Comparative Study of Quantum Algorithms: A Comprehensive Analysis

Quantum computing is a rapidly growing field. Quantum algorithms play a significant role and have applications in cryptography, machine learning, optimization, and computational issues [1][2]. They quantum features like entanglement and superposition that help carryout tasks that would be difficult for a classical computer. More Interest has been developed in Quantum algorithms due to their ability to solve specific computational problems quicker than that in classical algorithms [3]. These algorithms use fundamentals of quantum physics to carryout calculations quickly and effectively than traditional algorithms. Here in-depth analysis of quantum algorithms and classical algorithms is done by looking at the time and space complexity of quantum and classical algorithms including their capacity to tackle specific types of issues.First, we conduct a general comparison of Classical and Quantum Algorithm along with Background and motivation. We also discuss Simon's algorithm first and then Grover's algorithm in depth and their comparison with few other algorithms in a table format [5][6][7][8]. We also cover some recent advancements, Quantum supremacy, Post-Quantum Cryptography, 8 Quantum Artificial Intelligence, Hybrid Quantum-Classical Algorithms and few other important parameters. We also discuss the plausible impact of quantum algorithms on cybersecurity and cryptography [13][9]. Overall, this comparative study shows the uses and challenges involved in implementing quantum algorithms while offering an overview of quantum algorithms. We conclude by the fundamental ideas of quantum algorithms. Adding to this we also discuss the challenges and limitations of using quantum algorithms in practically. At the end, we provide a summary of the primary findings from this comparative study of Quantum and classical algorithms.