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

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. 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.