  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.
