Much recent work on distributed quantum computing have focused on the use of entangled pairs and distributed two qubit gates. But there has also been work on efficient schemes for achieving multipartite entanglement between nodes in a single shot, removing the need to generate multipartite entangled states using many entangled pairs. This paper looks at how multipartite entanglement resources (e.g., GHZ states) can be useful for distributed fan-out operations; we also consider the use of qudits of dimension four for distributed quantum circuit compression. In particular, we consider how such fan-out operations and qudits can be used to implement circuits which are challenging for distributed quantum computation, involving pairwise qubit interactions, i.e., what has been called global gates (a.k.a. global Mølmer-Sørensen gates). Such gates have been explored to possibly yield more efficient computations via reduced circuit depth, and can be carried out efficiently in some types of quantum hardware (e.g., trapped-ion quantum computers); we consider this as an exploration of an ``extreme'' case for distribution given the global qubit-qubit interactions. We also conclude with some implications for future work on quantum circuit compilation and quantum data centre design.

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