As an alternative to CMOS-VLSI, researchers have proposed new technologies like FINFET, CNTFET, MTJ to reduce the scalability of the device. A new computing paradigm with quantum dots called Quantum dot Cellular Automata (QCA) is a polarization based digital logic architecture. QCA cell is the basic unit to build logic gates and devices in quantum domain. It proposes an effective design of logic gates and arithmetic circuit using QCA. Here the half and full adder is designed using minimum number of QCA cells with no crossover and compared with previous results. So these designs can be used to construct complex circuits. The simulations of the present work have been carried out by means of QCA designer tools. The simulation results help to implement large digital circuits in nanoscalerange.