Multiplex-controlled phase gate with qubits distributed in a multicavity system

Abstract

We present a way to realize a multiplex-controlled phase gate of $n\ensuremath{-}1$ control qubits simultaneously controlling one target qubit, with $n$ qubits distributed in $n$ different cavities. This multiqubit gate is implemented by using $n$ qutrits ( three-level natural or artificial atoms) placed in $n$ different cavities, which are coupled to an auxiliary qutrit. Here, the two logic states of a qubit are represented by the two lowest levels of a qutrit placed in a cavity. We show that this $n$-qubit controlled phase gate can be realized using only $2n+2$ basic operations, i.e., the number of required basic operations only increases linearly with the number $n$ of qubits. Since each basic operation employs the qutrit-cavity or qutrit-pulse resonant interaction, the gate can be fast implemented when the number of qubits is not large. Numerical simulations show that a three-qubit controlled phase gate, which is executed on three qubits distributed in three different cavities, can be high-fidelity implemented by using a circuit QED system. This proposal is quite general and can be applied to a wide range of physical systems, with atoms, NV centers, quantum dots, or various superconducting qutrits distributed in different cavities. Finally, this method can be applied to implement a multiqubit controlled phase gate with atoms using a cavity. A detailed discussion on implementing a three-qubit controlled phase gate with atoms and one cavity is presented.