Abstract: Quantum optimization has attracted much attention in recent years. It mainly studies how to accelerate the solution of optimization problems with quantum computing. This overview will classify the quantum optimization algorithm according to whether the optimization variable is continuous, and focus on introducing the continuous variable optimization algorithm. Through the investigation of existing work, this article obtains the following observations: 1)The works of discrete variable quantum optimization were distributed five years ago, while the works of continuous variable quantum optimization has attracted more attention in the last five years; 2)The main basic technologies used in quantum optimization were mainly proposed ten to twenty years ago, and basic innovations are needed; 3)In most works of quantum optimization, theoretical acceleration of time complexity or query complexity is achieved, but more rigorous theoretical analysis is still needed; 4)There are still many problems worthy of exploration by quantum computing researchers in the optimization field, especially in the field of non-convex optimization, which is considered to be difficult in classical computing.

Key words: quantum computing, quantum optimization, mathematical programming, discrete variable optimization, continuous variable optimization