InQuIR: Intermediate Representation for Interconnected Quantum Computers

Various physical constraints limit the number of qubits that can be implemented in a single quantum processor, and thus it is necessary to connect multiple quantum processors via quantum interconnects. While several compiler implementations for interconnected quantum computers have been proposed, there is no suitable representation as their compilation target. The lack of such representation impairs the reusability of compiled programs and makes it difficult to reason formally about the complicated behavior of distributed quantum programs. We propose InQuIR, an intermediate representation that can express communication and computation on distributed quantum systems. InQuIR has formal semantics that allows us to describe precisely the behaviors of distributed quantum programs. We give examples written in InQuIR to illustrate the problems arising in distributed programs, such as deadlock. We present a roadmap for static verification using type systems to deal with such a problem. We also provide software tools for InQuIR and evaluate the computational costs of quantum circuits under various conditions. Our tools are available at https://github.com/team-InQuIR/InQuIR.