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

Recently various physical systems have been proposed for modeling Ising spin Hamiltonians appealing to solve combinatorial optimization problems with remarkable performance. However, how to implement arbitrary spin-spin interactions is a critical and challenging problem in various kinds of unconventional Ising machines. Here we propose a general gauge transformation scheme to enable arbitrary spin-spin interactions and external magnetic fields as well, by decomposing an Ising Hamiltonian into multiple Mattis-type interactions. Based on this scheme, a wavelength-division multiplexing spatial photonic Ising machine (SPIM) is developed to show the programmable capability of general spin coupling interactions. We exploit the wavelength-division multiplexing SPIM to simulate three spin systems: pm J models, Sherrington-Kirkpatrick models, and only locally connected J1/J2 models and observe the phase transitions among the spin-glass, the ferromagnetic, the paramagnetic and the stripe-antiferromagnetic phases. We also demonstrate the ground state search for solving the Max-Cut problem with the wavelength-division multiplexing SPIM. These results promise the realization of ultrafast-speed and high-power-efficiency Boltzmann sampling of a generalized large-scale Ising model.