  Based on a new coupling approach, we prove that the transition step of the
Hamiltonian Monte Carlo algorithm is contractive w.r.t. a carefully designed
Kantorovich (L1 Wasserstein) distance. The lower bound for the contraction rate
is explicit. Global convexity of the potential is not required, and thus
multimodal target distributions are included. Explicit quantitative bounds for
the number of steps required to approximate the stationary distribution up to a
given error are a direct consequence of contractivity. These bounds show that
HMC can overcome diffusive behaviour if the duration of the Hamiltonian
dynamics is adjusted appropriately.
