Paper:

# Emulating Qubits with Fuzzy Logic

## M. Skander Hannachi, Yutaka Hatakeyama, and Kaoru Hirota

Department of Computational Intelligence and Systems Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, G3-49, 4259 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.11 No.2, pp. 242-249, 2007.

- [1] D. S. Abrams and S. Lloyd, “Nonlinear Quantum Mechanics Implies Polynomial-Time Solution for
*NP*-Complete and*#P*Problems,” Physical Review Letters, Vol.81, p. 3992, 1998. - [2] L. Adleman, J. DeMarrais, and M. Huang, “Quantum computability,” SIAM Journal on Computing, Vol.26, pp. 1524-1540, 1997.
- [3] N. Bhattacharya, H. B. van Linden van den Heuvell, and R. J. C. Spreeuw, “Implementation of Quantum Search Algorithm using Classical Fourier Optics,” Physical Review Letters, Vol.88, 137901, 2002.
- [4] A. Bolotin, “Quantum mechanical approach to fuzzy logic modeling,” Mathematical and Computer Modelling, Vol.34, No.7-8, pp. 937-945, 2001.
- [5] S. Dasgupta, A. Biswas, and G. S. Agarwal, “Implementing Deutsch-Jozsa algorithm using light shifts and atomic ensembles,” Physical Review A, Vol.7, No.1, 012333, 2005.
- [6] D. Deutsch, “Quantum theory, the church-turing principle and the universal quantum computer,” Proceedings of the Royal Society London, Vol.A400, pp. 97-117, 1985.
- [7] B. D’hooghe, J. Pykacz, and R. R. Zapatrin, “Quantum Computation of Fuzzy Numbers,” International Journal of Theoretical Physics, Vol.43, No.6, pp. 1423-1432, 2004.
- [8] S. Dick, “Toward complex fuzzy logic,” IEEE Transactions on Fuzzy Systems, Vol.13, No.3, pp. 405-414, 2005.
- [9] D. K. Ferry, R. Akis, and J. Harris, “Quantum wave processing,” Superlattices and Microstructures, Vol.30, No.2, pp. 81-94, 2001.
- [10] T. Gopinath and A. Kumar, “Geometric quantum computation using fictitious spin-1/2 subspaces of strongly dipolar coupled nuclear spins,” Physical Review A, Vol.73, 022326, 2006.
- [11] L. K. Grover, “Quantum computers can search arbitrarily large databases by a single query,” Physical Review Letters, Vol.79, pp. 4709-4712, 1997.
- [12] K. Hirota and K. Ozawa, “The concept of fuzzy flip-flop,” IEEE Transactions on Systems, Man and Cybernetics, Vol.19, No.5, pp. 980-997, 1989.
- [13] A. M. Ibrahim, “Bringing fuzzy logic into focus,” Circuits and Devices Magazine, IEEE, Vol.17, No.5, pp. 33-38, 2001.
- [14] M. A. Nielsen and I. L. Chuang, “Quantum Computation and Quantum Information,” Cambridge Univ. Press, Cambridge, U.K., 2000.
- [15] R. Orús and J. I. Latorre, “Universality of entanglement and quantum-computation complexity,” Physical Review A, Vol.69, 052308, 2004.
- [16] S. Ouchi, M. Fujishima, and K. Hoh, “An 8-Qubit Quantum-Circuit Processor,” IEEE Symp. on Circuits and Systems, pp. V-209-212, 2002.
- [17] J. Pykacz, “Fuzzy set ideas in quantum logics,” International Journal of Theoretical Physics, Vol.31, pp. 1767-1783, 1992.
- [18] J. Pykacz, “Fuzzy quantum logics as a basis for quantum probability theory,” International Journal of Theoretical Physics, Vol.37, pp. 281-290, 1998.
- [19] D. Ramot, M. Friedman, G. Langholz, and A. Kandel, “Complex fuzzy logic,” IEEE Transactions on Fuzzy Systems, Vol.11, No.4, pp. 450-461, 2003.
- [20] G. G. Rigatos and S. G. Tzafestas, “Parallelization of a fuzzy control algorithm using quantum computation,” IEEE Transactions on Fuzzy Systems, Vol.10, No.4, pp. 451-460, 2002.
- [21] G. G. Rigatos and S. G. Tzafestas, “Quantum learning for neural associative memories,” Fuzzy Sets and Systems, Vol.157, No.13, pp. 1797-1813, 2006.
- [22] J. Siewert and R. Fazio, “Quantum algorithms for Josephson Networks,” Physical Review Letters, Vol.87, 257905, 2001.
- [23] S. Sinha, T. Munakata, and W. L. Ditto, “Parallel computing with extended dynamical systems,” Physical Review E, Vol.65, 036214, 2002.
- [24] J. Virant, N. Zimic, and M. Mraz, “T-type fuzzy memory cells,” Fuzzy Sets and Systems, Vol.102, No.2, pp. 175-183, 1999.
- [25] H. Peyravi, A. Khoei, and K. Hadidi, “Design of an analog CMOS fuzzy logic controller chip,” Fuzzy Sets and Systems, Vol.132, No.2, pp. 245-260, 2002.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.