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A Novel Approach Towards Optimized Synthesis of Four Variable Reversible Function Using Toffoli-Fredkin Based Mixed Templates

  • Kushal Shaw
  • Subham Pal
  • Sinjini Banerjee
  • Priyabrata SahooEmail author
  • Atal Chaudhuri
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 836)

Abstract

In the arena of reversible computation, several algorithms for synthesizing reversible circuit have contributed a major part. Good number of algorithms for optimized reversible circuit design is available in literature. In our previous work we proposed a synthesis algorithm for four variable reversible circuits using Toffoli Gates only, which outperforms already proposed synthesis algorithm in terms of both gate count and as well as quantum cost. The current work proposes another synthesis algorithm for four bit reversible functions using pre-designed templates combining both Toffoli and Fredkin gates. Template design considers optimal Control Sets for combined Toffoli and Fredkin gates in terms of gate count. These combined Toffoli-Fredkin templates further improve upon the gate count. Comparative study of previously proposed synthesized algorithms having Toffoli gates alone with mixed Toffoli-Fredkin version clearly exhibits the gate count improvements.

Keywords

Four variable reversible gate Reversible logic Reversible logic synthesis algorithm Toffoli Netlist Fredkin Netlist 

References

  1. 1.
    Toffoli, T.: Reversible computing. MIT Lab for Computer Science, Tech Memo MIT/LCS/TM-151 (1980)Google Scholar
  2. 2.
    Landauer, R.: Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5(3), 183–191 (1961)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Feynman, R.P.: Simulating physics with computers. Int. J. Theor. Phys. 21(6), 467–488 (1982)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Agrawal, A., Jha, N.K.: Synthesis of reversible logic. In: Proceedings of DATE, pp. 21 384–21 385, February 2004Google Scholar
  5. 5.
    Peres, A.: Reversible logic and quantum computers. Phys. Rev. A 32(6), 3266 (1985)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Bennett, C.: Logical reversibility of computation. IBM J. Res. Dev. 17(6), 525–532 (1973)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Soeken, M., Dueck, G.W., Miller, D.M.: A fast symbolic transformation based algorithm for reversible logic synthesis. In: Devitt, S., Lanese, I. (eds.) RC 2016. LNCS, vol. 9720, pp. 307–321. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-40578-0_22CrossRefzbMATHGoogle Scholar
  8. 8.
    Wille, R., Große, D., Dueck, G.W., Drechsler, R.: Reversible logic synthesis with output permutation. In: 22nd International Conference on VLSI Design, New Delhi, pp. 189–194 (2009)Google Scholar
  9. 9.
    Arabzadeh, M., Saeedi, M: RCViewer+ : a viewer/analyzer for reversible and quantum circuits (2008–2013, version 2.5). http://ceit.aut.ac.ir/QDA/RCV.htm
  10. 10.
    Rashmi, S.B., Umarani, T.G., Shreedhar, H.K.: Optimized reversible montgomery multiplier. Int. J. Comput. Sci. Inf. Technol. 2(2), 701–706 (2011)Google Scholar
  11. 11.
    Datta, K., Sengupta, I., Rahaman, H.: A post-synthesis optimization technique for reversible circuits exploiting negative control lines. IEEE Trans. Comput. 64(4), 1208–1214 (2015)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Datta, K., Ghuku, B., Sandeep, D., Sengupta, I., Rahaman, H.: A cycle based reversible logic synthesis approach. In: Third International Conference on Advances in Computing and Communications, pp. 316–319 (2013)Google Scholar
  13. 13.
    Frank, M.P.: Introduction to reversible computing: motivation, progress and challenges. In: 2nd Conference on Computing Frontiers, pp. 385–390 (2005)Google Scholar
  14. 14.
    Dueck, G.W., Maslov, D.: Reversible function synthesis with minimum garbage outputs. In: Proceedings of 6th International Symposium on Representations and Methodology of Future Computing Technologies, pp. 154–161, March 2003Google Scholar
  15. 15.
    Dueck, G.W., Maslov, D., Miller, D.M.: Transformation-based synthesis of networks of Toffoli/Fredkin gates. In: Proceedings of IEEE Canadian Conference on Electrical and Computer Engineering, pp. 211–214, May 2003Google Scholar
  16. 16.
    Miller, D.M., Maslov, D., Dueck, G.W.: A transformation based algorithm for reversible logic synthesis. In: Proceedings of DAC, pp. 318–323, June 2003Google Scholar
  17. 17.
    Maslov, D., Dueck, G.W., Miller, D.M.: Toffoli network synthesis with templates. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 24(6), 807–817 (2005)CrossRefGoogle Scholar
  18. 18.
    Barenco, A., et al.: Elementary gates for quantum computation. Phys. Rev. A Gen. Phys. 52(5), 3457–3467 (1995)CrossRefGoogle Scholar
  19. 19.
    Fredkin, E., Toffoli, T.: Conservative logic. Int. J. Theor. Phys. 21, 219–253 (1982)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Sultana, M., Prasad, M., Roy, P., Sarkar, S., Das, S., Chaudhuri, A.: Comprehensive quantum analysis of existing four variable reversible gates. In: Devices for Integrated Circuit (DevIC), Kalyani, 23–24 March 2017 (2017)Google Scholar
  21. 21.
    Chaudhuri, A., Sultana, M., Sengupta, D., Chaudhuri, A.: A novel reversible two’s complement gate (TCG) and its quantum mapping. In: Devices for Integrated Circuit (DevIC), Kalyani, 23–24 March 2017 (2017)Google Scholar
  22. 22.
    Banerjee, S., Sahoo, P., Sultana, M., Chaudhuri, A., Sengupta, D., Chaudhuri, A.: Toffoli Netlist based synthesis of four variable reversible functions. In: 3rd IEEE International Conference on Research in Computational Intelligence and Communication Network, Kolkata (ICRCICN-2017), pp. 315–320 (2017)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Kushal Shaw
    • 1
  • Subham Pal
    • 1
  • Sinjini Banerjee
    • 1
  • Priyabrata Sahoo
    • 1
    Email author
  • Atal Chaudhuri
    • 1
  1. 1.Department of Computer Science and EngineeringJadavpur UniversityKolkataIndia

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