The paper discusses three approaches to quantum simulation of classical fluids using the Carleman linearization method: Lattice Boltzmann (CLB), Navier-Stokes (CNS), and Grad (CG). CLB shows excellent convergence but suffers from nonlocality, leading to exponential circuit depth. CNS reduces the number of Carleman variables, potentially enabling viable simulations with moderate iterates. CG combines the best aspects of CLB and CNS. The authors explore the challenges of quantum computing, including decoherence and noise, and how these affect fluid simulations. CLB's nonlocality makes it impractical for large-scale simulations, while CNS offers better locality and fewer variables. CG may provide an optimal balance between the two. The paper highlights the potential of quantum computing for simulating turbulent flows, which are computationally intensive for classical computers. However, practical implementation faces challenges such as the exponential depth of quantum circuits and the need for error correction. The study concludes that further research is needed to determine the feasibility of these approaches for quantum simulation of classical fluids.The paper discusses three approaches to quantum simulation of classical fluids using the Carleman linearization method: Lattice Boltzmann (CLB), Navier-Stokes (CNS), and Grad (CG). CLB shows excellent convergence but suffers from nonlocality, leading to exponential circuit depth. CNS reduces the number of Carleman variables, potentially enabling viable simulations with moderate iterates. CG combines the best aspects of CLB and CNS. The authors explore the challenges of quantum computing, including decoherence and noise, and how these affect fluid simulations. CLB's nonlocality makes it impractical for large-scale simulations, while CNS offers better locality and fewer variables. CG may provide an optimal balance between the two. The paper highlights the potential of quantum computing for simulating turbulent flows, which are computationally intensive for classical computers. However, practical implementation faces challenges such as the exponential depth of quantum circuits and the need for error correction. The study concludes that further research is needed to determine the feasibility of these approaches for quantum simulation of classical fluids.