Arbitrary and Fast Quantum Gate with Semiconductor Double-Dot Molecules on a Chip

We propose a scheme to achieve a kind of nontrivial two-qubit operation using controllable electrons in double-dot molecules coupled to a transmission line resonator. The implemented operation is geometrical in nature and insensitive to the state of the transmission line resonator. In particular, we are able to avoid conventional dispersive coupling so that a high speed gate operation can be achieved, which is important in view of decoherence. Meanwhile, we are able to further generalize the operation to an arbitrary phase case by dynamic decoupling with two sequences.