Quantum circuit optimization for multiple QPUs using local structure

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.