  Networks of optical oscillators simulating coupled Ising spins have been
recently proposed as a heuristic platform to solve hard optimization problems.
These networks, called coherent Ising machines (CIMs), exploit the fact that
the collective nonlinear dynamics of coupled oscillators can drive the system
close to the global minimum of the classical Ising Hamiltonian, encoded in the
coupling matrix of the network. To date, realizations of large-scale CIMs have
been demonstrated using hybrid optical-electronic setups, where optical
oscillators simulating different spins are subject to electronic feedback
mechanisms emulating their mutual interaction. While the optical evolution
ensures an ultrafast computation, the electronic coupling represents a
bottleneck that causes the computational time to severely depend on the system
size. Here, we propose an all-optical scalable CIM with fully-programmable
coupling. Our setup consists of an optical parametric amplifier with a spatial
light modulator (SLM) within the parametric cavity. The spin variables are
encoded in the binary phases of the optical wavefront of the signal beam at
different spatial points, defined by the pixels of the SLM. We first discuss
how different coupling topologies can be achieved by different configurations
of the SLM, and then benchmark our setup with a numerical simulation that
mimics the dynamics of the proposed machine. In our proposal, both the spin
dynamics and the coupling are fully performed in parallel, paving the way
towards the realization of size-independent ultrafast optical hardware for
large-scale computation purposes.
