Efficient binary to quaternary and vice versa converters: embedding in quaternary arithmetic circuits

Reversible logic is a nowadays promising choice for circuit design technologies since it is having diversified applications in the fields of digital signal processing, cryptography, quantum computing, and low power CMOS design. Since every two qubits in the binary logic are equivalent to one qudit in the quaternary logic, the optimum designed primary binary building blocks such as adders and subtractors easily can be used in quaternary logic design. In this paper, we first proposed a novel quaternary to a binary decoder and also binary to quaternary encoder circuits. Secondly, we have used these converters to the synthesis of the quaternary quantum reversible full adder, half subtractor, and full subtractor circuits. The proposed converter circuits have promised accomplishment compared to the existing designs; these circuits are built on the elementary quantum gates, which are realizable using the liquid ion trap in the quantum technology. The designed strategy (using the converters to realize computational circuits) is easily applicable in the large-scale quaternary quantum circuit designs.