  The space of local operators in three-dimensional quantum electrodynamics
contains monopole operators that create $n$ units of gauge flux emanating from
the insertion point. This paper uses the state-operator correspondence to
calculate the anomalous dimensions of these monopole operators perturbatively
to next-to-leading order in the $1/N_f$ expansion, thus improving on the
existing leading order results in the literature. Here, $N_f$ is the number of
two-component complex fermion flavors. The scaling dimension of the $n=1$
monopole operator is $0.265 N_f - 0.0383 + O(1/N_f)$ at the infrared conformal
fixed point.
