  To tackle challenging combinatorial optimization problems, analog computing
machines based on the nature-inspired Ising model are attracting increasing
attentions in order to disruptively overcome the impending limitations on
conventional electronic computers. Photonic spatial Ising machine has become an
unique and primitive solution with all-to-all connections to solve large-scale
Max-cut problems. However, spin configuration and flipping requires two
independent sets of spatial light modulators (SLMs) for amplitude and phase
modulation, which will lead to tremendous engineering difficulty of optical
alignment and coupling. We report a novel quadrature photonic spatial-Euler
Ising machine to realize large-scale and flexible spin-interaction
configuration and spin-flip in a single spatial light modulator, and develop a
noise enhancement approach by adding digital white noise onto detected optical
signals. We experimentally show that such proposal accelerates solving
(un)weighted, (non)fully connected, 20736-node Max-cut problems, which offers
obvious advantages over simulation and heuristic algorithm results in digital
computers.
