Abstract
In conventional binary reversible circuit synthesis, reversible gates are decomposed into quantum gates using some standard quantum gate library. In recent years there has been increased attention in synthesis using ternary reversible gates since it leads to a reduction in the number of lines. However, very few works exist that address the problem of decomposing ternary reversible gates based on some ternary quantum gate library. Most of these works use Muthukrishnan-Stroud (M-S) gates for decomposition of ternary Toffoli gate, and they use a naive approach that requires an exponential (in number of control lines) number of M-S gates. Also the number of ancilla lines required is (\(c-1\)), where c is the number of control lines. The present paper proposes a method for decomposing ternary Toffoli gates to M-S gates that requires less number of ancilla lines, and also requires a number of M-S gates that is linear in c. A template-based post-decomposition optimization step has also been used to further reduce the number of M-S gates required. Decomposition results for up to 16 control lines have been presented.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Basu, S., Mandal, S.B., Chakrabarti, A., Sur-Kolay, S.: An efficient synthesis method for ternary reversible logic. In: International Symposium on Circuits and Systems (ISCAS), pp. 2306–2309 (2016)
Bennett, C.: Logical reversibility of computation. J. IBM Res. Dev. 17(6), 525–532 (1973)
Cirac, J.I., Zoller, P.: Quantum computations with cold trapped ions. Phys. Rev. Lett. 74, 4091–4094 (1995)
Khan, M.H.A.: Design of reversible/quantum ternary multiplexer and demultiplexer. In: Engineering Letters, pp. 174–178 (2006)
Khan, M.H.A., Perkowski, M.A., Khan, M.R., Kerntopf, P.: Ternary GFSOP minimization using Kronecker decision diagrams and their synthesis with quantum cascades. J. Multi Valued Logic Soft Comput. 11, 567–602 (2005)
Khan, M.H.A.: GFSOP-based ternary quantum logic synthesis. In: Proceedings of the SPIE 7797, Optics and Photonics for Information Processing IV, pp. 1–15 (2010)
Landauer, R.: Irreversibility and heat generation in the computing process. J. IBM Res. Dev. 5, 183–191 (1961)
Li, X., Yang, G., Zheng, D.: Logic synthesis of ternary quantum circuits with minimal qutrits. J. Comput. 8(3), 1941–1946 (2013)
Lucac, M., Perkowski, M.A., Goi, H., Pivtoraiko, M., Yu, C.H., Chung, K., Jeech, H., Kim, B.G., Kim, Y.D.: Evolutionary approach to quantum and reversible circuits synthesis, artificial intelligence in logic design. Artif. Intell. Rev. 20(3), 361–417 (2003)
Maslov, D., Dueck, G., Miller, D., Negrevergne, C.: Quantum circuit simplification and level compaction. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 27(3), 436–444 (2008)
Miller, D.M., Dueck, G., Maslov, D.: A synthesis method for MVL reversible logic. In: 34th International Symposium on Multiple-Valued Logic (ISMVL), pp. 74–80 (2004)
Miller, D., Sasanian, Z.: Lowering the quantum gate cost of reversible circuits. In: Proceedings of the International Midwest Symposium on Circuits and Systems, pp. 260–263 (2010)
Muthukrishnan, A., Stroud Jr., C.R.: Multivalued logic gates for quantum computation. Phys. Rev. A 62(5), 052309/1-8 (2000)
Sasanian, Z., Wille, R., Miller, D.M.: Realizing reversible circuits using a new class of quantum gates. In: Proceedings of the Design Automation Conference, pp. 36–41 (2012)
Yang, G., Song, X., Perkowski, M., Wu, J.: Realizing ternary quantum switching networks without ancilla bits. J. Phys. A: Math. Gen. 38, 1–10 (2005)
Yang, G., Xie, F., Song, X., Perkowski, M.: Universality of 2-qudit ternary reversible gates. J. Phys. A: Math. Gen. 39, 7763–7773 (2006)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Rani, P.M.N., Kole, A., Datta, K., Sengupta, I. (2017). Improved Decomposition of Multiple-Control Ternary Toffoli Gates Using Muthukrishnan-Stroud Quantum Gates. 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_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-59936-6_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-59935-9
Online ISBN: 978-3-319-59936-6
eBook Packages: Computer ScienceComputer Science (R0)