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 Engineering Karmaveer Bhaurao Patil College of EngineeringSatara, Maharashtra, 415001, IndiaView full profile → , ^*Archana R. PanhalkarCorresponding authorarchana10bhosale@rediffmail.comDepartment of Artificial Intelligence & Data Science Amrutvahini College of EngineeringSangamner, Maharashtra, 422608, IndiaView full profile → , Natasha Martinnatasha.martin@symlaw.ac.inSymbiosis Centre for Advanced Legal Studies and Research (SCALSAR) Symbiosis Law School Pune (SLS-P) Symbiosis International (Deemed University)Symbiosis Centre for Advanced Legal Studies and Research Symbiosis Law School Pune (SLS-P) Symbiosis International (Deemed University)Pune, Maharashtra, Symbiosis Centre for Advanced Legal Studies and Research Symbiosis Law School Pune (SLS-P) Symbiosis International (Deemed University), IndiaView full profile → , Pallavi Vasudev Baviskarpalbaviskar@gmail.comDepartment of Computer Engineering Sandip Foundation Sandip Institute of Engineering and ManagementDepartment of Computer Engineering Sandip Institute of Engineering and Management Sandip FoundationNashik, Maharashtra, 422213, IndiaView full profile → , Tanveer Ahmad Wanitanveer.ahmad@niu.edu.inDepartment of Physics Noida International UniversityNoida, Uttar Pradesh, 203201, DelhiView full profile → , Erkin Kholiyaroverkin_xoliyarov@tues.uzDepartment of Information Technology and Exact Sciences Termez 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

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