International Conference on Computational Performance Evaluation (ComPE)

A Review on Fundamentals of Ternary Reversible Logic Circuits

P. Mercy Nesa Rani, Phrangboklang Lyngton Thangkhiew

Published Jul 1, 2020• 9 citations

Abstract

One of the main motivations for using ternary logic systems is the amount of information per circuit line is higher as compared to the corresponding binary logic representation, thereby leading to more compact circuit realizations. This is particularly attractive for quantum computing as qutrits are expensive resources and minimizing their number is one of the main objectives during synthesis. Therefore, ternary reversible logic synthesis has drawn significant attention among researchers. It deals with fundamental unit of information called qutrits that can exist in one of the three states |0>, |1> and |2>. Hence, the aim of this paper is to bridge the knowledge gap for the beginners in this domain than searching the entire space. Therefore, the present work discusses the basic concepts of ternary reversible logic and ternary reversible gates. The detailed discussion of the various ternary reversible logic synthesis will enable the beginners in this domain to understand the ternary reversible logic in a better way.

DOI: 10.1109/compe49325.2020.9200021

Related papers

Improved Ternary Reversible Logic Synthesis Using Group Theoretic Approach

P. Mercy Nesa Rani, Kamalika Datta

Quantum computation relies on exploiting quantum mechanical phenomena, and has received significant attention in recent years. Higher-dimensional quantum systems increase the density of encoded information per computing element (e.g., qutrit for three-level system), resulting in less resource overhead. For instance, 63% reduction in the number of qutrits is possible for ternary quantum systems as compared to the corresponding binary systems. The proposed work exploits this fact to synthesize ternary reversible circuits employing a cycle-based technique. The method starts from the ternary reversible specification of a given function in the form of a permutation. The permutation cycles are factored into simpler three-cycles and two-cycles, which are then mapped to ternary reversible gates. Different gate libraries are used to synthesize three-cycles and two-cycles, respectively. A gate decomposition approach is also proposed to synthesize a quantum gate netlist in terms of elementary ternary quantum gates, viz. Muthukrishnan–Stroud gate and shift gate. Synthesis results on benchmark functions indicate that the proposed method results in 27% and 6% improvements in quantum cost and gate count, respectively, over existing works in the literature.

Journal of Circuits Systems and ComputersDec 23, 20198 citations

SAT-based Exact Synthesis of Ternary Reversible Circuits using a Functionally Complete Gate Library

Abhoy Kole, Kamalika Datta, Indranil Sengupta +1 more

The problem of synthesis and optimization of reversible and quantum circuits have drawn the attention of researchers for the last two decades due to increasing interest in quantum computing. Although lot of works have been done on the synthesis of binary reversible circuits, very less works have been reported on the synthesis of ternary reversible circuits. Ternary circuits have lower cost of implementation as compared to their binary counterparts. However, the synthesis approaches that exist for ternary reversible circuits either use too many circuit lines (qutrits) or too many gates. Only one prior work has discussed the problem of generating cost-optimal ternary reversible circuits, but for a very restrictive gate library, which limits the approach to a specific subset of ternary reversible functions and often the solution becomes sub-optimal due to the imposed restrictions. The present paper overcomes that restriction, and uses multiple control ternary Toffoli gates with all possible ternary target operations as the gate library. This gate library is functionally complete and can be used to synthesize any arbitrary function. The proposed SAT-based synthesis approach provides low cost solutions in terms of the number of gates for any arbitrary ternary reversible function. Experimental results on various randomly generated permutations as well as standard ternary benchmarks establish this claim. The results can be used as template for other synthesis approaches by observing how far they deviate from the optimal solutions.

Euromicro Conference on Digital System Design (DSD)Aug 1, 20221 citation

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

P. Mercy Nesa Rani, Leniency Marbaniang, Majid Haghparast +1 more

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.

Journal of Advanced Database Management & SystemsJul 6, 20190 citations

Design of Quantum/Reversible Ternary Adder Circuit

Chteoui Henchir, Lamjed Touil, Abdellatif Mtibaa

The ternary quantum circuit is very useful in arithmetic and logic operations. This circuit has several advantages as it reduces power dissipation, step time, etc. Adder circuit is the main block of various computing units and for several other complex computer designs. In this current paper, we have used generalized ternary gate (GTG) and reversible gates for the synthesis of reversible half adder and a full adder circuits. The presented designs offer reduced constant inputs and less quantum cost, compared to existing designs. Our proposed design allows a reduction of 40% of the cost and 25% of the number of gates used.

International Conference on Sciences and Techniques of Automatic Control and Computer EngineeringDec 19, 20223 citations

A Quick Guide to Implement Reversible Logic

Shaveta Thakral, Dipali Bansal

Increasing miniaturization and demand of low power electronics is highly motivating research on reversible logic. Reversible logic has attracted signification attention in fields of Low power VLSI design, computer graphics, quantum computing and communication. A lot of work has been done on synthesis and optimization of reversible circuits followed by quantitative analysis on various optimization metrics like ancillary inputs, garbage outputs and quantum cost. It is therefore obvious to present a quick guide on reversible logic implementation to bridge gap between theory and implementation. Taxonomy diagrams of work done in reversible logic domain are also presented to give a quick review of all about reversible logic. Quantum realization of popular reversible Fredkin gates using RCViewer tool is also presented which will be stepping stone for a new researcher to synthesize and optimize any complex reversible logic based circuit.

International Conference on Computing, Communication and AutomationDec 1, 20181 citation

Generalizing the Concept of Scalable Reversible Circuit Synthesis for Multiple-Valued Logic

Alwin Zulehner, P. Mercy Nesa Rani, Kamalika Datta +2 more

Research on reversible circuits has gained significance due to its application in quantum computations and many further areas such as the design of encoders. At the same time, the use of multiple-valued logic gained importance since this reduces the number of required entities in physical systems (e.g. in a future quantum computer). While most research is still conducted in the Boolean domain, there exist only few approaches which realize reversible circuits for multiple-valued logic. Moreover, most of the previously proposed solutions for synthesis of multiple-valued reversible circuits are not scalable and consider ternary (i.e. 3-valued circuits) only. Instead of overcoming these issues by developing new synthesis approaches for multiple-valued reversible circuits from scratch, we propose to utilize the recent accomplishments in the design of Boolean reversible circuits and to generalize them for multiple-valued logic. To this end, we discuss how to generalize Quantum Multiple-valued Decision Diagram based (QMDD-based) synthesis - a synthesis approach for Boolean reversible circuits which has been proven to be scalable and which has been used in several recently developed design flows. The discussions eventually show how to bridge the development gap between Boolean and multiple-valued logic for reversible circuits.

IEEE International Symposium on Multiple-Valued Logic (ISMVL)May 1, 20182 citations