  In this paper, we construct twist automorphisms on quantum unipotent cells,
which are quantum analogues of the Berenstein-Fomin-Zelevinsky twist
automorphisms on unipotent cells. We show that those quantum twist
automorphisms preserve the dual canonical bases of quantum unipotent cells.
Moreover, we prove that quantum twist automorphisms are described by the syzygy
functors for representations of preprojective algebras in the symmetric case.
This is the quantum analogue of Gei{\ss}-Leclerc-Schr\"oer's description, and
Gei{\ss}-Leclerc-Schr\"oer's results are essential in our proof. As a
consequence, we show that quantum twist automorphisms are compatible with
quantum cluster monomials. The 6-periodicity of specific quantum twist
automorphisms is also verified.
