Before revision:  For (not-necessarily-strongly-) convex and L-smooth potentials, exponential convergence in \chi^2 divergence  is proved, with a rate analogous to  state-of-the-art results of underdamped Langevin dynamics, plus an additional acceleration.
After revision:  For (not-necessarily-strongly-) convex and L-smooth potentials, exponential convergence in \chi^2 divergence /2-Wasserstein distance is proved, with a rate analogous to state-of-the-art results of underdamped Langevin dynamics, plus an additional acceleration.