InterQnet is a project to advance the state of the art in scalable quantum communications through work aimed at realizing two interrelated overarching goals: (1) practical realization of a full-stack heterogeneous quantum network (InterQnet-Demo) and (2) systems study of a scalable quantum network architecture (InterQnet-Scale). By realizing these two goals, InterQnet will provide a fundamental building block and foundational architectural choices toward realizing national-scale quantum networks.