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A reversible circuit synthesis algorithm with progressive increase of controls in generalized Toffoli gates

Edinelço Dalcumune, Luis Antonio Brasil Kowada, André da Cunha Ribeiro, Celina Miraglia Herrera de Figueiredo, Franklin de Lima Marquezino
2021 Journal of universal computer science (Online)  
We present a new algorithm for synthesis of reversible circuits for arbitrary n-bit bijective functions. This algorithm uses generalized Toffoli gates, which include positive and negative controls.  ...  Our algorithm is divided into two parts. First, we use partially controlled gen- eralized Toffoli gates, progressively increasing the number of controls.  ...  Concluding remarks In this work, we presented a new algorithm of reversible circuit synthesis using generalized Toffoli gates (GT gates).  ... 
doi:10.3897/jucs.69617 fatcat:3kln7txad5ctnd3d6cf26on4ni

Heuristic Synthesis of Reversible Logic – A Comparative Study

Chua Shin Cheng, Ashutosh Kumar Singh
2014 Advances in Electrical and Electronic Engineering  
Thus a new set of algorithms are developed correctly to synthesize reversible logic circuit.  ...  Comparing the synthesis algorithm outputs over the years, it can be observed that different approach has been used for the synthesis of reversible circuit.  ...  The general structure of NOT, CNOT and Toffoli gate is illustrated in Fig. 1 . 2) Multi-Control Fredkin Gate A multi-control Fredkin gate [17] can be written as (x 1 , x 2 , ..., x n , x n+1 , x n  ... 
doi:10.15598/aeee.v12i3.916 fatcat:nneplactibbgfocpl35nizzql4

Improved ant colony optimization for quantum cost reduction

Shaveta Thakral, Dipali Bansal
2020 Bulletin of Electrical Engineering and Informatics  
Heuristic algorithms play a significant role in synthesize and optimization of digital circuits based on reversible logic yet suffer with multiple disadvantages for multiqubit functions like scalability  ...  Synthesis of reversible logic circuit ends up with trade off between number of gates, quantum cost, ancillary inputs and garbage outputs. Research on optimization of quantum cost seems intractable.  ...  Application of ant colony optimization to reversible logic function leads to the generation of a low quantum cost based circuit by applying Toffoli gates to bring reversible function to its identity function  ... 
doi:10.11591/eei.v9i4.1657 fatcat:ffsxg37aqbairmmxzqlemifia4

Automatic design of low-power encoders using reversible circuit synthesis

R. Wille, R. Drechsler, C. Osewold, A. Garcia-Ortiz
2012 2012 Design, Automation & Test in Europe Conference & Exhibition (DATE)  
Here, much progress has been made in the last years.  ...  Both, an exact and a heuristic synthesis approach, are introduced which rely on reversible design principles but also incorporate objectives from on-chip interconnect architectures.  ...  A Toffoli gate with no control always inverts the target line and is a NOT gate. A Toffoli gate with a single control line is called a controlled-NOT gate (also known as the CNOT gate).  ... 
doi:10.1109/date.2012.6176648 dblp:conf/date/WilleDOO12 fatcat:yvnjeka6r5drddddmc4u2duztu

Quantum cost realization of new reversible gates with transformation based synthesis technique

Jayashree H. V, V K Agrawal, Shishir Bharadwaj N
2015 2015 International Conference on VLSI Systems, Architecture, Technology and Applications (VLSI-SATA)  
Simplified version of transformation technique 13,51 to synthesize new reversible gates with Fredkin and Toffoli gates network is presented in this paper.  ...  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.  ...  There is a large amount of work currently going on in the domaill of design and synthesis techniques to realize reversible circuits. In this regard there are many reversible logic gates proposed.  ... 
doi:10.1109/vlsi-sata.2015.7050491 fatcat:mxjbvvtqtvbi5bls7yvq5rfpm4

Synthesis and optimization of reversible circuits—a survey

Mehdi Saeedi, Igor L. Markov
2013 ACM Computing Surveys  
Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping.  ...  Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain.  ...  Smita Krishnaswamy for proofreading early versions of the manuscript and for helpful discussions.  ... 
doi:10.1145/2431211.2431220 fatcat:r5eb6eurkzahrjktxtak24qshq

Improving ESOP-Based Synthesis of Reversible Logic Using Evolutionary Algorithms [chapter]

Rolf Drechsler, Alexander Finder, Robert Wille
2011 Lecture Notes in Computer Science  
As a result, researchers developed various approaches for synthesis of this kind of logic. In this paper, we consider the ESOP-based synthesis method.  ...  Reversible circuits, i.e. circuits which map each possible input vector to a unique output vector, build the basis for emerging applications e.g. in the domain of low-power design or quantum computation  ...  -Transistor cost model: The transistor cost of Toffoli gate increases linearly with 8 · s where s is the number of control lines in the gate (see Table 1 (b)).  ... 
doi:10.1007/978-3-642-20520-0_16 fatcat:bakzjfrmxfg6pg4q5ddnhcocae

Techniques for the synthesis of reversible Toffoli networks

D. Maslov, G. W. Dueck, D. M. Miller
2007 ACM Transactions on Design Automation of Electronic Systems  
This paper presents novel techniques for the synthesis of reversible networks of Toffoli gates, as well as improvements to previous methods. Gate count and technology oriented cost metrics are used.  ...  A novel "resynthesis" approach is introduced wherein a sequence of gates is chosen from a network, and the reversible specification it realizes is resynthesized as an independent problem in hopes of reducing  ...  Cost of a Reversible Toffoli Network It is a common practice in reversible logic synthesis area [27, 19, 2, 8, 14] to synthesize a network using multiple control Toffoli gates and report its cost as  ... 
doi:10.1145/1278349.1278355 fatcat:kmrrrselpvb7zo4tlmpluvpfda

