Networking quantum networks with minimum cost aggregation

A quantum internet holds promise for accomplishing distributed quantum sensing and large-scale quantum computer networks, as well as quantum communication among arbitrary clients all over the globe. The main building block is efficient distribution of entanglement, entangled bits (ebits), across quantum networks. This could be achieved by aggregating quantum repeater protocols. However, the existing protocol is not practical as it requires point-to-point entanglement generation, the first step of the protocol, not only to suppress the error, depending on the whole size of the networks, but also to be run more than necessary. Here we present a practical recipe on how to aggregate quantum networks in order to present ebits to clients with minimum cost. This is combined with a conception of concatenation to enable arbitrary clients to have arbitrary long-distance communication with fixed error across quantum networks, regardless of the overall size. Our recipe forms the basis of designing a quantum internet protocol to control a self-organizing large-scale quantum network.