Enabling quantum communication in ultra-large-scale networks

The recent development of small-scale quantum networks poses the question of whether such a technology could also operate at scale in the futuristic Quantum Internet. The question can be answered with a classical approach where an arbitrary quantum network is represented as a classical graph, and communication reliability is assessed using methods proper of network theory. Unfortunately, sufficient conditions for viable network-wide communication have been established only for special topologies like regular lattices. No practical communication protocols have been developed so far for real network topologies, if not for relatively small networks. Here, we overcome these limitations by devising a family of quantum communication protocols that can be applied to networks with arbitrary topology, composed of even hundreds of millions nodes. By performing a systematic analysis on both real and synthetic graphs, we show that the proposed protocols are sustainable on heterogeneous networks. For random scale-free graphs, we analytically prove that viable quantum communication persists in the thermodynamic limit. Our findings provide evidence that the Quantum Internet will be capable of sustaining a ultra-large-scale growth comparable to one already experienced by its classical predecessor.