Control of amplitude homogeneity in coherent Ising machines with artificial Zeeman terms

A coherent Ising machine (CIM) is an open-dissipative Ising solver using optical pulses generated from a degenerate optical parametric oscillator as analog magnetizations. When solving real-world optimization problems with CIM, this solver has two difficulties: mutual coupling induced amplitude inhomogeneity and absence of natural way to implement Zeeman terms. For the approximate Gaussian formulation of CIMs with amplitude control feedback, we add artificial Zeemam terms using the target amplitude information. Here we show, for 16-spin CIM with Zeeman terms, the amplitude control increases the performance, particularly when Zeeman terms are competing against mutual coupling coefficients.