IMPLEMENTATION OF THE ALGORITHM FOR TRANSFORMING A CLASSICAL IMAGE INTO A QUANTUM CONDITION, ALLOCATION OF BORDERS AND TRANSFORMATION OF A HALFTONE IMAGE TO A BINARY ONE

  • V. S. Potapov Southern Federal University
Keywords: Quantum simulation, quantum algorithm, quantum bit, quantum computing model, quantum entanglement, superposition, quantum parallelism

Abstract

This article is devoted to solving the problem of research and development of methods for the functioning of quantum algorithms and models of quantum computing devices. The quantum algorithm implemented in the work allows the classical image to be transformed into a quantum state, the selection of boundaries and the transformation of a halftone image into a binary one, shows the possibilities of quantum information theory in interpreting classical problems. The aim of the work is a computer simulation of a quantum algorithm for solving the problem of transform-ing a classical image using quantum computing means and methods, studying existing pattern recognition algorithms and creating an effective recognition model using properties and methods of quantum computing. This article is devoted to solving the problem of research and development of methods for the functioning of quantum algorithms and models of quantum computing devices. The relevance of these studies lies in the mathematical and software modeling and implementation of a quantum algorithm for solving classes of problems of a classical nature. The scientific novelty of this area is primarily expressed in the constant updating and addition of the field of quantum research in a number of areas, and computer simulation of quantum physical phenomena and features is poorly covered in the world. Currently, in many advanced countries of the world inten-sively conducted research work on the development and creation of quantum computers and their software, there is a rapid growth of interest in quantum computers. A large number of articles and monographs are published. The paper presents the main theoretical and practical results in the field of quantum computing.

References

1. Raedt K.D., Michielsen K., De Raedt H., Trieu B., Arnold G., Marcus Richter, Th Lip-pert, Watanabe H., and Ito N. Massively parallel quantum computer simulator // Computer Physics Communications. – Vol. 176. – P. 121-136;
2. Boixo S., Isakov S.V., Smelyanskiy V.N., Babbush R., Ding N., Jiang Z., Martinis J.M., and Neven H. Characterizing quantum supremacy in near-term devices. arXiv pre-print arXiv:1608.00263;
3. Stierhoff G.C., Davis A.G. A History of the IBM Systems Journal In: IEEE Annals of the His-tory of Computing. – Vol. 20, Issue1. – P. 29-35.
4. Lipschutz S., Lipson M. Linear Algebra (Schaum’s Outlines). – 4th ed. McGraw Hill.
5. Collier, David. The Comparative Method. In Ada W. Finifter, ed. Political Sciences: The State of the Discipline II. Washington, DC: American Science Association. – P. 105-119.
6. Vectorization.https://en.wikipedia.org/w/index.php?title=Vectorization&ldid=829988201.
7. Williams C.P. Explorations in Quantum Computing. Texts in Computer Science, Chapter 2. Quantum Gates. – Springer, 2011. – P. 51-122.
8. Olukotun K. Chip Multiprocessor Architecture – Techniques to Improve Throughput and La-tency. Morgan and Claypool Publishers (2007);
9. Potapov V., Guzik V., Gushanskiy S., Polenov M. Complexity Estimation of Quantum Algo-rithms Using Entanglement Properties In: Informatics, Geoinformatics and Remote Sensing // Proceedings of 16-th International Multidisciplinary Scientific Geoconference, SGEM 2016, Bulgaria. – 2016. – Vol. 1. – P. 133-140. STEF92 Technology Ltd.
10. Inverter (logic gate). – https://en.wikipedia.org/w/index.php?title=Inverter_ (log-ic_gate)&oldid=844691629.
11. Lachowicz P. Walsh – Hadamard Transform and Tests for Randomness of Financial Re-turn-Series. – 2015. – http://www.quantatrisk.com/2015/04/07/walsh-hadamard-transform-python-tests-for-randomness-of-financial-return-series/.
12. Potapov V., Gushanskiy S., Guzik V., Polenov M. The Computational Structure of the Quantum Computer Simulator and Its Performance Evaluation In: Software Engineering Perspectives and Application in Intelligent Systems. Advances in Intelligent Systems and Computing. – Springer, 2019. – Vol. 763. – P. 198-207.
13. Quantum phase estimation algorithm. (2016, Nov. 03). In Wikipedia, The Free Encyclopedia. Retrieved 05:15, July 27, 2016. – https://en.wikipedia.org/w/index.php? Ti-tle=Quantum_phase_estimation_algorithm& oldid=731732789.
14. Richard G. Milner. A Short History of Spin // Contribution to the XVth International Work-shop on Polarized Sources, Targets, and Polarimetry. – Charlottesville, Virginia, USA, Sep-tember 9-13, 2013. – arXiv:1311.5016.
15. Гушанский С.М., Потапов В.С. Методика разработки и построения квантовых алгорит-мов // Информатизация и связь. – 2017. – № 3. – С. 101-104.
16. Гузик В.Ф., Гушанский С.М., Поленов М.Ю., Потапов В.С. Реализация компьютерного моделирования системы с частицей в одномерном и двухмерном пространстве на кван-товом уровне // Известия ЮФУ. Технические науки. – 2017. – № 6 (191). – С. 223-233.
17. Гушанский С.М., Поленов М.Ю., Потапов В.С. Реализация модуля конвертации мо-делей для среды MATLAB // Известия ЮФУ. Технические науки. – 2017. – № 6 (191). – С. 212-223.
18. Hales S. Hallgren. An improved quantum Fourier transform algorithm and applications // Pro-ceedings of the 41st Annual Symposium on Foundations of Computer Science, November 12 – 14, 2000. – P. 515.
19. Potapov V., Gushanskiy S., Polenov M. The Methodology of Implementation and Simulation of Quantum Algorithms and Processes // 11th International Conference on Application of In-formation and Communication Technologies (AICT). – Institute of Electrical and Electronics Engineers, 2017. – P. 437-441.
20. Quantum programming. (2016, Nov 03). In Wikipedia, The Free Encyclopedia. Retrieved 17:50, September 20, 2016. – https://en.wikipedia.org/ w/index.php?title=Quantum_ pro-gramming&oldid=740376291.
21. Wikipedia contributors. (2018, November 27). IBM Q Experience. In Wikipedia, The Free Encyclopedia. Retrieved 17:28, January 31, 2019. – https://en.wikipedia.org/w/ in-dex.php?title=IBM_Q_Experience&oldid=87087480.
22. Quantum mechanics. (2017, March 29). In Wikipedia, The Free Encyclopedia. Retrieved 15:50, March 30, 2017. – URL: https://en.wikipedia.org/w/index.php? title=Quantum_ me-chanics&oldid=772744105.
23. Boneh D., Zhandry M. Quantum-secure message authentication codes // In Proceedings of Eurocrypt. – 2013. – P. 592-608.
24. Potapov V., Gushansky S., Guzik V., Polenov M. Architecture and Software Implementation of a Quantum Computer Model // Advances in Intelligent Systems and Computing. – Springer Verlag, 2016. – Vol. 465. – P. 59-68.
25. Bennett С.H., Shor P.W., Smolin J.A., Thapliyal A.V. Entanglement-assisted Capacity of a Quantum Channel and the Reverse Shannon Theorem // IEEE Transactions on Information Theory. – 2002. – Vol. 48. – P. 26-37.
26. Kleppner D., Kolenkow R. An Introduction to Mechanics (Second ed.). Cambridge: Cambridge University Press, 2014. – 49 p.
Published
2019-09-24
Section
SECTION I. INFORMATION PROCESSING ALGORITHMS.