General Oscillator-Based Ising Machine Models with Phase-Amplitude Dynamics and Polynomial Interactions
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| Format: | Preprint |
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2025
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| _version_ | 1866911516570157056 |
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| author | Sun, Lianlong Burns, Matthew X. Huang, Michael C. |
| author_facet | Sun, Lianlong Burns, Matthew X. Huang, Michael C. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_00329 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | General Oscillator-Based Ising Machine Models with Phase-Amplitude Dynamics and Polynomial Interactions Sun, Lianlong Burns, Matthew X. Huang, Michael C. Emerging Technologies 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. |
| title | General Oscillator-Based Ising Machine Models with Phase-Amplitude Dynamics and Polynomial Interactions |
| topic | Emerging Technologies |
| url | https://arxiv.org/abs/2504.00329 |