  Neutral atoms are among the leading platforms toward realizing fault-tolerant
quantum computation (FTQC). However, scaling up a single neutral-atom device
beyond $\sim 10^4$ atoms to meet the demands of FTQC for practical applications
remains a challenge. To overcome this challenge, we clarify the criteria and
technological requirements for further scaling based on multiple neutral atom
quantum processing units (QPUs) connected through photonic networking links.
Our quantitative analysis shows that nanofiber optical cavities have the
potential as an efficient atom-photon interface to enable fast entanglement
generation between atoms in distinct neutral-atom modules, allowing multiple
neutral-atom QPUs to operate cooperatively without sacrificing computational
speed. Using state-of-the-art millimeter-scale nanofiber cavities with the
finesse of thousands, over a hundred atoms can be coupled to the cavity mode
with an optical tweezer array, with expected single-atom cooperativity
exceeding 100 for telecom-band transition of ytterbium atoms. This enables
efficient time-multiplexed entanglement generation with a predicted Bell pair
generation rate of 100 kHz while maintaining a small footprint for channel
multiplexing. These proposals and results indicate a promising pathway for
building large-scale multiprocessor fault-tolerant quantum computers using
neutral atoms, nanofiber optical cavities, and fiber-optic networks.
