<p>This paper introduces a quantum lattice Boltzmann method for simulating complex flows. The proposed quantum scheme effectively overcomes the mismatch between the nonlinear collision in the standard lattice Boltzmann method (LBM) and the linear quantum computing (QC) through a linearized non-equilibrium collision operator, and is successfully extended to the Navier-Stokes systems by designing a modular circuit for density and velocity calculations. Most importantly, the present approach ensures the unitary of quantum algorithms while keeping the collision relaxation parameter adjustable for simulating flows with different Reynolds numbers. The accuracy and practicality of the proposed method are demonstrated by simulating two typical flows, including lid-driven and natural convection flows in a square cavity at different Reynolds and Rayleigh numbers, respectively. This work offers a practical application of QC-based LBM for complex fluid dynamics problems.</p>