The design of adders on quantum dot cellular automata (QCA) has been of recent interest. While few designs exist, investigations on reduction of QCA primitives (majority gates and inverters) for various adders are limited. In this paper, we present a number of new results on majority logic. We use these results to present efficient QCA designs for the ripple carry adder (RCA) and various prefix adders. We derive bounds on the number of majority gates for -bit RCA and -bit Brent-Kung, Kogge-Stone, Ladner-Fischer, and Han-Carlson adders. We further show that the Brent-Kung adder has lower delay than the best existing adder designs as well as other prefix adders. In addition, signal integrity and robustness studies show that the proposed Brent-Kung adder is fairly well-suited to changes in time-related parameters as well as temperature. Detailed simulations using QCADesigner are presented.