In this paper, we give a characterization of generalized quantum gates. We also show that many important operators are generalized quantum gates, moreover, some of these operators can be represented as the convex combination of only two unitary operators. Our results answer what kinds of operations a duality quantum computing admits. We point out that the set of all generalized quantum gates coincides with the set of all restricted allowable generalized quantum gates. Thus, our results are also valid for restricted allowable generalized quantum gates