Abstract

Abstract Quantum computing as the emerging paradigm for scientific computing has attracted significant research attention in the past decade. Quantum algorithms to solve the problems of linear systems, eigenvalue, optimization, machine learning, and others have been developed. The main advantage of utilizing quantum computer to solve optimization problems is that quantum superposition allows for massive parallel searching of solutions. This article provides an overview of fundamental quantum algorithms that can be utilized in solving optimization problems, including Grover search, quantum phase estimation, quantum annealing, quantum approximate optimization algorithm, variational quantum eigensolver, and quantum walk. A review of recent applications of quantum optimization methods for engineering design, including materials design and topology optimization, is also given. The challenges to develop scalable and reliable quantum algorithms for engineering optimization are discussed.