  We study monopole operators at the conformal critical point of the
$\mathbb{CP}^{N_b - 1}$ theory in $2+1$ spacetime dimensions. Using the
state-operator correspondence and a saddle point approximation, we compute the
scaling dimensions of these operators to next-to-leading order in $1/N_b$. We
find remarkable agreement between our results and numerical studies of quantum
antiferromagnets on two-dimensional lattices with SU($N_b$) global symmetry,
using the mapping of the monopole operators to valence bond solid order
parameters of the lattice antiferromagnet.
