Abstract: Quantum computing is a new computing model based on the principles of quantum mechanics. Because of its powerful parallelism far superior to classical computing, quantum computing is considered as a computational method that may have a subversive impact on the future, providing a new way to solve some complex problems. The algorithms and applications of quantum solvers in numerical computation-related problems of large-scale science and engineering are reviewed. In particular, systems of linear equations, eigenvalue problems, differential equations, Hamiltonian and graph computation, quantum machine learning, quantum solver platform, and practical numerical simulation have been introduced. Aiming at different numerical computing problems, the current mainstream quantum computing algorithms are introduced in detail, and the research progress of relevant algorithms at home and abroad in recent years is comprehensively summarized. Finally, the future development trend of quantum computing in numerical algebra solving is prospected.