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Gain-dissipative platforms consisting of lasers, optical parametricoscillators and nonequilibrium condensates operating at thecondensation/coherence threshold have been recently proposed as efficientanalog simulators of 2-local spin Hamiltonians with continuous or discretedegrees of freedom. We show that nonequilibrium condensates above the thresholdarranged in an interacting network may realise k-local Hamiltonians with k>2and lead to nontrivial phase configurations. The principle of the operation ofsuch a system lays the ground for physics-inspired computing and the newefficient methods for finding solutions to the higher order binary optimizationproblems. We show how to facilitate the search for the global solution byinvoking complex couplings in the system and demonstrate the efficiency of themethod on tensors with million entries. This approach offers a highly flexiblenew kind of computation based on gain-dissipative simulators with complexcoupling switching. g.

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