Development of Tool for Mapping Conventional Circuit to Reversible Logic [article]

Piyush Gautam
2014 arXiv   pre-print
In this dissertation a logic circuit design entry based on binary logic system has been taken up that can provide the ease of circuit design in binary logic system and output as reversible circuit.  ...  A need for convertibility of irreversible circuit to reversible circuit was felt that can make a quick start and keep the development on track.  ...  These three gates compose the universal NCT library. Multiple-Control Fredkin Gate : In 1982 Toffoli and Fredkin given a gate that can be generalized up to n lines .  ... 
arXiv:1407.0632v1 fatcat:worl3n5eincddlbdrxnxogvlhu

Evolutionary Approach to Quantum and Reversible Circuits Synthesis [chapter]

Martin Lukac, Marek Perkowski, Hilton Goi, Mikhail Pivtoraiko, Chung Hyo Yu, Kyusik Chung, Hyunkoo Jee, Byung-Guk Kim, Yong-Duk Kim
2004 Artificial Intelligence in Logic Design  
It is also shown that our approach can be used alternatively for synthesis of either reversible or quantum circuits without a major change in the algorithm.  ...  The paper discusses the evolutionary computation approach to the problem of optimal synthesis of Quantum and Reversible Logic circuits.  ...  Acknowledgments The authors would like to thank Professor Soonchil Lee from Physics Department of KAIST in Korea for discussions about NMR computing and to Dr.  ... 
doi:10.1007/978-1-4020-2075-9_7 fatcat:k4up4734mrez7cyu2ksdbkgzqa

Reversible Circuits: Recent Accomplishments and Future Challenges for an Emerging Technology [chapter]

Rolf Drechsler, Robert Wille
2012 Lecture Notes in Computer Science  
Hence, much progress in the development of design solutions for this kind of circuits has been made in the last decade.  ...  We discuss recent accomplishments and, finally, have a look on future challenges in the design of circuits for this emerging technology.  ...  A Toffoli gate is composed of a (possibly empty) set of control lines C = {x i1 , . . . , x i k } ⊂ X and a single target line x j ∈ X \ C.  ... 
doi:10.1007/978-3-642-31494-0_53 fatcat:ro75dexforb45l3pgmz4h2ebjy

Logic Synthesis for Quantum Computing [article]

Mathias Soeken, Martin Roetteler, Nathan Wiebe, Giovanni De Micheli
2017 arXiv   pre-print
Establishing a connection between LUTs in a LUT network and reversible single-target gates in a reversible network allows us to bridge conventional logic synthesis with logic synthesis for quantum computing  ...  Thus, the benchmarks and, more generally, the LHRS framework are an essential step towards the goal of understanding which quantum algorithms will be practical in the first generations of quantum computers  ...  All circuits in this paper were drawn with the qpic tool [70] .  ... 
arXiv:1706.02721v1 fatcat:444j2rrdxvgitdgserclc4mtoi

Delay Reduced 4 Bit Reversible Arithmetic Logic Units

Vineeta Dwivedi, Pankaj Soni, Manish Gurjar
2017 International Journal of Computer Applications  
This proposed design is compared in terms of gate count, quantum cost and propagation delay. This reversible CPU designed using Feynman gate, Peres gate, Toffoli gate and DKG gate.  ...  Growing market of electronic system replaces the conventional digital system by reversible logic circuit to solve the problem of loss of information which was dissipated in the form of heat in irreversible  ...  circuit implementation TOFFOLI GATE It is 3*3 reversible gate, designed to produce following output states with inputs (A, B, C) is (P=A Q=B C B A R   .  ... 
doi:10.5120/ijca2017915467 fatcat:xlqmxmtnl5el7jmhttneuuecd4

QUANTIFY: A framework for resource analysis and design verification of quantum circuits [article]

Oumarou Oumarou, Alexandru Paler, Robert Basmadjian
2020 arXiv   pre-print
It is based on Google Cirq and is developed with Clifford+T circuits in mind, and it includes the necessary methods to handle Toffoli+H and more generalised controlled quantum gates, too.  ...  Key features of QUANTIFY include: (1) analysis and optimisation methods which are compatible with the surface code, (2) choice between different automated (mixed polarity) Toffoli gate decompositions,  ...  For example, arithmetic circuits are very often formulated using Toffoli+H gates or even more general MPMCT (Mixed Polarity Multiple Control Toffoli) gates.  ... 
arXiv:2007.10893v1 fatcat:n6klug22cnds5a5wpk2rq3gmhu

From Truth Tables to Programming Languages: Progress in the Design of Reversible Circuits

Rolf Drechsler, Robert Wille
2011 2011 41st IEEE International Symposium on Multiple-Valued Logic  
In this paper, the progress in the development of design methods for reversible circuits is reviewed -with a particular focus on the synthesis steps.  ...  After a brief review on reversible circuits, the general idea of common synthesis approaches is described.  ...  In this context, we would like to thank the German Academic Exchange Service (DAAD) which enabled the close contact with the groups in Canada.  ... 
doi:10.1109/ismvl.2011.40 dblp:conf/ismvl/DrechslerW11 fatcat:c27oimt4d5aaliedtbllyjustm
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