  We study the collective decay rates of multi-dimensional quantum networks in
which one-dimensional waveguides form an intersecting hyper-rectangular
lattice, with qubits located at the lattice points. We introduce and motivate
the \emph{dimensional reduction of poles} (DRoP) conjecture, which identifies
all collective decay rates of such networks via a connection to waveguides with
a one-dimensional topology (e.g. a linear chain of qubits). Using DRoP, we
consider many-body effects such as superradiance, subradiance, and bound-states
in continuum in multi-dimensional quantum networks. We find that, unlike
one-dimensional linear chains, multi-dimensional quantum networks have
superradiance in distinct levels, which we call multi-dimensional
superradiance. Furthermore, we generalize the $N^{-3}$ scaling of subradiance
in a linear chain to $d$-dimensional networks.
