A compact representation of a quantum controlled ternary barrel shifter

In this paper, we propose two new designs for the barrel shifter: i) a quantum ternary unidirectional barrel shifter (Design I) and ii) a quantum ternary bidirectional barrel shifter (Design II). We present the design of Ternary Peres Gate (TPG). The designs of ternary barrel shifters show that circuits are composed of proposed Ternary Peres Gates, Modified Fredkin Gates and Ternary Feynman Gates. A new technique to calculate the ternary quantum gate calculation complexity of ternary circuits has been proposed in the paper. Our circuits perform better than the existing ones in terms of quantum gates, garbage outputs and ternary quantum gate calculation complexity.