Quantum Computing Optimization: An Introduction

This review provides a comprehensive introduction to the current state of optimization through quantum computing, as well as its main methods and highlights. It begins with an overview of the history and principles of quantum computing, followed by a concise explanation of classical optimization techniques. References to key mathematical tools essential for understanding quantum optimization are introduced to assist readers new to the field. The review then explores various quantum optimization techniques, categorized by hardware requirements, pipelining strategies, kernel methods, order, continuity, heuristic and metaheuristic approaches. Graphs and charts are included to illustrate the interconnections between these techniques, enhancing understanding of their complementarity. Finally, the review concludes with some considerations about societal, economic and environmental impacts and a detailed table summarizing the different methods and their applications.