Author(s): K Janardhana Rao, Yedla Rajasekhar, Yeluri Vijayalakshmi and Nalli Veera Malathi

Abstract: Quantum computing, leveraging the principles of quantum mechanics, represents a transformative frontier in computational technology, capable of addressing complex problems intractable to classical computers. This research review systematically examines the mathematical foundations and core algorithms underpinning quantum computing. Specifically, the objectives of this paper include a comprehensive exploration of quantum computational theory, algorithmic strategies, and their practical implications. A rigorous approach encompassing critical analysis of recent advances and prominent algorithms is employed. Key quantum algorithms such as Shor’s factoring algorithm, Grover’s search algorithm, Quantum Fourier Transform, and quantum error correction codes are detailed. The review further examines recent developments in variational quantum algorithms (VQAs) and quantum machine learning (QML). Findings highlight significant efficiency gains provided by quantum algorithms, alongside prevailing challenges in scalability, coherence, and error mitigation. The implications suggest promising potential for quantum algorithms in fields like cryptography, optimization, and drug discovery. However, limitations in hardware capabilities necessitate continued theoretical and experimental advancements. This article concludes with future research directions emphasizing quantum algorithm optimization, hybrid quantum-classical frameworks, and error correction methodologies, laying groundwork for progressive computational breakthroughs.

Pages: 97-102 | Views: 59 | Downloads: 7

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