A new design of the reversible subtractor circuit

Abstract—In [1] we have presented the reversible subtractor designs based on a new reversible TR gate (TR refers to Thapliyal Ranganathan). In [1] as the quantum gates imple-mentation of the TR gate was not known, only the upper bound on the quantum cost of the reversible subtractors units were established. In this work, we present a new design of the reversible half subtractor based on the quantum gates implementation of the reversible TR gate. The reversible TR gate is designed from 2x2 quantum gates such as CNOT and Controlled-V and Controlled-V + gates. The design of the proposed reversible half subtractor is shown to be better than the design presented in [2], [1] in terms of the quantum cost and delay while maintaining the minimum number of garbage outputs. Further, we present a new design of the reversible full subtractor based on the proposed quantum gates implementation of the TR gate. The proposed reversible full subtractor is optimized in terms of quantum cost, delay and garbage outputs by utilizing the identity property of V and V + reversible gates. The proposed reversible full subtractor is shown to be better than the existing design reported in [3], [1]. The reversible subtractors proposed in this work will be useful in a number of digital signal processing applications. I