Erdos-Turan photonic Ising machines with record-high coupling resolution
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912623284453376 |
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| author | Li, Huaqiang Wang, Guangfeng Hasman, Erez Wang, Bo Chen, Xianfeng |
| author_facet | Li, Huaqiang Wang, Guangfeng Hasman, Erez Wang, Bo Chen, Xianfeng |
| contents | Ising machines have emerged as promising platforms for efficiently tackling a wide range of combinatorial optimization problems relevant to resource allocation, statistical inference and deep learning, yet their practical utility is fundamentally constrained by the coarse resolution of spin-spin couplings (Jij). Current implementations, relying on direct modulation of physical parameters, achieve at most 256 discrete coupling levels, which severely hinder the faithfully modeling of arbitrary real-valued interactions in realistic applications. Here we present a novel photonic Ising machine that encodes spins in random lattices while programming couplings in the momentum space of light. By introducing the Sidon set-a mathematical structure ensuring pairwise difference uniqueness - and employing the Erdos-Turan bound, we establish an optical framework in which each spin pair can be assigned a unique Jij. This approach decouples the resolution limit from hardware modulation to the spatial precision in the momentum space of light. Experimentally, we demonstrate a record-high coupling resolution of 7,038 on a simple photonic platform, surpassing previous Ising machines. Our results highlight the power of uniting discrete mathematics with momentum-space photonics, paving the way toward scalable Ising machines capable of faithfully modeling real-world optimization problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01998 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Erdos-Turan photonic Ising machines with record-high coupling resolution Li, Huaqiang Wang, Guangfeng Hasman, Erez Wang, Bo Chen, Xianfeng Optics Mathematical Physics Ising machines have emerged as promising platforms for efficiently tackling a wide range of combinatorial optimization problems relevant to resource allocation, statistical inference and deep learning, yet their practical utility is fundamentally constrained by the coarse resolution of spin-spin couplings (Jij). Current implementations, relying on direct modulation of physical parameters, achieve at most 256 discrete coupling levels, which severely hinder the faithfully modeling of arbitrary real-valued interactions in realistic applications. Here we present a novel photonic Ising machine that encodes spins in random lattices while programming couplings in the momentum space of light. By introducing the Sidon set-a mathematical structure ensuring pairwise difference uniqueness - and employing the Erdos-Turan bound, we establish an optical framework in which each spin pair can be assigned a unique Jij. This approach decouples the resolution limit from hardware modulation to the spatial precision in the momentum space of light. Experimentally, we demonstrate a record-high coupling resolution of 7,038 on a simple photonic platform, surpassing previous Ising machines. Our results highlight the power of uniting discrete mathematics with momentum-space photonics, paving the way toward scalable Ising machines capable of faithfully modeling real-world optimization problems. |
| title | Erdos-Turan photonic Ising machines with record-high coupling resolution |
| topic | Optics Mathematical Physics |
| url | https://arxiv.org/abs/2510.01998 |