General Oscillator-Based Ising Machine Models with Phase-Amplitude Dynamics and Polynomial Interactions
This work strengthens the theoretical foundation and practical applicability of oscillator-based Ising machines for complex optimization problems, though it appears incremental in advancing existing models.
The authors tackled combinatorial optimization problems with polynomial cost functions by developing an oscillator-based Ising machine model with phase-amplitude dynamics, which demonstrated monotonic energy decrease and reliable convergence, showing significant performance improvements on 3-SAT problems over existing models.
We present an oscillator model with both phase and amplitude dynamics for oscillator-based Ising machines (OIMs). The model targets combinatorial optimization problems with polynomial cost functions of arbitrary order and addresses fundamental limitations of previous OIM models through a mathematically rigorous formulation with a well-defined energy function and corresponding dynamics. The model demonstrates monotonic energy decrease and reliable convergence to low-energy states. Empirical evaluations on 3-SAT problems show significant performance improvements over existing phase-amplitude models. Additionally, we propose a flexible, generalizable framework for designing higher-order oscillator interactions, from which we derive a practical method for oscillator binarization without compromising performance. This work strengthens both the theoretical foundation and practical applicability of oscillator-based Ising machines for complex optimization problems.