  A central task towards building a practical quantum computer is to protect
individual qubits from decoherence while retaining the ability to perform
high-fidelity entangling gates involving arbitrary two qubits. Here we propose
and demonstrate a dephasing-insensitive procedure for storing and processing
quantum information in an all-to-all connected superconducting circuit
involving multiple frequency-tunable qubits, each of which can be controllably
coupled to any other through a central bus resonator. Although it is generally
believed that the extra frequency tunability enhances the control freedom but
induces more dephasing impact for superconducting qubits, our results show that
any individual qubit can be dynamically decoupled from dephasing noise by
applying a weak continuous and resonant driving field whose phase is reversed
in the middle of the pulse. More importantly, we demonstrate a new method for
realizing two-qubit phase gate with inherent dynamical decoupling via the
combination of continuous driving and qubit-qubit swapping coupling. We find
that the weak continuous driving fields not only enable the conditional
dynamics essential for quantum information processing, but also protect both
qubits from dephasing during the gate operation.
