  A process tomography based optimization scheme for open quantum systems is
used to determine the performance limits of Josephson charge qubits within
current experimental means. The qubit is modeled microscopically as an open
quantum system taking into account state leakage, as well as
environment-induced dephasing based on experimental noise spectra. Within
time-optimal control theory, we show that the competing requirements for
suppression of state leakage and dephasing can be met by an external control of
the effective qubit-environment interaction, yielding minimal gate fidelity
losses of around $\Delta F \approx 10^{-3}$ under typical experimental
conditions.
