  In this work, we introduce a method to construct fault-tolerant
measurement-based quantum computation (MBQC) architectures and numerically
estimate their performance over various types of networks. A possible
application of such a paradigm is distributed quantum computation, where
separate computing nodes work together on a fault-tolerant computation through
entanglement. We gauge error thresholds of the architectures with an efficient
stabilizer simulator to investigate the resilience against both circuit-level
and network noise. We show that, for both monolithic (i.e., non-distributed)
and distributed implementations, an architecture based on the diamond lattice
may outperform the conventional cubic lattice. Moreover, the high erasure
thresholds of non-cubic lattices may be exploited further in a distributed
context, as their performance may be boosted through entanglement distillation
by trading in entanglement success rates against erasure errors during the
error-decoding process. These results highlight the significance of lattice
geometry in the design of fault-tolerant measurement-based quantum computing on
a network, emphasizing the potential for constructing robust and scalable
distributed quantum computers.
