  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.
