Quantum lattice Boltzmann method for simulating nonlinear fluid dynamics

Quantum computing holds transformative potential for simulating nonlinear physical systems, such as fluid turbulence. However, mapping nonlinear dynamics to the linear operations required by quantum hardware remains a fundamental challenge. Here we bridge this gap by introducing a novel node-level ensemble description of lattice gas, which enables the simulation of nonlinear fluid dynamics on quantum computers.

This approach combines the advantages of the lattice Boltzmann method with low-dimensional representation (computational cost) and lattice gas cellular automata with linear collision treatment (quantum compatibility). Building on this framework, we propose a quantum lattice Boltzmann method that relies on linear operations with medium dimensionality, offering the potential for exponential speedup. We validated the algorithm through simulations of vortex-pair merging and decaying turbulence on up to 16.8 million computational grid points. The results demonstrate remarkable agreement with direct numerical simulation, effectively capturing the essential nonlinear mechanisms of fluid dynamics. This work potentially advances the development of quantum algorithms for other nonlinear problems across various transport phenomena in engineering.