  Geometric phases induced in quantum evolutions have built-in noise-resilient
characters, and thus can find applications in many robust quantum manipulation
tasks. Here, we propose a feasible and fast scheme for universal quantum
computation on superconducting circuits with nonadiabatic non-Abelian geometric
phases, using resonant interaction of three-level quantum system. In our
scheme, arbitrary single-qubit quantum gates can be implemented in a
single-loop scenario by shaping both the amplitudes and phases of the two
driving microwave fields resonantly coupled to a transmon device. Moreover,
nontrivial two-qubit gates can also be realized with an auxiliary transmon
simultaneously coupled to the two target transmons in an effective resonant
way. In particular, our proposal can be compatible to various optimal control
techniques, which further enhances the robustness of the quantum operations.
Therefore, our proposal represents a promising way towards fault-tolerant
quantum computation on solid-state quantum circuits.
