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We present a detailed study of the nuclear quantum effects in H/D sticking to graphene, comparing classical, quantum and mixed quantum/classical simulations to results of scattering experiments. Agreement with experimentally derived sticking probabilities is improved when nuclear quantum effects are included using ring polymer molecular dynamics. Specifically, the quantum motion of the carbon atoms enhances sticking, showing that an accurate description of graphene phonons is important to capturing the adsorption dynamics. We also find an inverse H/D isotope effect arising from Newtonian mechanics.