  Many proposals to scale quantum technology rely on modular or distributed
designs where individual quantum processors, called nodes, are linked together
to form one large multinode quantum computer (MNQC). One scalable method to
construct an MNQC is using superconducting quantum systems with optical
interconnects. However, a limiting factor of these machines will be internode
gates, which may be two to three orders of magnitude noisier and slower than
local operations. Surmounting the limitations of internode gates will require a
range of techniques, including improvements in entanglement generation, the use
of entanglement distillation, and optimized software and compilers, and it
remains unclear how improvements to these components interact to affect overall
system performance, what performance from each is required, or even how to
quantify the performance of each. In this paper, we employ a `co-design'
inspired approach to quantify overall MNQC performance in terms of hardware
models of internode links, entanglement distillation, and local architecture.
In the case of superconducting MNQCs with microwave-to-optical links, we
uncover a tradeoff between entanglement generation and distillation that
threatens to degrade performance. We show how to navigate this tradeoff, lay
out how compilers should optimize between local and internode gates, and
discuss when noisy quantum links have an advantage over purely classical links.
Using these results, we introduce a roadmap for the realization of early MNQCs
which illustrates potential improvements to the hardware and software of MNQCs
and outlines criteria for evaluating the landscape, from progress in
entanglement generation and quantum memory to dedicated algorithms such as
distributed quantum phase estimation. While we focus on superconducting devices
with optical interconnects, our approach is general across MNQC
implementations.
