2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/227927F-polynomials and g-vectors were defined by Fomin and Zelevinsky to give a formula which expresses cluster variables in a cluster algebra in terms of the initial cluster data. A quantum cluster algebra is a certain noncommutative deformation of a cluster algebra. In this paper, we define and prove the existence of analogous quantum F-polynomials for quantum cluster algebras. We prove some properties of quantum F-polynomials. In particular, we give a recurrence relation which can be used to compute them. Finally, we compute quantum F-polynomials and g-vectors for a certain class of cluster variables, which includes all cluster variables in type A quantum cluster algebras.36 pages, 1 figureRings and AlgebrasCombinatoricsRepresentation Theory16S99 (Primary), 05E15, 20G42 (Secondary)text