Complex quantum networks on a lattice of spins*

Recent findings have suggested that a future quantum internet could benefit from network complexity, as characterized by a heavy-tailed degree distribution, small world property, etc. However, the impact of complexity on quantum communication networks is still not fully understood, and there are known challenges. Here, we present a model of complex quantum communication networks in the context of interacting quantum spin systems on a lattice. In particular, we consider the two-dimensional Random Transverse Ising Model (RTIM), which has a ground state that conveniently factorizes into independent GHZ spin clusters. We show that these GHZ clusters can act as quantum communication links between local regions of spins on the lattice. By appropriately choosing many local regions of spins from a broad size distribution, the GHZ clusters can connect the regions in a network which we show can have considerable network complexity. The resulting model of a complex quantum communication network is generalizable to other interacting quantum spin systems, and is amenable to further studies towards understanding the role of complexity in a future quantum internet.