  We have numerically studied a non-adiabatic charge transport in the quantum
Hall system pumped by a magnetic flux, as one of the simplest theoretical
realizations of non-adiabatic Thouless pumping. In the adiabatic limit, a
pumped charge is quantized, known as Laughlin's argument in a cylindrical
lattice. In a uniform electric field, we obtained a formula connecting
quantized pumping in the adiabatic limit and no-pumping in the sudden limit.
The intermediate region between the two limits is determined by the Landau gap.
A randomness or impurity effect is also discussed.
