New Design of Reversible Full Adder/Subtractor using $R$ gate

TL;DR

This paper introduces new reversible quantum adder/subtractor designs using the $R$ gate, enhancing quantum arithmetic operations with optimized gate efficiency and versatility.

Contribution

The paper presents novel reversible quantum adder/subtractor architectures based on the $R$ gate, capable of performing multiple logical operations and optimized for quantum computing.

Findings

Designs outperform previous models in gate count and quantum cost.

Proposed circuits can perform multiple logical operations.

Implemented and tested using GAP software.

Abstract

Quantum computers require quantum processors. An important part of the processor of any computer is the arithmetic unit, which performs binary addition, subtraction, division and multiplication, however multiplication can be performed using repeated addition, while division can be performed using repeated subtraction. In this paper we present two designs using the reversible $R^3$ gate to perform the quantum half adder/ subtractor and the quantum full adder/subtractor. The proposed half adder/subtractor design can be used to perform different logical operations, such as $AND$, $XOR$, $NAND$, $XNOR$, $NOT$ and copy of basis. The proposed design is compared with the other previous designs in terms of the number of gates used, the number of constant bits, the garbage bits, the quantum cost and the delay. The proposed designs are implemented and tested using GAP software.