PhD student Carlos Bravo-Prieto posted a pre-print article as the result of his summer stay at Los Álamos (NM, USA):

“Variational Quantum Linear Solver: A Hybrid Algorithm for Linear Systems”, by C. Bravo-Prieto (~~@~~**charl_bp**), R. LaRose (~~@~~**ryanmlarose**), M. Cerezo (~~@~~**EntangledPhys**), Y. Subasi, L. Cincio and P. J. Coles (~~@~~**PatrickColes314**). preprint: https://scirate.com/arxiv/1909.05820

In this work, they presented a variational quantum algorithm for solving the quantum linear system problem. On the analytical side, they derived efficient quantum circuits to estimate faithful cost functions, while showing that they are difficult to estimate classically.

On the numerical side, they studied the scaling of the algorithm run time and found it to be efficient with respect to the condition number and the desired precision:

Furthermore, they implemented the variational algorithm in ~~@~~**rigetti**‘s quantum computer, for particular problems up to a size of 32×32, which is the largest implementation of a linear system on quantum hardware: