  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, whose architecture involves multiplexed GKP-qubit-based entanglement
link generation with clients, and their all-photonic storage, together enabled
by GKP-qubit graph state resources. For bipartite entanglement distribution
between clients via entanglement swapping, the switch uses a multi-client
generalization of a recently introduced $\textit{entanglement-ranking-based
link matching}$ protocol heuristic. 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 towards
the different client-pair connections served by the switch such that the sum
throughput of the switch 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.
