  We study supercooled dynamics in quantum hard-sphere liquid using quantum
mode-coupling formulation. In the moderate quantum regime, classical cage
effects lead to slower dynamics compared to strongly quantum regime, where
tunneling overcomes classical caging, leading to faster relaxation. As a
result, the glass transition critical density can become significantly higher
than for the classical liquids. Perturbative approach is used to solve time
dependent quantum mode-coupling equations to study in detail the dynamics of
the supercooled liquid in moderate quantum regime. Similar to the classical
case, relaxation time shows power-law increase with increasing density in the
supercooled regime. However, the power-law exponent is found to be dependent on
the quantumness; it increases linearly as the quantumness is increased in the
moderate quantum regime.
