Title of paper:

How to represent uncertainty via qudits: Probability distributions, regular, intuitionistic and picture fuzzy sets, Ftransforms, etc.

Author(s):

Olga Kosheleva

Department of Teacher Education, University of Texas at El Paso, 500 W. University, El Paso, Texas 79968, USA

olgak@utep.edu

Vladik Kreinovich

Department of Teacher Education, University of Texas at El Paso, 500 W. University, El Paso, Texas 79968, USA

vladik@utep.edu


Presented at:

25^{th} ICIFS, Sofia, 9—10 September 2022

Published in:

Notes on Intuitionistic Fuzzy Sets, Volume 28 (2022), Number 3, pages 203–210

DOI:

https://doi.org/10.7546/nifs.2022.28.3.203210

Download:

PDF (153 Kb, File info)

Abstract:

While modern computers are fast, there are still many important practical situations in which we need even faster computations. It turns out that, due to the fact that the speed of all communications is limited by the speed of light, the only way to make computers drastically faster is to drastically decrease the size of computer’s components. When we decrease their size to sizes comparable with microsizes of individual molecules, it becomes necessary to take into account specific physics of the microworld – known as quantum physics. Traditional approach to designing quantum computers – i.e., computers that take effect of quantum physics into account – was based on using quantum analogies of bits (2state systems). However, it has recently been shown that the use of multistate quantum systems – called qudits – can make quantum computers even more efficient.
When processing data, it is important to take into account that in practice, data always comes with uncertainty. In this paper, we analyze how to represent different types of uncertainty by qudits.

Keywords:

Quantum computing, Qudits, Uncertainty, Fuzzy, Intuitionistic fuzzy, Picture fuzzy, Probabilistic uncertainty, Ftransform.

AMS Classification:

68Q12, 81P68, 03B52, 03E72, 68T27, 68T37.

References:

 Atanassov, K. (1999). Intuitionistic Fuzzy Sets: Theory and Applications. SpringerVerlag, Berlin, Heidelberg.
 Baker, J. M., & Chong, F. T. (2021). Emerging technologies for quantum computing. IEEE Micro, 41(5), 41–47.
 Baker, J. M., Duckering, C., & Chong, F. T. (2020). Efficient quantum circuit decompositions via intermediate qudits. Proceedings of the IEEE 50th International Symposium on MultipleValued Logic ISMVL’2020, Miyazaki, Japan, November 9–11, 2020, 303–308.
 Belohlavek, R., Dauben, J. W., & Klir, G. J. (2017). Fuzzy Logic and Mathematics: A Historical Perspective. Oxford University Press, New York.
 Cuong, B. C., & Kreinovich, V. (2013). Picture Fuzzy Sets  a new concept for computational intelligence problems. Proceedings of the Third World Congress on Information and Communication Technologies WICT’2013, Hanoi, Vietnam, December 15–18, 2013, 1–6.
 Dick, S., Yager, R., & Yazdanbakhsh, O. (2016). On Pythagorean and complex fuzzy set operations. IEEE Transactions on Fuzzy Systems, 24(5), 1009–1021.
 Feynman, R., Leighton, R., & Sands, M. (2005). The Feynman Lectures on Physics. Addison Wesley, Boston, Massachusetts.
 Gokhale, P., Baker, J. M., Duckering, C., Brown, N. C., Brown, K. R., & Chong, F. T. (2019). Asymptotic improvements to quantum circuits via qutrits. Proceedings of the 46th International Symposium on Computer Architecture ISCA’19, Phoenix, Arizona, June 22–26, 2019, 554–566.
 Klir, G., & Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic. Prentice Hall, Upper Saddle River, New Jersey.
 Mendel, J. M. (2017). Uncertain RuleBased Fuzzy Systems: Introduction and New Directions. Springer, Cham, Switzerland.
 Nguyen, N. T., & Walker, E. A. (2006). A First Course in Fuzzy Logic. Chapman and Hall/CRC, Boca Raton, Florida.
 Nielsen, M. A., & Chuang, I. L. (2000). Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, U.K.
 Novak, V., Perfilieva, I., Holcapek, M., & Kreinovich, V. (2014). Filtering out high ´ frequencies in time series using Ftransform. Information Sciences, 274, 192–209.
 Novak, V., Perfilieva, I., & Kreinovich, V. (2012). Ftransform in the analysis of periodic signals. In: Inuiguchi, M., Kusunoki, Y., & Seki, M. (eds.), Proceedings of the 15th CzechJapan Seminar on Data Analysis and Decision Making under Uncertainty CJS’2012, Osaka, Japan, September 24–27, 2012.
 Novak, V., Perfilieva, I., & Močkoř, J. (1999). Mathematical Principles of Fuzzy Logic. Kluwer, Boston, Dordrecht.
 Pavlidis, A., & Floratos, E. (2017). Arithmetic circuits for multilevel qudits based on quantum Fourier transform, arXiv:1707.08834.
 Perfilieva, I. (2006). Fuzzy transforms: Theory and applications. Fuzzy Sets and Systems, 157, 993–1023.
 Perfilieva, I. (2015). Ftransform. In: Springer Handbook of Computational Intelligence, Springer Verlag, 113–130.
 Perfilieva, I., Dankova, M., & Bede, B. (2011). Towards a higher degree Ftransform. Fuzzy Sets and Systems, 180(1), 3–19.
 Perfilieva, I., Kreinovich, V., & Novak, V. (2012). Ftransform in view of trend extraction. In: Inuiguchi, M.; Kusunoki, Y.; Seki, M. (eds.), Proceedings of the 15th CzechJapan Seminar on Data Analysis and Decision Making under Uncertainty CJS’2012, Osaka, Japan, September 24–27, 2012.
 Sheskin, D. J. (2011). Handbook of Parametric and Nonparametric Statistical Procedures. Chapman and Hall/CRC, Boca Raton, Florida.
 Thorne, K. S., & Blandford, R. D. (2017). Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics. Princeton University Press, Princeton, New Jersey.
 Vassilev, P. M., & Atanassov, K. T. (2019). Modifications and Extensions of Intuitionistic Fuzzy Sets. “Prof. Marin Drinov” Academic Publishing House, Sofia, Bulgaria.
 Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353.

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