  The radial basis function (RBF) method is used for the numerical solution of
the Poisson problem in high dimension. The approximate solution can be found by
solving a large system of linear equations. Here we investigate the extent to
which the RBF method can be accelerated using an efficient quantum algorithm
for linear equations. We compare the theoretical performance of our quantum
algorithm with that of a standard classical algorithm, the conjugate gradient
method. We find that the quantum algorithm can achieve a polynomial speedup.
