  Implementing holonomic quantum computation is a challenging task as it
requires complicated interaction among multilevel systems. Here we propose to
implement nonadiabatic holonomic quantum computation based on dressed-state
qubits in circuit QED. An arbitrary holonomic single-qubit gate can be
conveniently achieved using external microwave fields and tuning their
amplitudes and phases. Meanwhile, nontrivial two-qubit gates can be implemented
in a coupled-cavities scenario assisted by a grounding SQUID with tunable
interaction, where the tuning is achieved by modulating the ac flux threaded
through the SQUID. In addition, our proposal is directly scalable, up to a
two-dimensional lattice configuration. In the present scheme, the dressed
states involve only the lowest two levels of each transmon qubit and the
effective interactions exploited are all of resonant nature. Therefore, we
release the main difficulties for physical implementation of holonomic quantum
computation on superconducting circuits.
