  We construct an efficient Monte Carlo algorithm that overcomes the severe
signal-to-noise ratio problems and helps us to accurately compute the conformal
dimensions of large-$Q$ fields at the Wilson-Fisher fixed point in the $O(2)$
universality class. Using it we verify a recent proposal that conformal
dimensions of strongly coupled conformal field theories with a global $U(1)$
charge can be obtained via a series expansion in the inverse charge $1/Q$. We
find that the conformal dimensions of the lowest operator with a fixed charge
$Q$ are almost entirely determined by the first few terms in the series.
