Robust control of Josephson charge qubits

Typical for qubit realizations are two performance-limiting shortcomings: the physical system is not a perfect two-level system and it couples to an environment. In this work we investigate the limits of performance of the Josephson charge qubit due to the interplay of leakage into unwanted states and dissipative effects due to environmental noise within optimal control theory. For the example of the Hadamard transformation, we show that external control field-gate bias and magnetic flux, which perform the operation for the ideal qubit perfectly, show different robustness regarding leakage into unwanted states and against dissipation. Proper selection of the temporal evolution of gate bias and magnetic flux leads to performance improvements of typically 20% regarding dissipative effects with a predicted optimal fidelity of typically 98%, presuming perfect initial-state preparation and switching times of the order of 500 ps.