Current Volume 9
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.
Citations
IRE Journals:
Dr. K V Rama Rao, M. Sriniva, T. V. Ram Babu, K. Anuradh "Trigonometric Near-Rings as a Unified Algebraic Framework for Quantum Computation" Iconic Research And Engineering Journals Volume 9 Issue 11 2026 Page 4916-4918 https://doi.org/10.64388/IREV9I11-1718493
IEEE:
Dr. K V Rama Rao, M. Sriniva, T. V. Ram Babu, K. Anuradh
"Trigonometric Near-Rings as a Unified Algebraic Framework for Quantum Computation" Iconic Research And Engineering Journals, 9(11) https://doi.org/10.64388/IREV9I11-1718493
About IRE Journals
IRE Journals is an open access online journals established with an aim to publish high quality of research work in various diciplines. We have more than 6 years in publications. Over 2500+ papers already published.
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