Quantum Computing Algorithms – Survey of Shor's, Grover's, and Future Directions

For decades, classical computers have been governed by predictable rules. But as we approach the physical limits of computation, a new paradigm is emerging. Quantum computing operates on the strange and powerful laws of quantum mechanics—superposition, entanglement, and interference—to tackle problems far beyond the reach of any classical machine. The true potential of this field was unlocked by two landmark discoveries: Shor’s algorithm, a revolutionary method for integer factorization that threatens to upend modern cryptography, and Grover’s algorithm, a versatile tool that offers a quadratic speedup for unstructured search problems. This paper serves as a guide to these foundational algorithms, detailing their inner workings and their profound impact. We also explore post-quantum cryptography, hybrid frameworks, and quantum machine learning—illustrating the evolving role of quantum algorithms in shaping the future of science and technology.