  Coherent Ising Machine (CIM) is a network of optical parametric oscillators
that solves combinatorial optimization problems by finding the ground state of
an Ising Hamiltonian. In CIMs, a problem arises when attempting to realize the
Zeeman term because of the mismatch in size between interaction and Zeeman
terms due to the variable amplitude of the optical parametric oscillator pulses
corresponding to spins. There have been three approaches proposed so far to
address this problem for CIM, including the absolute mean amplitude method, the
auxiliary spin method, and the chaotic amplitude control (CAC) method. This
paper focuses on the efficient implementation of Zeeman terms within the
mean-field CIM model, which is a physics-inspired heuristic solver without
quantum noise. With the mean-field model, computation is easier than with more
physically accurate models, which makes it suitable for implementation in field
programmable gate arrays (FPGAs) and large-scale simulations. Firstly, we
examined the performance of the mean-field CIM model for realizing the Zeeman
term with the CAC method, as well as their performance when compared to a more
physically accurate model. Next, we compared the CAC method to other Zeeman
term realization techniques on the mean-field model and a more physically
accurate model. In both models, the CAC method outperformed the other methods
while retaining similar performance.
