  We consider nonlinear boson states with a nontrivial phase structure in the
three-site Bose-Hubbard ring, {\em quantum discrete vortices} (or {\em
q-vortices}), and study their "melting" under the action of quantum
fluctuations. We calculate the spatial correlations in the ground states to
show the superfluid-insulator crossover and analyze the fidelity between the
exact and variational ground states to explore the validity of the classical
analysis. We examine the phase coherence and the effect of quantum fluctuations
on q-vortices and reveal that the breakdown of these coherent structures
through quantum fluctuations accompanies the superfluid-insulator crossover.
