Quantum Decision-Making Algorithms Modeling in the Classical Simulator

the Quantum Software Engineering Visualization for the Educational Process

Abstract

The difference between classical and quantum algorithms (QA) is as follows: the problem solved by QA is coded in the structure of the quantum operators. Input to QA in this case is always the same. Output of QA says which problem coded. In some sense, give a function to QA to analyze and QA returns its property as an answer without quantitative computing. QA studies qualitative properties of the functions. The core of any QA is a set of unitary quantum operators or quantum gates. In practical representation, quantum gate is a unitary matrix with particular structure. The size of this matrix grows exponentially with an increase in the number of inputs, which significantly limits the QA simulation on a classical computer with von Neumann architecture. Quantum search algorithm (QSA) - models apply for the solution of computer science problems as searching in unstructured database, quantum cryptography, engineering tasks, control system design, robotics, smart controllers, etc. Grover’s algorithm is explained in details, along with implementations on a local computer simulator. The presented article describes a practical approach to modeling one of the most famous QA on classical computers, the Grover algorithm.

Author Biographies

Viсtor Sergeevich Ulyanov, Moscow State University of Geodesy and Cartography

Associate Professor of the Department of Computer Science, Cand. Sci. (Eng.), Associate Professor

Sergey Victorovich Ulyanov, Dubna State University; Joint Institute for Nuclear Research

Professor of the Department of System Analysis and Management, Institute of System Analysis and Management; Chief researcher of the Meshcheryakov Laboratory of Information Technologies, Dr. Sci. (Phys.-Math.), Professor

