Solving Continuous Non-convex Optimization Problems Using a Coherent Optical Network

Real-world optimization problems frequently involve decision variables that are naturally continuous. Common discrete classical optimization techniques and various realizations of coherent Ising machines (CIM) normally require the binarization of the continuous variables. These reformulations typically cause significant errors, are very costly in terms of computational resources, and can result in energy landscapes that are difficult to optimize. We propose modifications to the CIM dynamics that allow the optical pulses in the ring cavity to behave like soft spins, providing a means for solving continuous non-convex optimization problems natively in a coherent optical network. We demonstrate the capabilities of the proposed technology by presenting a time-to-solution scaling analysis for solving the NP-hard box-constrained quadratic programming (BoxQP) problem. With the BoxQP problem serving as a case study, we propose a coherent continuous-variable machine (CCVM) that we benchmark against state-of-the-art heuristic solvers to solve this problem. We show that by pumping the optical parametric oscillator pulses of a standard CIM less aggressively than usual when solving binary-variable optimization problems, their mean-field amplitudes are able to converge to fractional values.