By using transport and magnetic measurements, the upper critical held H-c2(
T) and the irreversibility line H;,,(T) have been determined. A large separ
ation between H-c2(0) and H-irr(0) has been found showing the existence of
a quantum vortex liquid state induced by quantum fluctuation of vortices in
the new superconductor MgB2. Further investigation of the magnetic relaxat
ion shows that both the quantum tunnelling and the thermally activated flux
creep depend weakly on temperature. However, when the melting field Hi,, i
s approached, a drastic rise of the relaxation rate is observed. This may i
ndicate that the melting of the vortex matter at a finite temperature is al
so induced by the quantum fluctuation of vortices.