Exploring advanced mathematical concepts in quantum computing for algorithm enhancement

Modi, Shabina Jameer; Panhalkar, Archana R.; Martin, Natasha; Baviskar, Pallavi Vasudev; Wani, Tanveer Ahmad; Kholiyarov, Erkin

doi:10.47974/JIM-2487

Open Access Research Article

Exploring advanced mathematical concepts in quantum computing for algorithm enhancement

Shabina Jameer Modishabina.sayyad@kbpcoes.edu.inDepartment of Computer Science and EngineeringKarmaveer Bhaurao Patil College of EngineeringSatara, Maharashtra, 415001, IndiaView full profile → , ^*Archana R. PanhalkarCorresponding authorarchana10bhosale@rediffmail.comDepartment of Artificial Intelligence & Data ScienceAmrutvahini College of EngineeringSangamner, Maharashtra, 422608, IndiaView full profile → , Natasha Martinnatasha.martin@symlaw.ac.inSymbiosis Law School Pune (SLS-P)Symbiosis Centre for Advanced Legal Studies and Research (SCALSAR), Symbiosis International (Deemed University)Pune, Maharashtra, 411014, IndiaView full profile → , Pallavi Vasudev Baviskarpalbaviskar@gmail.comDepartment of Computer EngineeringSandip FoundationSandip Institute of Engineering and ManagementNashik, Maharashtra, 422213, IndiaView full profile → , Tanveer Ahmad Wanitanveer.ahmad@niu.edu.inDepartment of PhysicsNoida International UniversityGreater Noida, Uttar Pradesh, 203201, IndiaView full profile → , Erkin Kholiyaroverkin_xoliyarov@tues.uzDepartment of Information Technology and Exact SciencesTermez University of Economics and ServiceTermez, 190100, UzbekistanView full profile →

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pp. 527–535Vol. 29Issue 3March 2026DOI: 10.47974/JIM-2487XML

Received:: 01 Apr 2025
Published Online:: 18 Mar 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2487
Pages:: 527–535

Abstract

With this research, the design and performance of quantum programs will be enhanced by investigating the higher mathematical concepts that underlie quantum computers. The goals of the study also include better error correction and the creation of a more insightful perspective of quantum coupling as well as easier construction of quantum circuits through the integration of the complex theories such as group theory, topology, and operator theory. It demonstrates the way these mathematical infrastructure may contribute significantly to the performance of algorithms and fault tolerance via the analysis of theory and case studies. Moreover, the findings indicate the value of advanced mathematics in overcoming the existing issues and make room to more stable and scalable quantum computing solutions.

Keywords

Quantum computing Quantum algorithms Advanced mathematics Quantum error correction Algorithm optimization

Subject Classifications

68Q1268Q09

References

[1] J. Haferkamp, P. Faist, N. B. T. Kothakonda, J. Eisert, and N. Y. Halpern, “Linear growth of quantum circuit complexity,” Nature Physics, vol. 18, pp. 528–532 (2022).
[2] N. Srikanth and A. Ramarao, “AI-based Automated Seed Sowing and Soil Moisture Robot,” International Journal for Interdisciplinary Sciences and Engineering Applications, Volume 6, Issue 3, pp. 20–24 (2025), doi: 10.5281/zenodo.16728954
[3] Y. Cao, J. Romero, and A. Aspuru-Guzik, “Potential of quantum computing for drug discovery,” IBM Journal of Research and Development, vol. 62, no. 6, pp. 6:1–6:20 (2018).
[4] Dylan Herman, Cody Googin, Xiaoyuan Liu, Yue Sun, Alexey Galda, Ilya Safro, Marco Pistoia, and Yuri Alexeev, “Quantum computing for finance,” Nature Reviews Physics, vol. 5, pp. 450–465 (2023).
[5] C. Jurczak, “Investing in the Quantum Future: State of Play and Way Forward for Quantum Venture Capital,” arXiv preprint, arXiv:2311.17187, 2023.
[6] A. Woolnough, C. Lloyd, P. Hollenberg, and T. Prowse, “Quantum computing: A new paradigm for ecology,” Trends in Ecology & Evolution, vol. 38, pp. 727–735 (2023).
[7] H. Calvo, G. Cuartero, F. Gómez, J. González, M. Mezzini, and F. Pelayo, “Functional Matrices on Quantum Computing Simulation,” Mathematics, vol. 11, pp. 3742 (2023).
[8] J. W. Z. Lau, K. H. Lim, H. Shrotriya, and L. C. Kwek, “NISQ computing: Where are we and where do we go?,” AAPPS Bulletin, vol. 32, pp. 27 (2022).
[9] S. Vadyala and S. Betgeri, “General implementation of quantum physics-informed neural networks,” Array, vol. 18, pp. 100287 (2023).
[10] S. S. Patil and E. Rosemaro, “Blockchain-Based Smart Contracts: Implementation and Security Considerations,” International Journal of Advanced Computer Engineering and Communication Technology (IJACECT), vol. 12, no. 2, pp. 10–17 (Apr. 2025).
[11] A. B. Kathole, K. Vhatkar, S. A. Ubale, V. V. Kimbahune, A. Dhumane, and A. Goyal, “Enhanced security mechanism in vehicular networks using ensemble machine learning to detect malicious activity in VANETs,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 27, no. 7, pp. 2005–2014 (2024).
[12] C. Deshpande, C. Ramtirthkar, T. A. Wani, V. K. Bhosale, M. Gulhane, and K. S. Kumar, “Topology and knot theory applications in quantum field theory,” Journal of Interdisciplinary Mathematics, vol. 28, no. 6, pp. 2281–2287 (2025), doi: 10.47974/JIM-2370.
[13] G. Kaur, M. Kaur, J. Singh, M. M. Laishram, S. Lakhanpal, and M. Kumar, “Effective strategies for writing maintainable code in cryptographic software development,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 29, no. 2-A, pp. 609–616 (2026), doi: 10.47974/JDMSC-2503.

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