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arXiv · 2301.06032

Quantum radial basis function method for the Poisson equation

Lingxia Cui·Zongming Wu·Hua Xiang
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Abstract

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.

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Lingxia Cui, Zongming Wu, Hua Xiang. 2023-01-15. Quantum radial basis function method for the Poisson equation. https://arxiv.org/abs/2301.06032

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