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arXiv · 2504.00329

General Oscillator-Based Ising Machine Models with Phase-Amplitude Dynamics and Polynomial Interactions

Lianlong Sun·Matthew X. Burns·Michael C. Huang
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Abstract

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.

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Lianlong Sun, Matthew X. Burns, Michael C. Huang. 2025-04-01. General Oscillator-Based Ising Machine Models with Phase-Amplitude Dynamics and Polynomial Interactions. https://doi.org/10.1103/7s4v-4hs4

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