We measure the fluctuations ͑noise͒ of the vortex-flow voltage in the low-temperature liquid phase of thick amorphous ͑a-͒Mg x B 1−x and a-Mo x Si 1−x films with different transition temperatures and widths of the quantum-vortex-liquid ͑QVL͒ phase. An anomalous vortex flow with an asymmetric distribution of ͑real-time͒ voltage fluctuations is commonly observed in the QVL phase, independent of material as well as strength of quantum fluctuations. In the QVL phase we observe the Lorentzian-type noise spectra indicative of shot noise, whose origin is attributed to the vortex bundles that are depinned and pinned randomly in the stationary flow of QVL.