Modular Design for Symmetric Functions using Quantum Quaternary Logic

In this paper, we propose a method to realize symmetric binary functions as quaternary quantum/reversible circuits. In contrast to the existing binary synthesis methods, our design in quaternary domain offers a simple and regular cascade structure composed of quaternary quantum modules which enables significant reductions with respect to number of lines, levels and quantum costs. Further, a method to obtain an optimal realization is presented; this uses a few special quaternary quantum modules of low quantum cost. Experimental results confirm that our new method leads to realizations in quaternary domain with a significant reduction in number of lines, levels and quantum cost compared to the existing approaches in binary domain. Hence, our design in quaternary logic offers a useful alternative to existing designs in binary logic for realizing symmetric functions.