Novel quantum circuit synthesis using reversible Davio expansions is introduced. The new method uses two planes to synthesize the quantum circuits: 1) reversible butterfly circuit plane, and 2) plane of quantum gates to perform additions and multiplications. Since the reduction of power consumption is a major requirement for circuit design of future technologies, such as in quantum circuits, the main features of several future technologies will include reversibility, and thus the new synthesis method using reversible butterfly circuits can play an important role in the synthesis of circuits that consume minimal power.