  We investigate the possibility of solving continuous non-convex optimization
problems using a network of interacting quantum optical oscillators. We propose
a native encoding of continuous variables in analog signals associated with the
quadrature operators of a set of quantum optical modes. Optical coupling of the
modes and noise introduced by vacuum fluctuations from external reservoirs or
by weak measurements of the modes are used to optically simulate a diffusion
process on a set of continuous random variables. The process is run
sufficiently long for it to relax into the steady state of an energy potential
defined on a continuous domain. As a first demonstration, we numerically
benchmark solving box-constrained quadratic programming (BoxQP) problems using
these settings. We consider delay-line and measurement-feedback variants of the
experiment. Our benchmarking results demonstrate that in both cases the optical
network is capable of solving BoxQP problems over three orders of magnitude
faster than a state-of-the-art classical heuristic.
