Quantum Computing Algorithms for Solving Complex Optimization Problems

Abstract

In the pursuit of revolutionizing computational capabilities, quantum computing has emerged as a transformative frontier. This study delves into the exploration of Quantum Computing Algorithms designed to address the intricacies of solving complex optimization problems, aiming to unravel the potential and challenges that quantum approaches bring to the forefront of computational science. The main purpose of this study was to investigate the potential applications and effectiveness of quantum computing algorithms in solving complex optimization problems, with a focus on real-world systems and technological implications. This study was anchored on two major models, that is, Quantum Approximate Optimization Algorithm (QAOA) and the Grover's Quantum Search Algorithm. The study conducted a thorough review and synthesis of diverse scholarly works on quantum computing algorithms for solving complex optimization problems, aiming to gain insights into key theories, methodologies, findings, and gaps in the existing body of knowledge. In conclusion, this study significantly advances our understanding of quantum algorithms' potential and challenges in solving complex optimization problems. Quantum algorithms, particularly Quantum Approximate Optimization Algorithm (QAOA) and Grover's Quantum Search Algorithm, show promise in providing speedup and efficiency compared to classical counterparts, hinting at the transformative impact of quantum computing. Research gaps identified, such as the need for more empirical studies and exploration of fault-tolerant quantum computing, underscore the ongoing nature of quantum optimization research. The study contributes to theory by showcasing QAOA and Grover's Algorithm's potential, enriching our foundational understanding of quantum algorithms. On the policy front, the study emphasizes the importance of fostering an ecosystem supporting quantum computing integration into practical applications. The applicability of quantum-inspired genetic algorithms in logistics optimization suggests policies encouraging exploration and implementation of quantum-inspired approaches. Additionally, identified research gaps in scalability and fault tolerance highlight the need for policies promoting investments in quantum computing research and infrastructure. The study's contributions extend to ethical and regulatory considerations, urging policymakers to anticipate and address ethical implications, privacy concerns, and security risks associated with advancing quantum technologies. Policymakers are encouraged to consider the theoretical insights to inform policies facilitating the practical integration and ethical deployment of quantum computing technologies.