  We discuss the Carleman linearization approach to the quantum simulation of
classical fluids based on Grad's generalized hydrodynamics and compare it to
previous investigations based on lattice Boltzmann and Navier-Stokes
formulations. We show that the Carleman-Grad procedure exhibits intermediate
properties between the two. Namely, convergence of the Carleman iteration over
a few tens of timesteps and a potentially viable quantum circuit implementation
using quantum linear algebra solvers. However, both features still need
substantial improvements to yield a viable quantum algorithm for fluid flows.
