Abstract
Reversible logic finds applications in emerging technologies such as quantum computing, optical computing, etc. This has motivated research into development of synthesis and optimization algorithms for reversible circuits. In this paper, a set of rules is presented for the decomposition of a pair of multi-control Toffoli gates (MCT) to reduce the quantum cost of reversible circuits. These rules find pairs of MCT gates, which when decomposed to a network of smaller gates, result in reduced quantum cost. This technique is used in conjunction with an Exclusive-OR Sum-Of-Product (ESOP) based reversible circuit synthesis algorithm to check its efficiency. Results indicate that there is a reduction in quantum cost of several benchmark circuits when compared to the known ESOP based synthesis algorithms.
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Bandyopadhyay, C., Rahaman, H., Drechsler, R.: Improved cube list based cube pairing approach for synthesis of ESOP based reversible logic. In: Gavrilova, M.L., Tan, C.J.K., Thapliyal, H., Ranganathan, N. (eds.) Transactions on Computational Science XXIV. LNCS, vol. 8911, pp. 129–146. Springer, Heidelberg (2014). doi:10.1007/978-3-662-45711-5_8
Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P., Sleator, T., Smolin, J.A., Weinfurter, H.: Elementary gates for quantum computation. Phys. Rev. A 52(5), 3457 (1995)
Datta, K., Gokhale, A., Sengupta, I., Rahaman, H.: An ESOP-based reversible circuit synthesis flow using simulated annealing. In: Chaki, R., Saeed, K., Choudhury, S., Chaki, N. (eds.) Applied Computation and Security Systems. AISC, vol. 305, pp. 131–144. Springer, New Delhi (2015). doi:10.1007/978-81-322-1988-0_8
Drechsler, R., Finder, A., Wille, R.: Improving ESOP-based synthesis of reversible logic using evolutionary algorithms. In: Di Chio, C., et al. (eds.) EvoApplications 2011. LNCS, vol. 6625, pp. 151–161. Springer, Heidelberg (2011). doi:10.1007/978-3-642-20520-0_16
Fazel, K., Thornton, M., Rice, J.: ESOP-based Toffoli gate cascade generation. In: IEEE Pacific Rim Conference on Communications, Computers and Signal Processing, pp. 206–209 (2007)
Lin, C.C., Jha, N.K.: RMDDS: Reed-Muller decision diagram synthesis of reversible logic circuits. J. Emerg. Technol. Comput. Syst. 10(2), 14:1–14:25 (2014). http://doi.acm.org/10.1145/2564923
Miller, D.M., Sasanian, Z.: Recent developments on mapping reversible circuits to quantum gate libraries. In: International Symposium on Electronic System Design (ISED), pp. 17–22. IEEE (2012)
Mishchenko, A., Perkowski, M.: Fast heuristic minimization of exclusive-sums-of-products. In: Proceedings of the 5th Reed-Muller Workshop, pp. 242–250 (2001)
Nayeem, N.M., Rice, J.E.: A shared-cube approach to ESOP-based synthesis of reversible logic. Facta Univ. Ser. Electron. Energ. 24(3), 385–402 (2011)
Rice, J., Fazel, K., Thornton, M., Kent, K.: Toffoli gate cascade generation using ESOP minimization and QMDD-based swapping. In: Proceedings of the Reed-Muller Workshop (RM 2009), pp. 63–72 (2009)
Rice, J., Nayeem, N.: Ordering techniques for ESOP-based Toffoli cascade generation. In: IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (PacRim), pp. 274–279. IEEE (2011)
Saeedi, M., Markov, I.L.: Synthesis and optimization of reversible circuits - a survey. ACM Comput. Surv. (CSUR) 45(2), 21 (2013)
Sanaee, Y., Dueck, G.W.: ESOP-based Toffoli network generation with transformations. In: 40th IEEE International Symposium on Multiple-Valued Logic (ISMVL), pp. 276–281. IEEE (2010)
Soeken, M., Frehse, S., Wille, R., Drechsler, R.: RevKit: a toolkit for reversible circuit design. Mult. Valued Log. Soft Comput. 18(1), 55–65 (2012)
Toffoli, T.: Reversible computing. In: Bakker, J., Leeuwen, J. (eds.) ICALP 1980. LNCS, vol. 85, pp. 632–644. Springer, Heidelberg (1980). doi:10.1007/3-540-10003-2_104
Wille, R., Grosse, D., Teuber, L., Dueck, G., Drechsler, R.: RevLib: an online resource for reversible functions and reversible circuits. In: 38th International Symposium on Multiple Valued Logic. ISMVL 2008. pp. 220–225, May 2008
Wille, R., Drechsler, R.: BDD-based synthesis of reversible logic for large functions. In: Proceedings of the 46th Annual Design Automation Conference, pp. 270–275. ACM (2009)
Wille, R., Drechsler, R.: Towards a Design Flow for Reversible Logic. Springer, Dordrecht (2010)
Acknowledgements
This work was supported in part by Council of Scientific & Industrial Research (CSIR) grant (ref.-09/1026(0007)/2012-EMR-I).
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Parlapalli, S.P., Vudadha, C., Srinivas, M.B. (2017). An ESOP Based Cube Decomposition Technique for Reversible Circuits. In: Phillips, I., Rahaman, H. (eds) Reversible Computation. RC 2017. Lecture Notes in Computer Science(), vol 10301. Springer, Cham. https://doi.org/10.1007/978-3-319-59936-6_10
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DOI: https://doi.org/10.1007/978-3-319-59936-6_10
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