  In this paper, we study non-commutative projective schemes whose associated
non-commutative graded algebras are finite over their centers. We study their
moduli spaces of stable sheaves, and construct a symmetric obstruction theory
in the Calabi-Yau-3 case. This allows us to define Donaldson-Thomas type
invariants. We also discuss the simplest examples, called quantum Fermat
quintic threefolds.
