I will describe recent results in the QRAM model that improve the sparsity dependance for quantum linear system solvers to \mu(A) = \min (||A||_F, ||A||_1) where ||A||_1 is the maximum l-1 norm of the rows and columns of A and ||A||_F is the Frobenius norm. These results achieve a worst case quadratic speedup over the HHL algorithm and its improvements and exponential speedups for some cases. I will also present some applications of the improved linear system solvers to quantum machine learning.