the input graph, and their relative compatibility. In this work, we explore the concept of designing different dynamical systems that minimize the same objective function but exhibit drastically different dynamical properties. Our goal is to leverage this diversification in dynamics to reduce the sensitivity of the computational performance to the underlying graph, and subsequently, enhance the overall effectiveness of such physics-based computational methods. To this end, we introduce a novel dynamical system, the Dynamical Ising Machine (DIM), which, like the OIM, minimizes the Ising Hamiltonian but offers significantly different dynamical properties. We analyze the characteristic properties of the DIM and compare them with those of the OIM. We also show that the relative performance of each model is dependent on the input graph. Our work illustrates that using multiple dynamical systems with varying properties to solve the same COP enables an effective method that is less sensitive to the input graph, while producing robust solutions.

cs.LG↗