PARALLELISM AND SUPERPOSITION: REASONS FOR THE SUPERIORITY OF QUBIT OVER CLASSICAL BIT

Authors

  • Oybek Primqulov Tashkent University of Information Technologies named after Muhammad al-Khwarizmi

Keywords:

Qubit, Classical bit, Quantum computing, Superposition, Quantum parallelism, Quantum entanglement, Quantum supremacy, Quantum algorithms, Shor’s algorithm

Abstract

The future of computing is greatly influenced by the revolutionary characteristics of quantum bits (qubits) and quantum superposition, which offer significant advantages over classical computing. This paper explores the superiority of qubits compared to classical bits, delving into the principles of quantum superposition and its mathematical representation. Additionally, it examines the differences between Shor's algorithm and classical algorithms. Qubits, with their ability to exist in multiple states simultaneously due to quantum superposition, dramatically enhance computational efficiency. This paper provides an in-depth analysis of the mathematical aspects of qubits, highlights the advantages of quantum computing through algorithms like Shor's, and compares quantum and classical algorithms, discussing the capabilities and limitations of quantum computing.

References

Shor, P. W. (1994). Algorithms for Quantum Computation: Discrete Logarithms and Factoring. Proceedings of the 35th Annual Symposium on Foundations of Computer Science (FOCS), pp. 124-134.

Nielsen, M. A., & Chuang, I. L. (2010). Quantum Computation and Quantum Information (10th Anniversary Edition). Cambridge University Press.October 27-28, 2013. pp. 43–48. ACM,2013.

Grover, L. K. (1996). A Fast Quantum Mechanical Algorithm for Database Search. Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing (STOC), pp. 212-219.

Bernstein, E., & Vazirani, U. (1993). Quantum Complexity Theory. Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing (STOC), pp. 11-20.

Arora, S., & Barak, B. (2009). Computational Complexity: A Modern Approach. Cambridge University Press.

Preskill, J. (2018). Quantum Computing in the NISQ era and beyond. Quantum 2, 79.

Kitaev, A. Y., Shen, A., & Vyalyi, M. N. (2002). Classical and Quantum Computation. American Mathematical Society.

Nielsen, M. A. (2004). Quantum Computation and Quantum Information. Cambridge University Press.

Watrous, J. (2018). The Theory of Quantum Information. Cambridge University Press.

Ladd, T. D., Jelezko, F., Laflamme, R., Pan, J.-W., Monroe, C., & Kimble, H. J. (2010). Quantum computers. Nature 464, 45-53.

N.Raximov, O.Primqulov, “The comparison of Grover's algorithm and classical algorithms in search”, International Conference on Information Science and Communications Technologies (ICISCT 2023),

N.Raximov, J.Kuvandikov, D.Khasanov, “The importance of loss function in artificial intelligence”, International Conference on Information Science and Communications Technologies (ICISCT 20222), DOI: 10.1109/ICISCT55600.2022.10146883

Khasanov Dilmurod, Tojiyev Ma’ruf, Primqulov Oybek., “Gradient Descent In Machine”. International Conference on Information Science and Communications Technologies (ICISCT), https://ieeexplore.ieee.org/document/9670169

Oliver Theobald. ¬ Machine Learning for Absolute Beginners. – Scatterplot Press. 2017. pg.43-98.

N.Raximov, B.Esanovna, O.Primkulov. Аxborot tizimlаridа mаntiqiy xulosаlаsh sаmаrаdorligini oshirish yondаshuvi.Algoritmlar va dasturlashning dolzarb muammolari mavzusidagi xalqaro ilmiy-amaliy anjuman Qarshi- 2023 y. –B. 444-447

N.Raximov, O.Primqulov, B.Daminova,“Basic concepts and stages of research development on artificial intelligence”, International Conference on Information Science and Communications Technologies (ICISCT), www.ieeexplore.ieee.org/document/9670085/metrics#metrics

Rahimov Nodir, Khasanov Dilmurod. (2022). The Mathematical Essence Of Logistic Regression For Machine Learning. https://doi.org/10.5281/zenodo.7239169

Ma’ruf Tojiyev, Ravshan Shirinboyev, Jahongirjon Bobolov. Image Segmentation By Otsu Method. International Journal of Contemporary Scientific and Technical Research, (Special Issue), 2023. 64–72, https://zenodo.org/record/7630893

N.Raximov, M.Doshchanova, O.Primqulov, J.Quvondikov. Development of architecture of intellectual information system supporting decision-making for health of sportsmen.// 2022 International Congress on Human-Computer Interaction, Optimization and Robotic Applications (HORA)

Тоджиев М., Улугмуродов Ш., Ширинбоев Р. Tasvirlar sifatiniyaxshilashning chiziqlikontrast usuli //Современные инновационные исследования актуальные проблемы и развитие тенденции: решения и перспективы. – 2022. – Т. 1. – №. 1. – С. 215-217.

Рахимов Н., Ширинбаев Р., Саидова З. Ma’lumotlarni intellektual tahlillash uchun oldindan tasniflash va yakuniy konvolyutsion neyron tarmog ‘i //Информатика и инженерные технологии. – 2023. – Т. 1. – №. 2. – С. 55-61.

Dilmurod H., Shirinboyеv R. Thе mаin thеory of linеаr rеgrеssion modеls in dаtа mining //Sun’iy Intellekt Nazariyasi va Amaliyoti: Tajribalar, Muammolar va Istiqbollari. – 2024. – С. 143-147.

Published

2024-09-11

How to Cite

Primqulov, O. (2024). PARALLELISM AND SUPERPOSITION: REASONS FOR THE SUPERIORITY OF QUBIT OVER CLASSICAL BIT. DTAI – 2024, 1(DTAI), 49–54. Retrieved from https://dtai.tsue.uz/index.php/DTAI2024/article/view/oybek