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General oscillator-based Ising-machine models with phase-amplitude dynamics and polynomial interactions

Lianlong Sun*, Matthew X. Burns†, and Michael C. Huang‡

  • *Contact author: lianlongsun@rochester.edu
  • †Contact author: mburns13@ur.rochester.edu
  • ‡Contact author: michael.huang@rochester.edu
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Phys. Rev. Applied 24, 044035 – Published 10 October, 2025

DOI: https://doi.org/10.1103/7s4v-4hs4

Abstract

This paper is a contribution to the Physical Review Applied collection titled Physics-Inspired Computing.

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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This article appears in the following collection:

Collection on Physics-Inspired Computing

Physical Review Applied is pleased to present a Collection on Physics-Inspired Computing, highlighting the rapidly evolving field of energy-efficient computing techniques, from hardware technologies to algorithms, where physics inspiration serves as the crucial link. Contributions to this collection will be published throughout 2025. This Collection is being curated by Guest Editors Kerem Camsari and Supriyo Datta.

Article Text

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Phys. Rev. Applied 24, 044035– Published 10 October, 2025
  • Received 31 March 2025
  • Revised 17 July 2025
  • Accepted 11 September 2025
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