The development of quantum computing theory can lead to very powerful and energy-efficient integrated infrastructures in the near future. Research in this area is already very active and promising. In this paper, we present the design of a binary adder of the 2n − 1 type, built on the basis of the technology of cellular automata on quantum dots. The proposed adder effectively uses internal logic and uses fewer quantum cells in its structure compared to conventional analogs. The developed adder was built taking into account the reduction of the logical operator, which does not affect the change of the intermediate result, and its reduction directly affects the speed of calculation and the number of types of cells used. The adder’s performance was compared with a conventional adder, as well as intermediate architectures developed during the implementation process. Software modeling of the developed circuits showed the operability and correctness of the obtained results.