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Trigonometric Near-Rings as a Unified Algebraic Framework for Quantum Computation
Subject area: Science,Engineering and Technology · Area of research: Maths and physics
DOI: https://doi.org/10.64388/IREV9I11-1718493
Abstract
We introduce a unified algebraic framework for quantum computation based on finite trigonometric near-rings. Motivated by unification ideas in physics, the proposed structure connects trigonometric functions, non-commutative algebra, and quantum gate operations within a single finite system. By constructing near-rings generated by discrete phase operators and the Hadamard operator, we show that quantum phase interference and basis transformations naturally give rise to non-commutative near-ring structures. The developed framework generalizes earlier Heisenberg-type matrix near-rings to a trigonometric setting, providing a discrete algebraic model for quantum circuits involving phase and Clifford gates. Explicit finite examples including a non-commutative near-ring of order sixteen are presented to illustrate the theory. This approach offers a conceptually simple yet mathematically rigorous bridge between trigonometry and quantum computation and highlights the relevance of near-ring theory as a foundational tool for modeling finite quantum systems.
Keywords
Trigonometric Near-Rings, Quantum Computing; Non-Commutative Algebra, Hadamard Gate, Phase Gates, Finite Near-Rings, Heisenberg Near-Rings, Quantum Circuits, Algebraic Unification.
How to cite this paper
@article{1718493,
author = {Dr. K V Rama Rao, M. Sriniva, T. V. Ram Babu, K. Anuradh},
title = {Trigonometric Near-Rings as a Unified Algebraic Framework for Quantum Computation},
journal = {Iconic Research And Engineering Journals},
year = {2026},
volume = {9},
number = {11},
pages = {4916-4918},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1718493.pdf},
abstract = {We introduce a unified algebraic framework for quantum computation based on finite trigonometric near-rings. Motivated by unification ideas in physics, the proposed structure connects trigonometric functions, non-commutative algebra, and quantum gate operations within a single finite system. By constructing near-rings generated by discrete phase operators and the Hadamard operator, we show that quantum phase interference and basis transformations naturally give rise to non-commutative near-ring structures. The developed framework generalizes earlier Heisenberg-type matrix near-rings to a trigonometric setting, providing a discrete algebraic model for quantum circuits involving phase and Clifford gates. Explicit finite examples including a non-commutative near-ring of order sixteen are presented to illustrate the theory. This approach offers a conceptually simple yet mathematically rigorous bridge between trigonometry and quantum computation and highlights the relevance of near-ring theory as a foundational tool for modeling finite quantum systems.},
keywords = {Trigonometric Near-Rings, Quantum Computing; Non-Commutative Algebra, Hadamard Gate, Phase Gates, Finite Near-Rings, Heisenberg Near-Rings, Quantum Circuits, Algebraic Unification.},
month = {May},
doi = {https://doi.org/10.64388/IREV9I11-1718493}
}