  We propose and demonstrate a nonlinear optics approach to emulate Ising
machines containing up to a million spins and with tailored two and four-body
interactions with all-to-all connections. It uses a spatial light modulator to
encode and control the spins in the form of the binary phase values of wavelets
in coherent laser beams, and emulates the high-order interaction with frequency
conversion in a nonlinear crystal at the Fourier plane. By adaptive feedback
control, 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 new tool to probe
complex, many-body physics and give rise to exciting applications in big data
optimization, computing, and analytics.
