The lattice Boltzmann method with Quantum Inspired Algorithm

This study applies the tensor network method to the lattice Boltzmann method. Tensor network methods were developed in the field of quantum computation and have also attracted attention in the field of computational fluid dynamics in recent years. Previous studies [1,2] proposed tensor network-based finite difference methods to efficiently compress fluid parameter data while retaining important information. A reduction in computation time can be expected by performing time evolution calculations with the compressed fluid parameters. In those finite difference-based approaches, it is necessary to compress the data for each fluid variable, such as velocity and pressure. In contrast, the lattice Boltzmann method performs flow computations using only distribution functions. Therefore, all the parameters required for flow computation can be compressed together, which is expected to result in more efficient data storage and less computational cost. Also, although it is well known that the lattice Boltzmann method requires more parameters for flow computations than finite difference methods, the tensor network may address this well-known. To assess the effectiveness of the proposed approach, numerical experiments using the tensor network-based lattice Boltzmann method are conducted, evaluating both computation time and accuracy.

1. Gourianov et al., Nature Computational Science, 2(1) (2022) 30-37.

2. Kiffner and Jaksch, Physical Review Fluids, 8(12) (2023) 124101.