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.