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Recently, spatial photonic Ising machines (SPIMs) have demonstrated theabilities to compute the Ising Hamiltonian of large-scale spin systems, withthe advantages of ultrafast speed and high power efficiency. However, suchoptical computations have been limited to specific Ising models with fullyconnected couplings. Here we develop a wavelength-division multiplexing SPIM toenable programmable spin couplings and external magnetic fields as well forgeneral Ising models. We experimentally demonstrate such a wavelength-divisionmultiplexing SPIM with a single spatial light modulator, where the gaugetransformation is implemented to eliminate the impact of pixel alignment. Toshow the programmable capability of general spin coupling interactions, weexplore three spin systems: $\pm J$ models, Sherrington-Kirkpatrick models, andonly locally connected ${{J}_{1}}\texttt{-}{{J}_{2}}$ models and observe thephase transitions among the spin-glass, the ferromagnetic, the paramagnetic andthe stripe-antiferromagnetic phases. These results show that thewavelength-division multiplexing approach has great programmable flexibility ofspin couplings and external magnetic fields, which provides the opportunitiesto solve general combinatorial optimization problems with large-scale andon-demand SPIM.

Wavelength-division multiplexing optical Ising simulator enabling fully programmable spin couplings and external magnetic fields