Fig. 2: Ground state energy and magnetization of the nonlinear optical Ising machine.

a Experimentally measured Ising energy and (b) magnetization of the spin model as a function of the Monte-Carlo iterations for four-body coefficient γ = 1 (blue) and 500 (orange). The inset of panel (b) shows the converged spin configurations of the Ising model at the end of the time evolution, with the blue and yellow pixels corresponding to opposite spins. c Experimentally measured magnetization as a function of temperature for γ = 0, 100, 500. d The same results obtained from full Monte-Carlo numerical simulation. Error bars in each measurement are less than the size of the dots. Errors in the experiment could be arise due to the slight laser power fluctuations, temperature variation, and optical misalignment, etc. In (c, d), the magnetization drops to zero continuously at γ = 1 (blue), 100 (orange) and abruptly at γ = 500 (green) with the thick lines the guides to the eyes.