  Let $(S,M,U)$ be a marked orbifold with or without punctures and let
$\mathcal A_v$ be a quantum cluster algebra from $(S,M,U)$ with arbitrary
coefficients and quantization. We provide combinatorial formulas for quantum
Laurent expansion of quantum cluster variables of $\mathcal A_v$ concerning an
arbitrary quantum seed. Consequently, the positivity for the quantum cluster
algebra $\mathcal A_v$ is proved.
