  Interconnecting clusters of qubits will be an essential element of scaling up
future quantum computers. Operations between quantum processing units (QPUs)
are usually significantly slower and costlier than those within a single QPU,
so usage of the interconnect must be carefully managed. This is loosely
analogous to the need to manage shared caches or memory in classical multi-CPU
machines. Unlike classical clusters, however, quantum data is subject to the
no-cloning theorem, which necessitates a rethinking of cache coherency
strategies. Here, we consider a simple strategy of using EPR-mediated remote
gates and teleporting qubits between clusters as necessary. Crucially, we
develop optimizations at compile-time that leverage local structure in a
quantum circuit, so as to minimize inter-cluster operations at runtime. We
benchmark our approach against existing quantum compilation and optimization
routines, and find significant improvements in circuit depth and interconnect
usage.
