  Quantum resource theories (QRTs) provide a comprehensive and practical
framework for the analysis of diverse quantum phenomena. A fundamental task
within QRTs is the quantification of resources inherent in a given quantum
state. In this letter, we introduce a unified computational framework for a
class of widely utilized quantum resource measures, derived from convex roof
extensions. We establish that the computation of these convex roof resource
measures can be reformulated as an optimization problem over a Stiefel
manifold, which can be further unconstrained through polar projection. Compared
to existing methods employing semi-definite programming (SDP), gradient-based
techniques or seesaw strategy, our approach not only demonstrates superior
computational efficiency but also maintains applicability across various
scenarios within a streamlined workflow. We substantiate the efficacy of our
method by applying it to several key quantum resources, including entanglement,
coherence, and magic states. Moreover, our methodology can be readily extended
to other convex roof quantities beyond the domain of resource theories,
suggesting broad applicability in the realm of quantum information theory.
