Discrete Polynomial Optimization with Coherent Networks of Condensates and Complex Coupling Switching

Gain-dissipative platforms consisting of lasers, optical parametric oscillators and nonequilibrium condensates operating at the condensation or coherence threshold have been recently proposed as efficient analog simulators of the two-local spin Hamiltonians with continuous or discrete degrees of freedom. We show that nonequilibrium condensates above the threshold arranged in an interacting network may realize k-local Hamiltonians with k>2 and lead to nontrivial phase configurations. Similarly, many gain-dissipative systems that can be manipulated by optical means can bring about the ground state of the k-local Hamiltonians and solve higher-order binary optimization problems. We show how to facilitate the search for the global solution by invoking complex couplings in the system and demonstrate the efficiency of the method on the sets of complex problems. This approach offers a highly flexible new kind of computation based on gain-dissipative simulators with complex coupling switching.