QUANTUM COMPUTING: THEORETICAL FOUNDATIONS AND RESEARCH GAPS.

Abstract

Quantum computing has emerged as a revolutionary paradigm that harnesses the principles of quantum mechanics, such as superposition, entanglement, and quantum interference, to solve problems that are intractable for classical computers. The theoretical foundations of quantum computing lie in quantum information theory, quantum algorithms, and computational complexity, providing a framework for understanding the potential and limitations of quantum systems. Despite remarkable advancements in quantum hardware and algorithmic design, significant research gaps remain. Challenges such as quantum error correction, scalability of qubit architectures, coherence time enhancement, and the development of universal fault-tolerant quantum computers hinder practical implementation. Furthermore, there is a pressing need to bridge the gap between theoretical algorithmic models and real-world applications, particularly in cryptography, optimization, material science, and machine learning. This paper aims to synthesize the theoretical underpinnings of quantum computing while highlighting the key areas where further research is required to unlock its full potential.