  We prove non asymptotic total variation estimates for the kinetic Langevin
algorithm in high dimension when the target measure satisfies a Poincar\'e
inequality and has gradient Lipschitz potential. The main point is that the
estimate improves significantly upon the corresponding bound for the non
kinetic version of the algorithm, due to Dalalyan. In particular the dimension
dependence drops from $O(n)$ to $O(\sqrt n)$.
