  We construct "quantum theta bases," extending the set of quantum cluster
monomials, for various versions of skew-symmetric quantum cluster algebras.
These bases consist precisely of the indecomposable universally positive
elements of the algebras they generate, and the structure constants for their
multiplication are Laurent polynomials in the quantum parameter with
non-negative integer coefficients, proving the quantum strong cluster
positivity conjecture for these algebras. The classical limits recover the
theta bases considered by Gross-Hacking-Keel-Kontsevich. Our approach combines
the scattering diagram techniques used in loc. cit. with the Donaldson-Thomas
theory of quivers.
