Large-scale Ising emulation with four body interaction and all-to-all connections

• Published in: Communications physics 2020-06, Vol.3 (1), Article 108
• Main Authors: Kumar, Santosh, Zhang, He, Huang, Yu-Ping
• Format: Article
• Language: English
• Subjects: 639/624/400/482; 639/766/400/385; Adaptive systems; Combinatorial analysis; Digital computers; Ising model; Many body problem; Nonlinear optics; Optimization; Physics; Physics and Astronomy; Spatial light modulators
• ISSN: 2399-3650; 2399-3650
• DOI: 10.1038/s42005-020-0376-5

Optical Ising machines with two-body interactions have shown potential in solving combinatorial optimization problems which are extremely hard to solve with digital computers. Yet, some physical systems cannot be properly described by only two-body interactions. Here, we propose and demonstrate a nonlinear optics approach to emulate Ising machines containing many spins (up to a million in the absence of optical imperfections) and with tailored all-to-all two and four-body interactions. Our approach employs a spatial light modulator to encode and control the spins in the form of the binary-phase values, and emulates the high-order interaction with frequency conversion in a nonlinear crystal. By implementing adaptive feedback, the system can be evolved into effective spin configurations that well-approximate the ground-states of Ising Hamiltonians with all-to-all connected many-body interactions. Our technique could serve as a tool to probe complex, many-body physics and give rise to exciting applications in big-data optimization, computing, and analytics. Optical Ising machines provide a means to process and optimise large data sets but cannot fully capture many-body interactions yet. This work experimentally demonstrates adjustable two- and four-body interactions and all-to-all connections for up to a million emulated spins.