A Comparative Study of Classical and Quantum Computing: Concepts, Circuits, and Real-World Applications
K.V. Rama Raoa, N. Srinivasb, K. Rama Krishnaiahc, A. Brahmaiah · International Journal of Research Publication and Reviews · 2025
Quantum computing leverages quantum-mechanical phenomena such as superposition, entanglement and interference to solve classes of problems that are intractable on classical machines.This paper unifies three complementary perspectives: (i) the central role of complex matrices in modelling quantum states, gates and error-correction protocols; (ii) the pervasive use of trigonometric functions in qubit representation, phase manipulation and the quantum Fourier transform (QFT); and (iii) a systematic comparison of classical and quantum computing paradigms with illustrative circuits and real-world applications.By integrating these dimensions, the study provides a consolidated reference that elucidates the mathematical foundations, circuit constructions, algorithmic advantages and practical challenges that define contemporary quantum information processing.