Algebraic characterization of reversible logic gates

Theory of Computing Systems

Volumn 39, Issue 2, 2006, Pages 311-319

  Song, Xiaoyu ^a   Yang, Guowu ^a   Perkowski, Marek ^a   Wang, Yuke ^b  

^a Department of Electrical and Computer Engineering   (United States)

^b The University of Texas at Dallas   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

QUANTUM COMPUTING; REVERSIBLE GATES; REVERSIBLE LOGIC; REVERSIBLE LOGIC GATES; SYMMETRIC GROUPS;

ALGEBRA; QUANTUM COMPUTERS;

LOGIC GATES;

EID: 33646466960     PISSN: 14324350     EISSN: 14330490     Source Type: Journal    
DOI: 10.1007/s00224-004-1166-2     Document Type: Article

References (17)

1. E. Fredkin and T. Toffoli, Conservative logic, International Journal of Theoretical Physics, 21 (1982), 219-253.
2. R. P. Feynmann, Quantum mechanical computers, Optic News, 11 (1985), 11-20.
3. J. I. Cirac and P. Zoller, Quantum computation with cold trapped ions, Physical Review Letters, 74 (1995), 4091-4094.
4. A. Peres, Reversible logic and quantum computers, Physical Review A, 32 (1985), 3266-3276.
5. C. Monroe, D. M Meekhof, B. E. King, D. Leibriefd, W. M. Itano, and D. J. Wineland, Manipulating the motion of a single trapped atom, Preprint, 1998.
6. J. Kim, J.-S. Lee, and S. Lee, Implementing unitary operators in quantum computation, Physical Review A, 61 (2000), 032312.
7. J.-S. Lee, Y. Cheong, J. Kim, and S. Lee, A practical method of constructing quantum combinational logic circuits, e-print, quant-ph/9911053.
8. J. Kim, J.-S. Lee, S. Lee, and Ch. Cheong, Implementation of the refined Deutsch-Jozsa algorithm on a three-bit NMR quantum computer, Physical Review A, 62 (2000), 022312.
9. V. V. Shende, A. K. Prasad, I. L. Markov, and J. P. Hayes, Reversible logic circuit synthesis, Proc. IWLS, pp. 125-130, 2002.
10. M. Perkowski et al., A hierarchical approach to computer-aided design of quantum circuits, Proc. 6th International Symposium on Representations and Methodology of Future Computing Technologies (RM 2003), pp. 201-209, 2003.
11. J. D. Dixon and B. Mortimer, Permutation Groups, Springer-Verlag, New York. 1996.
12. M. I. Kargapolov and Ju. I. Merzljakov, Fundamentals of the Theory of Groups, Springer-Verlag, New York, 1979.
13. L. Storme, A. De Vos, and G. Jacobs, Group theoretical aspects of reversible logic gates, Journal of Universal Computer Science, 5 (1999), 307-321.
14. A. Khlopotine, M. Perkowski, and P. Kerntopf, Reversible logic synthesis by gate composition. Proc. IEEE/ACM International Workshop on Logic Synthesis, pp. 261-266, 2002.
15. T. Toffoli, Bicontinuous extensions of invertible combinatorial functions, Mathematical Systems Theory, 14 (1981), 13-23.
16. M. Perkowski, P. Kerntopf, A. Buller, M. Chrzanowska-Jeske, A. Mishchenko, X. Song, A. Al-Rabadi, L. Jozwiak, A. Coppola, and B. Massey, Regularity and symmetry as a base for efficient realization of reversible logic circuits, Proc. IEEE/ACM International Workshop on Logic Synthesis, pp. 90-95, 2001.
17. J. A. Smolin and D. P. DiVincenzo, Five two-bit quantum gates are sufficient to implement the quantum Fredkin gate. Physical Review A, 53 (1996), 2855-2856.