  Quantum networking at many scales will be critical to future quantum
technologies and experiments on quantum systems. Photonic links enable quantum
networking. They will connect co-located quantum processors to enable
large-scale quantum computers, provide links between distant quantum computers
to support distributed, delegated, and blind quantum computing, and will link
distant nodes in space enabling new tests of fundamental physics. Here, we
discuss recent work advancing photonic tools and protocols that support quantum
networking. We provide analytical results and numerics for the effect of
distinguishability errors on key photonic circuits; we considered a variety of
error models and developed new metrics for benchmarking the quality of
generated photonic states. We review a distillation protocol by one of the
authors that mitigates distinguishability errors. We also review recent results
by a subset of the authors on the efficient simulation of photonic circuits via
approximation by coherent states. We study some interactions between the theory
of universal sets, unitary t-designs, and photonics: while many of the results
we state in this direction may be known to experts, we aim to bring them to the
attention of the broader quantum information science community and to phrase
them in ways that are more familiar to this community. We prove, translating a
result from representation theory, that there are no non-universal infinite
closed $2$-designs in $U(V)$ when $\dim V \geq 2$. As a consequence, we observe
that linear optical unitaries form a $1$-design but not a 2-design. Finally, we
apply a result of Oszmaniec and Zimbor\'{a}s to prove that augmenting the
linear optical unitaries with any nontrivial SNAP gate is sufficient to achieve
universality.
