Cyber Times International Journal of Technology & Management

Quantum computing has emerged as one of the most transformative paradigms in computational science, promising to fundamentally redefine the boundaries of problem-solving capability across a broad spectrum of scientific and industrial domains. Drawing upon the principles of quantum mechanics — specifically superposition, entanglement, and quantum interference — quantum computers offer computational architectures that are architecturally and algorithmically distinct from their classical counterparts. This paper presents a comprehensive survey of the theoretical foundations, major algorithmic developments, practical applications, and prevailing challenges associated with quantum computing, with all analyses confined to research and developments available through 2019. The work provides a detailed examination of pivotal quantum algorithms, including Shor's algorithm for integer factorization, Grover's algorithm for unstructured search, and the Quantum Fourier Transform as a foundational subroutine. The paper further surveys the hardware landscape, discussing the state of IBM Q, D-Wave Systems, and Google's quantum research initiatives as of 2019. Comparative analyses are provided through structured tables to facilitate scholarly discourse on the relative merits and constraints of various quantum computing paradigms. The implications of quantum computing for cryptographic security, optimization, drug discovery, and machine learning are assessed critically. The persistent challenges of decoherence, gate error rates, and scalability are discussed alongside the then-current mitigation strategies.