Eigenvector continuation is a computational method for parametric eigenvalue problems that uses subspace projection with a basis derived from eigenvector snapshots from different parameter sets. It is part of a broader class of subspace-projection techniques called reduced-basis methods. In this colloquium article, we present the development, theory, and applications of eigenvector continuation and projection-based emulators. We introduce the basic concepts, discuss the underlying theory and convergence properties, and present recent applications for quantum systems and future prospects.

翻译：特征向量延续是一种用于参数化本征值问题的计算方法，该方法利用从不同参数集的本征向量快照中导出的基，通过子空间投影进行求解。它属于更广泛的子空间投影技术类别——即降基方法。在本综述文章中，我们阐述了特征向量延续与基于投影的仿真器的发展历程、理论基础及其应用。我们介绍了基本概念，讨论了其理论基础与收敛特性，并展示了近期在量子系统中的应用案例及未来展望。