Quantum Switches for Gottesman-Kitaev-Preskill Qubit-Based All-Photonic Quantum Networks

The Gottesman-Kitaev-Preskill (GKP) code, being information theoretically near optimal for quantum communication over Gaussian thermal-loss optical channels, is likely to be the encoding of choice for advanced quantum networks of the future. Quantum repeaters based on GKP-encoded light have been shown to support high end-to-end entanglement rates across large distances despite realistic finite squeezing in GKP code preparation and homodyne detection inefficiencies. Here, we introduce a quantum switch for GKP qubit-based quantum networks. Its architecture involves multiplexed GKP qubit-based entanglement link generation with clients and their all-photonic storage, enabled by GKP qubit graph state resources. The switch uses a multiclient generalization of a recently introduced entanglement-ranking-based link matching heuristic for bipartite entanglement distribution between clients via entanglement swapping. Since generating the GKP qubit graph state resource is hardware intensive, given a total resource budget and an arbitrary layout of clients, we address the question of their optimal allocation to the different client-pair connections served by the switch such that the switch's sum throughput is maximized while also being fair in terms of the individual entanglement rates. We illustrate our results for an exemplary data center network, where the data center is a client of a switch, and all of its other clients aim to connect to the data center alone-a scenario that also captures the general case of a gateway router connecting a local area network to a global network. Together with compatible quantum repeaters, our quantum switch provides a way to realize quantum networks of arbitrary topology.