  Charge qubits formed in double quantum dots represent quintessential
two-level systems that enjoy both ease of control and efficient readout.
Unfortunately, charge noise can cause rapid decoherence, with typical
single-qubit gate fidelities falling below $90\%$. Here, we develop analytical
methods to study the evolution of strongly driven charge qubits, for general
and $1\!/\!f$ charge-noise spectra. We show that special pulsing techniques can
simultaneously suppress errors due to strong driving and charge noise, yielding
single-qubit gates with fidelities above $99.9\%$. These results demonstrate
that quantum dot charge qubits provide a potential route to high-fidelity
quantum computation.
