  We consider a heterogeneous network of quantum computing modules, sparsely
connected via Bell states. Operations across these connections constitute a
computational bottleneck and they are likely to add more noise to the
computation than operations performed within a module. We introduce several
techniques for transforming a given quantum circuit into one implementable on a
network of the aforementioned type, minimising the number of Bell states
required to do so.
  We extend previous works on circuit distribution over fully connected
networks to the case of heterogeneous networks. On the one hand, we extend the
hypergraph approach of [Andres-Martinez & Heunen. 2019] to arbitrary network
topologies. We additionally make use of Steiner trees to find efficient
realisations of the entanglement sharing within the network, reusing already
established connections as often as possible. On the other hand, we extend the
embedding techniques of [Wu, et al. 2022] to networks with more than two
modules. Furthermore, we discuss how these two seemingly incompatible
approaches can be made to cooperate. Our proposal is implemented and
benchmarked; the results confirming that, when orchestrated, the two approaches
complement each other's weaknesses.
