High-fidelity simulation of complex transport phenomena is important for modern fluid dynamics research. However, on large-scale applications, computational cost is often prohibitive. Specifically, the massive memory required for Direct Numerical Simulation (DNS) limits what can be solved on classical architectures. Quantum computing presents a theoretical avenue to overcome these hardware constraints, and the Lattice Boltzmann Method (LBM) serves as a primary candidate for implementation [1,2,3]. Yet, the collision operator remains a significant barrier for quantum implementation, as its inherent nonlinearity and non-unitary character hinder direct mapping onto gate-based quantum circuits. To address this limitation, we introduce a hybrid approach utilising a quantum machine learning surrogate model to approximate the nonlinear collision dynamics of the LBM. It effectively offloads the non-unitary operations that challenge pure quantum solvers. The surrogate’s expressivity is grounded in interpreting parameterised quantum circuits with data re-uploading as truncated Fourier series expansions of nonlinear functions. This enables the model to recover the complete Bhatnagar-Gross-Krook (BGK) collision dynamics, including effective relaxation behaviour. We rigorously evaluate the surrogate’s performance through direct comparison with the classical BGK operator on standard benchmarks, including the Taylor-Green vortex to assess energy dissipation and the lid-driven cavity flow for boundary interactions. Our results demonstrate that the hybrid model achieves high accuracy and strong generalisation while closely replicating classical solutions. These findings suggest that hybrid quantum-classical strategies offer a practical path toward realising the potential of quantum computing in fluid engineering. REFERENCES [1] B. N. Todorova, R. Steijl, Quantum algorithm for the collisionless boltzmann equation, Journal of Computational Physics 409 (2020) 109347. [2] L. Budinski, Quantum algorithm for the advection–diffusion equation simulated with the lattice boltzmann method, Quantum Information Processing 20 (2) (2021). [3] D. Wawrzyniak, J. Winter, S. Schmidt, T. Indinger, C. F. Janßen, U. Schramm, N. A. Adams, Linearized quantum lattice-boltzmann method for the advection-diffusion equation using dynamic circuits, Computer Physics Communications 317 (2025) 109856.