Construction of two-qubit logical gates by transmon qubits in a three-dimensional cavity

We report the implementation of qubit-qubit coupling in a three-dimensional (3D) cavity, using the exchange of virtual photons, to realize logical operations. We measure single photon and multi-photon transitions in this qubit-qubit coupling system and obtain its energy avoided-crossing spectrum. With ac-Stark effect, fast control of the qubits is achieved to tune the effective coupling on and off and the state-swap gate √SWAP is successfully constructed. Moreover, using two-photon transition between the ground state and doubly excited states, a kind of two-photon Rabi-like oscillation is observed. A quarter period of this oscillation corresponds to the logical gate √bSWAPP, which is used for generating Bell states. √bSWAPP and √iSWAP are the foundations of future preparation of two-qubit Bell states and realization of CNOT gate.