  We investigate the influence of quantum fluctuations and weak disorder on the
vortex dynamics in a two-dimensional superconducting
Berezinskii-Kosterlitz-Thouless system. The temperature below which quantum
fluctuations dominate the vortex creep is determined, and the transport in this
quantum regime is described. The crossover from quantum to classical regime is
discussed and the quantum correction to the classical current-voltage relation
is determined. It is found that weak disorder can effectively reduce the
critical current as compared to that in the clean system.
