An Overview of Quantum Optimization
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摘要: 量子优化是量子计算领域近年来颇受关注的一个研究分支，主要研究如何利用量子计算加速优化问题的求解.根据优化问题的变量是否连续分类梳理量子优化算法，侧重介绍连续变量优化算法.通过对现存工作的调研梳理得到一些观察：1)5~20年前的研究主要集中在离散变量的量子优化技术，近5年的研究则更关注连续变量的量子优化技术；2)量子优化使用的主要基础技术都是10~20年前提出的，在基础技术方面需要进一步革新；3)量子优化算法相比于对应的经典算法通常在理论上有加速优势，既有体现在时间复杂度的加速，也有体现在查询复杂度的加速，但仍然有待更为严格的理论分析；4)优化领域依然存在许多值得量子计算研究人员探索的问题，特别是非凸优化领域，亦即经典计算上认为较难的优化问题.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.
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