Coherent Ising Machines: The Good, The Bad, The Ugly

Abstract: Analog computing using bosonic computational states is a leading approach to surpassing the computational speed and energy limitations of von Neumann architectures. But the challenges of manufacturing large-scale photonic integrated circuits (PIC) has led to hybrid solutions that integrate optical analog and electronic digital components. A notable example is the coherent Ising machine (CIM), that was primarily invented for solving quadratic binary optimization problems. In this paper, we focus on a mean-field interpretation of the dynamics of optical pulses in the CIM as solutions to Langevin dynamics, a stochastic differential equation (SDE) that plays a key role in non-convex optimization and generative AI. This interpretation establishes a computational framework for understanding the system's operation, the computational role of each component, and its performance, strengths, and limitations. We then infer that the CIM is inherently a continuous state machine, capable of integrating a broad range of SDEs, in particular for solving a continuous global (or mildly constrained) optimization problems. Nevertheless, we observe that the iterative digital-to-analog and analog-to-digital conversions within the protocol create a bottleneck for the low power and high speed of optics to shine. This observation underscores the need for major advances in PIC technologies as we envision that fully analog opto-electronic realizations of such experiments can open doors for broader applications, and orders of magnitude improvements in speed and energy consumption.