An Improved Ternary Logic Synthesis Approach Using Ternary Max-Min Algebra

Abstract

Abstract

Quantum computation which relies on exploiting quantum mechanical phenomena, has received significant attention in recent years. Higher dimensional quantum systems increase the density of encoded information per computing element (e.g. qutrit for the 3-level system), resulting in less resource overhead. Recently, there have been several works in the synthesis of ternary reversible functions, most of which are not scalable. Therefore, this study proposes a scalable approach for the synthesis of ternary logic functions using Max-Min algebra. In this approach, from a ternary truth table, Max-Min expressions are first generated with the help of ternary Max-Min algebra. Then, the expressions are minimized using Boolean simplification rules. After that, the minimized expressions are mapped to ternary reversible gates. We have also proposed a decomposition structure to map the ternary reversible gates into ternary elementary gates. Experimental evaluation shows that the proposed synthesis approach is more scalable as compared to existing synthesis approaches.

Keywords: Ternary reversible circuit, quantum computing, qutrit, reversible literals, non-reversible literals

Cite this Article

P. Mercy Nesa Rani, Leniency Marbaniang, Majid Haghparast, Kamalika Datta. An Improved Ternary Logic Synthesis Approach Using Ternary Max-Min Algebra. Journal of Advanced Database Management & Systems. 2019; 6(2): 40–47p.