Fast holonomic quantum computation on superconducting circuits with optimal control

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.