  Gain-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.
