  We analyze the coupling of qubits mediated by a tunable and fast element
beyond the adiabatic approximation. The nonadiabatic corrections are important
and even dominant in parts of the relevant parameter range. As an example, we
consider the tunable capacitive coupling between two charge qubits mediated by
a gated Josephson junction, as suggested by Averin and Bruder. The
nonadiabatic, inductive contribution persists when the capacitive coupling is
tuned to zero. On the other hand, the total coupling can be turned off (in the
rotating wave approximation) if the qubits are operated at symmetry points.
