  We propose a scheme for controlling the gradiometric flux qubit (GFQ) by
applying an ac bias current in a circuit-QED architecture. The GFQ is
insensitive to the magnetic flux fluctuations, which at the same time makes it
challenging to manipulate the qubit states by an external magnetic field. In
this study, we demonstrate that an ac bias current applied to the
$\alpha$-junction of the GFQ can control the qubit states. Further, the present
scheme is robust against the charge fluctuation as well as the magnetic flux
fluctuations, promising a long coherence time for quantum gate operations. We
introduce a circuit-QED architecture to perform the single and two-qubit
operations with a sufficiently strong coupling strength.
