AbstractGain-dissipative systems of various physical origin have recently shown the ability to act as analogue minimisers of hard combinatorial optimisation problems. Whether or not these proposals will lead to any advantage in performance over the classical computations depends on the ability to establish controllable couplings for sufficiently dense short- and long-range interactions between the spins. Here, we propose a polaritonic XY-Ising machine based on a network of geometrically isolated polariton condensates capable of minimising discrete and continuous spin Hamiltonians. We elucidate the performance of the proposed computing platform for two types of couplings: relative and absolute. The interactions between the network nodes might be controlled by redirecting the emission between the condensates or by sending the phase information between nodes using resonant excitation. We discuss the conditions under which the proposed machine leads to a pure polariton simulator with pre-programmed couplings or results in a hybrid classical polariton simulator. We argue that the proposed architecture for the remote coupling control offers an improvement over geometrically coupled condensates in both accuracy and stability as well as increases versatility, range, and connectivity of spin Hamiltonians that can be simulated with polariton networks.
BRST approach to Lagrangian construction for bosonic continuous spin field