  We establish a quantum cluster algebra structure on the quantum Grothendieck
ring of a certain monoidal subcategory of the category of finite-dimensional
representations of a simply-laced quantum affine algebra. Moreover, the
(q,t)-characters of certain irreducible representations, among which
fundamental representations, are obtained as quantum cluster variables. This
approach gives a new algorithm to compute these (q,t)-characters. As an
application, we prove that the quantum Grothendieck ring of a larger category
of representations of the Borel subalgebra of the quantum affine algebra,
defined in a previous work as a quantum cluster algebra, contains indeed the
well-known quantum Grothendieck ring of the category of finite-dimensional
representations. Finally, we display our algorithm on a concrete example.
