Quantum cellular automaton (QCA) is an efficient and emerging nanotechnology to create quantum computing devices. It is polarization based digital logic architecture. QCA cell is the basic unit to build logic gates and devices in quantum domain. This paper proposes an effective design of logic gates and arithmetic circuit using QCA. Here the gates and circuits are designed using minimum number of QCA cells and with no crossovers. 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 the digital circuits in nanoscale range.