VQLS is a variational approach to solving linear system of equations. The method was originally proposed in [1]. The vqls-prototype facilitate the use of VQLS for any applications requiring solivng linear systems on simulators or real backends.
In addition to the original reference the qiskit textbook contains a very clear and concise explanation of the VQLS algorithm [2]. We refer readers to this excellent material for further discussion
[1] Variational Quantum Linear Solver, Carlos Bravo-Prieto, Ryan LaRose, M. Cerezo, Yigit Subasi, Lukasz Cincio, Patrick J. Coles, arXiv.1909.05820, 2020