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International Conference on Circuits, Control, Communication and Computing (I4C)

Post synthesis optimization of reversible logic functions with extended template matching

H. V. Jayashree, V.K. Agrawal, N Shishir Bharadwaj

Published Nov 1, 2014• 1 citation
Publisher

Abstract

Research affinity towards Reversible Computing is increasing day to day due to its lower energy dissipation computing capability. To evaluate any reversible function it is necessary to build the system with reversible gates. In view of this there are many new reversible logic gates proposed by many authors. Quantum cost of few reversible gates are unpublished. Simplified version of transformation technique to synthesize new reversible gates with Fredkin and Toffoli gates network are presented in this paper. Post synthesis optimization with the new set of templates are carried out to reduce the Quantum cost.

DOI
10.1109/cimca.2014.7057825

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Research affinity towards Reversible Computing is increasing day to day due to its lower energy dissipation computing capability. To evaluate any reversible function it is necessary to build the system with reversible gates. In view of this there are many new reversible logic gates proposed by many authors. Quantum cost of few reversible gates are unpublished. Simplified version of transformation technique to synthesize new reversible gates with Fredkin and Toffoli gates network are presented in this paper. Post synthesis optimization with the new set of templates are carried out to reduce the Quantum cost.
Reversible computing appears to be promising due its applications in emerging technologies. To compute any reversible function it is necessary to build the system with reversible gates. Simplified version of transformation technique [3,5] to synthesize new reversible gates with Fredkin and Toffoli gates network is presented in this paper. Basic and bidirectional transformation algorithms with an example are illustrated, which uncovers every step of the algorithm. The same example is used for both the algorithms to give clarity on the difference in the efficiency of the algorithms. Simple pseudo code is also presented to illustrate the steps of the algorithm. The best quantum cost obtained is listed in this paper.
Reversible logic computing is an emerging research area due to its high-speed computing abilities and generating the lossless information. Due to the ability of reverse operation and high-speed computing performance, reversible computation is considered as a future alternative to the conventional computing. The rapid progress of reversible computation in the current scenario, the reversible circuit is the way to solve this type of computation. Moreover, the reversible circuit computation is the higher level abstraction of the quantum circuit. The synthesis design of these circuits is an important aspect in the current literature. In this paper, we present our work in the field of synthesis design of a reversible circuit. In this work, we propose a modified transformation-based synthesis design using the FREDKIN/SWAP gate to reduce the quantum cost and minimizing the number of gates. To obtain this synthesis design approach, we have introduced some new templates which are defined by rules of replacing the k-CNOT/FREDKIN/SWAP gates using a template matching approach. Here, we are considering only k-CNOT ( k ≥ 1), FREDKIN and SWAP based gate in our templates. Finally, we provide our experimental results based on different benchmark reversible circuits. The experimental result has shown that the number of quantum cost and gate count are reduced using the FREDKIN/SWAP gate in the transformation-based approach with the help of proposed templates.
Reversible gates are gaining popularity in the field of circuit synthesis due to their property of having lower power loss and reduced dissipation of power as heat. These low power design models need to have better optimization properties. In this paper, we have ventured into the template and rule based optimization process. While most reversible netlists are built using the standard Toffoli gates, the proposed Modified Toffoli Gate has been used to achieve optimization. In this paper, the quantum realization of mixed control Modified Toffoli Gate and negative control Modified Toffoli Gates are proposed. Few templates and rules for transforming the original Toffoli network to the Modified Toffoli network are also proposed. This optimization yields a better quantum cost and gate count when compared to that of it's Toffoli counterpart.
Reversible computation is gaining increasing relevance in the context of several post-CMOS technologies, the most prominent of those being quantum computing. The problem of implementing a given Boolean function using a set of elementary reversible logic gates is known as reversible logic synthesis. Due to the presumed hardness of the reversible circuit synthesis problem, different heuristics have been proposed in the literature to reduce quantum cost (QC), gate count, and logical depth without using ancillary lines. Interestingly, none of these heuristics systematically utilize Fredkin gates. In this paper, we demonstrate, both theoretically and empirically, that accommodating Fredkin gates significantly improves the performance of reversible circuits.
Quantum cost is the most important criteria to evaluate reversible and quantum circuits. Also the fundamental building blocks of reversible and quantum circuits are Multiple-Control Toffoli (MCT) gates. The synthesis of MCT based reversible circuits are usually conducted into two steps. First, MCT circuits are decomposed into quantum circuits and then they are optimized using various techniques such as template matching, moving rules to reduce the quantum cost of reversible circuits. In this paper, we propose new techniques to decompose the Toffoli gates, in which MCT based circuits are mapped into a corresponding quantum realization. The main improvement is that the resulting quantum realization of MCT based circuits makes significantly better realization than those achieved in the earlier approaches and further reduction is possible using some other optimization techniques. Experimental results show that our new techniques enable to get sub-optimal realization of the MCT based reversible circuits in decomposition stage and quantum cost reduction of the reversible circuits is achieved by using that sub-optimal realization.
The research in reversible logic has been attracted in recent years. It has applications in quantum computing, low-power CMOS design and nanotechnology. Many methods on how to cascade a reversible network have been proposed. And all these networks are composed of Toffoli/Fredkin gates. In this paper, we present a method that synthesizes a network with family of Positive/Negative Control (PNC) gates. Through introducing some examples for 3×3 reversible functions, and comparing with the network which is composed of Toffoli gates, the results show that introducing the PNC gates can produce an improvement for the number of gates in the reversible network, and have an advantage in reducing the cost of network.