The paper discusses the application of Carleman linearization to quantum simulation of classical fluids, focusing on three formulations: Lattice Boltzmann (CLB), Navier-Stokes (CNS), and Grad (CG). CLB shows excellent convergence but suffers from nonlocality, leading to an exponential depth in the corresponding quantum circuit. CNS reduces the number of Carleman variables, potentially allowing for a viable depth if locality can be preserved and convergence achieved with moderate iterates at large Reynolds numbers. CG is proposed as a combination of the best features of CLB and CNS, offering a potentially optimal trade-off. The authors explore the advantages and limitations of each method, highlighting the need for further research to assess their potential for quantum simulation of classical fluids.The paper discusses the application of Carleman linearization to quantum simulation of classical fluids, focusing on three formulations: Lattice Boltzmann (CLB), Navier-Stokes (CNS), and Grad (CG). CLB shows excellent convergence but suffers from nonlocality, leading to an exponential depth in the corresponding quantum circuit. CNS reduces the number of Carleman variables, potentially allowing for a viable depth if locality can be preserved and convergence achieved with moderate iterates at large Reynolds numbers. CG is proposed as a combination of the best features of CLB and CNS, offering a potentially optimal trade-off. The authors explore the advantages and limitations of each method, highlighting the need for further research to assess their potential for quantum simulation of classical fluids.