  There is a growing interest in investigating new states of matter using
out-of-equilibrium lattice spin models in two dimensions. However, a control of
pairwise interactions in such systems has been elusive as due to their
nonequilibrium nature they maintain nontrivial particle fluxes even at the
steady state. Here we suggest how to overcome this problem and formulate a
method for engineering reconfigurable networks of nonequilibrium condensates
with control of individual pairwise interactions. Representing spin by
condensate phase, the effective two spin interactions are created with
nonresonant pumping, are directed with dissipative channels, and are further
controlled with dissipative gates. The dissipative barriers are used to block
unwanted interactions between condensates. Together, spatial anisotropy of
dissipation and pump profiles allow an effective control of sign and intensity
of the coupling strength between any two neighboring sites independent of the
rest of the spins, which we demonstrate with a two dimensional square lattice
of polariton condensates. Experimental realisation of such fully-controllable
networks offers great potential for an efficient analog Hamiltonian optimizer
and for reservoir computing.
