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http://dx.doi.org/10.12673/jkoni.2012.16.1.062

Realization of Multiple-Control Toffoli gate based on Mutiple-Valued Quantum Logic  

Park, Dong-Young (Dept. of Information & Telecommunication Eng., Gangnung-Wonju National University)
Abstract
Multiple-control Toffoli(MCT) gates are macro-level multiple-valued gates needing quantum technology dependent primitive gates, and have been used in Galois Field sum-of-product (GFSOP) based synthesis of quantum logic circuit. Reversible logic is very important in quantum computing for low-power circuit design. This paper presents a reversible GF4 multiplier at first, and GF4 multiplier based quaternary MCT gate realization is also proposed. In the comparisons of MCT gate realization, we show the proposed MCT gate can reduce considerably primitive gates and delays in contrast to the composite one of the smaller MCT gates in proportion to the multiple-control input increase.
Keywords
multiple-control Toffoli(MCT) gate; multiple-valued; reversible circuit; GF4 multiplier; Galois Field sum-of-product(GFSOP);
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  • Reference
1 M. Nielsen, I. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2000.
2 H. Bechmann-Pasquinucci, A. Peres, "Quantum cryptography with 3-state systems," Phys. Rev. Lett. 85, 2000.
3 M. Bourennane, A. Karlsson, G. Bjoerk, "Quantum key distribution using multilevel encoding," Phys. Rev. Lett. A 64, 2001.
4 A.D. Greentree, S.G. Schirmer, F. Green, L.C.L. Hollenberg, A.R. Hamilton, R.C. Clark, "Maximizing the Hilbert Space for a finite number of distinguishable states," Phys. Rev Lett. 92 ,2004.
5 A. Muthukrishnan, C.R. Stroud Jr., "Multivalued logic gates for quantum computation," Phys. Rev. A 62, 2000.
6 J. I. Cirac and P. Zoller, "Quantum computations with cold trapped ions," Phys. Rev. Lett. 74, 4091, 1995.   DOI   ScienceOn
7 A. Muthukrishnan, C.R. Stroud Jr., "Multivalued logic gates for quantum computation," Phys. Rev. A 62, 2000.
8 Mozammel H.A. Khan, "Quantum realization of Quaternary Feynman and Toffoli gates," 4th International Conference on Electrical and Computer Engineering ICECE, 19-21 December, Dhaka, Bangladesh, pp.157-160, 2006.
9 A.I. Khan, N. Nusrat, S.M. Khan, M. Hasan, and M.H.A. Khan, "Quantum realization of some ternary circuits using Muthukrishnan-Stroud gates", proceedings of 37th International Symposium on Multiple-Valued Logic (ISMVL 2007), 14-16, Oslo, Norway, May 2007.
10 Khan M.M.M., Biswas A.K., Chowdhury S., Tanzid M., Mohsin K.M., Hasan M., and Khan A.I., "Quantum realization of some quaternary circuits," TENCON 2008, IEEE Region 10 Conference, pp.1-5, 2008.
11 Mozammel H. A. Khan, "Quantum Realization of Multiple-Valued Feynman and Toffoli Gates Without Ancilla Input," Proc. of 39th IEEE Int. Symp. on Multiple-Valued Logic (ISMVL 2009), pp.103-108, 2009.
12 M.M.M. Khan, Ayan Kumar Biswas, Shuvro Chowdhury, Masud Hasan and Asif Islam Khan "Synthesis of GF(3) based Reversible/Quantum Logic Circuits Without Garbage Output," Proc. of 39th IEEE Int. Symp. on Multiple-Valued Logic (ISMVL 2009), pp.98-102, 2009.
13 Ayan Kumar Biswas, Shuvro Chowdhury, Md. Mahmud Muntakim Khan, Masud Hasan and Asif Islam Khan, "Some Basic Ternary Operations Using Toffoli Gates along with the Cost of Implementation," Proc. of 41th IEEE Int. Symp. on Multiple-Valued Logic (ISMVL 2011),Tuusula, Finland, May 23-25, pp. 142-146, 2011.