  Quantum optimal control theory is applied to two and three coupled Josephson
charge qubits. It is shown that by using shaped pulses a CNOT gate can be
obtained with a trace fidelity > 0.99999 for the two qubits, and even when
including higher charge states, the leakage is below 1%. Yet, the required time
is only a fifth of the pioneering experiment [T. Yamamoto et al., Nature 425
(2003), 941] for otherwise identical parameters. The controls have palindromic
smooth time courses representable by superpositions of a few harmonics. We
outline schemes to generate these shaped pulses such as simple network
synthesis. The approach is easy to generalise to larger systems as shown by a
fast realisation of TOFFOLI's gate in three linearly coupled charge qubits.
Thus it is to be anticipated that this method will find wide application in
coherent quantum control of systems with finite degrees of freedom whose
dynamics are Lie-algebraically closed.
