Quantum radial basis function method for the Poisson equation

Abstract

The radial basis function (RBF) method is widely used for the numerical solution of the Poisson problem in high dimension, where the approximate solution can be found by solving a large system of linear equations. We demonstrate that the RBF method can be accelerated on a quantum computer by using an efficient quantum algorithm for linear equations. We compare the theoretical performance of our quantum algorithm with that of a standard classical algorithm, and find that the quantum algorithm can achieve a polynomial speedup.