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

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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 achievedto 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 isobserved. A quarter period of this oscillation corresponds to the logical gate√bSWAP, which is used for generating Bell states. √bSWAP and√iSWAP are the foundations of future preparation of two-qubit Bell states and realization of CNOT gate.
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