References

1. Bagdasaryn N., Korenkov V., Reshetnikov P., Tyatyushkina O., Ulyanov S. Nonstandard logic of education background in end-to-end information technologies and cognitive computing. Pt. 1: Bcon s Problem, Big Data Analytic and Intelligent Model Theory of Cognition Physical Processes. Sistemnyj analiz v nauke i obrazovanii = System Analysis in Science and Education. 2019;(1):1-38. (In Russ., abstract in Eng.) EDN: SOJBID
2. Serrano M.A., Pérez-Castillo R., Piattini M. Quantum Software Engineering. Cham: Springer; 2022. 302 p. https://doi.org/10.1007/978-3-031-05324-5
3. Ivancova O., Korenkov V., Ryabov N., Ulyanov S. Quantum Software Engineering: Quantum Gate-Based Computational Intelligence Supremacy. In: Voevodin V., Sobolev S. (eds.) Supercomputing. RuSCDays 2020. Communications in Computer and Information Science. Vol. 1331. Cham: Springer; 2020. p. 110-121. https://doi.org/10.1007/978-3-030-64616-5_10
4. Ulyanov S.V., Tyatyushkina O.Yu., Korenkov V.V. Quantum software engineering Pt II: Quantum computing supremacy on quantum gate-based algorithm models. Sistemnyj analiz v nauke i obrazovanii = System Analysis in Science and Education. 2021;(1):81-129. EDN: EIMGEI
5. Ulyanov S.V., Reshetnikov A.G. Cognitive intelligent robust control system based on quantum fuzzy inference for robotics and mechatronics. In: 2017 IEEE 15th International Symposium on Intelligent Systems and Informatics (SISY). Subotica, Serbia: IEEE Computer Society; 2017. p. 000255-000260. https://doi.org/10.1109/SISY.2017.8080563
6. Fox M.F.J., Zwickl B.M., Lewandowski H.J. Preparing for the quantum revolution: What is the role of higher education? Physical Review Physics Education Research. 2020;16(2):020131. https://doi.org/10.1103/PhysRevPhysEducRes.16.020131
7. Uljanov S., Andreev E., Afanas'eva O., Barbashinov M., Reznikova N., Samigulina J. Logical and quantum paradoxes of quantum and soft computational intelligence. Sistemnyj analiz v nauke i obrazovanii = System Analysis in Science and Education. 2010;(2):112-129. (In Russ., abstract in Eng.) EDN: MSYRIF
8. Ulyanov S.V., Litvintseva L.V., Mishin A.A., Sorokin S.V., Fukuda T., Tyatushkina O.Yu., Kolbenko E.V., Nefedov N.Yu., Petrov S.P., Polunin A.S. "Paradox" of quantum self-organization of knowledge bases and robust intelligent control systems. Nechetkie Sistemy i Myagkie Vychisleniya = Fuzzy Systems and Soft Computing. 2011;6(1):67-106. (In Russ., abstract in Eng.) EDN: OTWEKP
9. Nielsen M.A., Chuang I.L. Quantum Computation and Quantum Information: 10th Anniversary Ed. Cambridge: Cambridge University Press; 2010. 702 p. https://doi.org/10.1017/CBO9780511976667
10. Benenti G., Casati G., Strini G. Principles of Quantum Computation and Information. Vol. I: Basic Concepts. Singapore: World Scientific; 2004. 272 p. https://doi.org/10.1142/5528
11. Benenti G., Casati G., Strini G. Principles of Quantum Computation and Information. Vol. II: Basic Tools and Special Topics. Singapore: World Scientific; 2007. 444 p. https://doi.org/10.1142/5838
12. Ulyanov S.V., Ulyanov V.S. Quantum Algorithmic Gate-Based Computing: Grover Quantum Search Algorithm Design in Quantum Software Engineering. arXiv:2304.13703. 2023. Available at: https://arxiv.org/abs/2304.13703 (accessed 01.04.2023).
13. Abhijith J. et al. Quantum Algorithm Implementations for Beginners. ACM Transactions on Quantum Computing 2022;3(4):18. https://doi.org/10.1145/3517340
14. Childs A.M., Coudron M., Gilani A.S. Quantum Algorithms and the Power of Forgetting. In: 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs). 2023. Vol. 251. p. 37:1-37:22. https://doi.org/10.4230/LIPIcs.ITCS.2023.37
15. Aaronson S. Open problems related to quantum query complexity. ACM Transactions on Quantum Computing, 2021;2(4):14. https://doi.org/10.1145/3488559
16. Cumming R., Thomas T. Using a quantum computer to solve a real-world problem what can be achieved today? arXiv:2211.13080. 2022. Available at: https://arxiv.org/abs/2211.13080 (accessed 01.04.2023).
17. Lin L. Lecture Notes on Quantum Algorithms for Scientific Computation. arXiv:2201.08309. 2022. Available at: https://arxiv.org/abs/2201.08309 (accessed 01.04.2023).
18. Nyman P. Simulation of Quantum Algorithms with a Symbolic Programming Language. arXiv:0705.3333. 2007. Available at: https://arxiv.org/abs/0705.3333 (accessed 01.04.2023).
19. Juliá-Díaz B., Burdis J.M., Tabakin F. QDENSITY A Mathematica quantum computer simulation. Computer Physics Communications. 2009;180(3):474. https://doi.org/10.1016/j.cpc.2008.10.006
20. Johansson N., Larsson J.-Å. Efficient classical simulation of the Deutsch Jozsa and Simon s algorithms. Quantum Information Processing. 2017;16:233. https://doi.org/10.1007/s11128-017-1679-7
21. Li H., Qiu D., Leo L. Distributed exact quantum algorithms for Deutsch-Jozsa problem. arXiv:2303.10663. 2023. Available at: https://arxiv.org/abs/2303.10663 (accessed 01.04.2023).
22. Satanassi S., Fantini P., Spada R., Levrini O. Quantum Computing for high school: an approach to interdisciplinary in STEM for teaching. Journal of Physics: Conference Series. 2021;1929:012053. https://doi.org/10.1088/1742-6596/1929/1/012053
23. Seegerer S., Michaeli T., Romeike R. Quantum Computing As a Topic in Computer Science Education. In: Proceedings of the 16th Workshop in Primary and Secondary Computing Education (WiPSCE '21). New York, NY, USA: Association for Computing Machinery; 2021. Article number: 13. https://doi.org/10.1145/3481312.3481348
24. Kushimo T., Thacker B. Investigating students strengths and difficulties in Quantum Computing. arXiv:2212.03726. 2022. Available at: https://arxiv.org/abs/2212.03726 (accessed 01.04.2023).
25. Angara P.P., Stege U., MacLean A., Müller H.A., Markham T. Teaching Quantum Computing to High-School-Aged Youth: A Hands-On Approach. IEEE Transactions on Quantum Engineering. 2022;3:3100115. https://doi.org/10.1109/TQE.2021.3127503
Published
2023-06-30
How to Cite
ULYANOV, Viсtor Sergeevich; ULYANOV, Sergey Victorovich. Quantum Decision-Making Algorithms Modeling in the Classical Simulator. Modern Information Technologies and IT-Education, [S.l.], v. 19, n. 2, p. 298-323, june 2023. ISSN 2411-1473. Available at: <http://sitito.cs.msu.ru/index.php/SITITO/article/view/936>. Date accessed: 16 sep. 2025. doi: https://doi.org/10.25559/SITITO.019.202302.298-323.
Section
Theoretical Questions of Computer Science, Computer Mathematics

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