  We revisit the problem of sampling from a target distribution that has a
smooth strongly log-concave density everywhere in $\mathbb R^p$. In this
context, if no additional density information is available, the randomized
midpoint discretization for the kinetic Langevin diffusion is known to be the
most scalable method in high dimensions with large condition numbers. Our main
result is a nonasymptotic and easy to compute upper bound on the Wasserstein-2
error of this method. To provide a more thorough explanation of our method for
establishing the computable upper bound, we conduct an analysis of the midpoint
discretization for the vanilla Langevin process. This analysis helps to clarify
the underlying principles and provides valuable insights that we use to
establish an improved upper bound for the kinetic Langevin process with the
midpoint discretization. Furthermore, by applying these techniques we establish
new guarantees for the kinetic Langevin process with Euler discretization,
which have a better dependence on the condition number than existing upper
bounds.
