  We analyse the implementation of a fast nonadiabatic CZ gate between two
transmon qubits with tuneable coupling. The gate control method is based on a
theory of dynamical invariants which leads to reduced leakage and robustness
against decoherence. The gate is based on a description of the resonance
between the $|11\rangle$ and $|20\rangle$ using an effective Hamiltonian with
the 6 lowest energy states. A modification of the invariants method allows us
to take into account the higher-order perturbative corrections of this
effective model. This enables a gate fidelity several orders of magnitude
higher than other quasiadiabatic protocols, with gate times that approach the
theoretical limit.
