From Lattice Boltzmann Acoustics to Quantum Lattice Boltzmann Methods: A Physics-Guided Roadmap for Quantum Flow Simulations

Journal article, 2026

Quantum computational fluid dynamics (QCFD) is an active but still immature research area, and quantum lattice Boltzmann methods (QLBM) provide a natural mesoscopic route because their collision–streaming structure can be decomposed into algorithmic blocks. This paper reviews QLBM and related hybrid quantum–classical fluid approaches from an engineering computational fluid dynamics (CFD) perspective, emphasizing physical scope, boundary realism, nonlinear collision treatment, measurement cost, hardware assumptions, and comparison with optimized classical baselines. The discussion is connected to computational aeroacoustics (CAA), where practical workflows already separate source generation, acoustic propagation, and design loops, creating possible insertion points for selective quantum or hybrid acceleration. As a concrete classical reference problem, we also develop a three-dimensional, 19-velocity (D3Q19) multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) acoustic benchmark. In this benchmark, harmonic monopole, dipole, and quadrupole sources are imposed through an additive particle source term, and the computed fields are validated against a D3Q19 MRT-specific Chapman–Enskog macroscopic reference derived from the implemented collision model and source moments using axial waveforms and far-field directivity. The same benchmark is then mapped to an illustrative QLBM architecture using Carleman lifting, linear combination of unitaries (LCU) or block encoding, conditional streaming, and acoustic readout. The resulting roadmap argues that near- and mid-term quantum contributions to aeroacoustics are more likely to appear through targeted hybrid kernels and benchmarked mesoscopic subproblems, rather than replacing mature industrial CFD/CAA pipelines.