Fig. 3: Hierarchical coupling to construct the hyperspin machine.
Specifically, we show here an N = 3 XY machine (D = 2) with antiferromagnetic linear coupling (Jqp = − J and \({{{{{{{\bf{G}}}}}}}}={{\mathbb{1}}}_{2}\), red lines and areas). We report the equations of motion for X1 and X2 [d = h/4 − 1/2, see Eq. (5)] for completeness. a Without common pump saturation (i.e., the pump for the Xj PO is saturated by \({X}_{j}^{2}\) only), the system consists of two disjoint PO networks (there is no coupling between X1,3,5 and X2,4,6), where each network is an Ising simulator yielding σj = ± 1. In this way, no continuous spin is defined following Fig. 1. b In contrast to a, with common pump saturation (gray dots and area) POs within each multiplet are now effectively coupled by a nonlinear coupling. This nonlinear coupling makes each PO multiplet suitable to represent an hyperspin (see Fig. 1). In addition to this nonlinear coupling, the linear coupling between POs in different multiplets realizes the hyperspin machine.
