Rotation Collision based Quantum Lattice Boltzmann Methods
Abstract
In the existing quantum algorithms for the lattice Boltzmann method, resolving the unitarity problem of the BGK collision operator from first principles remains a fundamental challenge, and a systematically constructed unitary alternative that reproduces the BGK relaxation structure to leading order has not yet been established in the literature. In this work, we propose a novel quantum lattice Boltzmann method (QLBM) based on the rotation collision operator, in which the non-unitary BGK relaxation is replaced by a unitary rotation in the amplitude space of the distribution function, and the corresponding gate-level quantum circuits are also constructed. Specifically, the rotation collision operator is developed for both the D2Q5 model of the convection-diffusion equation and the D2Q9 model of the incompressible Navier--Stokes equations. It is worth noting that, for the D2Q5 model, the equilibrium-state preparation circuit can be precompiled and reused, and the resulting unitary blocks can be sequentially composed once the state-dependent collision parameters are specified. Finally, some numerical experiments are performed to validate the developed QLBM, demonstrating its accuracy and effectiveness.
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BibTeX
@misc{zeng2026rotation,
title = {{Rotation Collision based Quantum Lattice Boltzmann Methods}},
author = {Kangyang Zeng and Changshen Huang and Xi Liu and Xiaodong Niu and Zhenhua Chai},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16721},
eprint = {2609.16721},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16721},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Rotation Collision based Quantum Lattice Boltzmann Methods
AU - Kangyang Zeng
AU - Changshen Huang
AU - Xi Liu
AU - Xiaodong Niu
AU - Zhenhua Chai
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.16721
UR - https://arxiv.org/abs/2609.16721
AB - In the existing quantum algorithms for the lattice Boltzmann method, resolving the unitarity problem of the BGK collision operator from first principles remains a fundamental challenge, and a systematically constructed unitary alternative that reproduces the BGK relaxation structure to leading order has not yet been established in the literature. In this work, we propose a novel quantum lattice Boltzmann method (QLBM) based on the rotation collision operator, in which the non-unitary BGK relaxation is replaced by a unitary rotation in the amplitude space of the distribution function, and the corresponding gate-level quantum circuits are also constructed. Specifically, the rotation collision operator is developed for both the D2Q5 model of the convection-diffusion equation and the D2Q9 model of the incompressible Navier--Stokes equations. It is worth noting that, for the D2Q5 model, the equilibrium-state preparation circuit can be precompiled and reused, and the resulting unitary blocks can be sequentially composed once the state-dependent collision parameters are specified. Finally, some numerical experiments are performed to validate the developed QLBM, demonstrating its accuracy and effectiveness.
ER -