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Quantum Dot Cellular Automata (QCA) as an emerging nanotechnology can be considered as a possible successor for the conventional silicon MOSFET technology, in the time to come. This paper presents novel efficient designs for QCA Full Adder and Adder circuits. The layouts of the proposed designs are simple and lead to very low complexity, small area and short latency. For verifying the functionality of the circuits, all of them are simulated exhaustively using QCADesigner tool. The proposed designs are also compared with the other classical and state-of-the-art Full Adders and Adders, which demonstrates the superiority of the proposed circuits, in terms of gate count, area and latency.