Universal Controlled-phase Gate With Cat-state Qubits In Circuit QED

Cat-state qubits(qubits encoded with cat states)have recently drawn intensive attention due to their enhanced lifetimes with quantum error correction.We here propose a method to implement a universal controlled-phase gate of two catstate qubits via two microwave resonators coupled to a superconducting transmon qutrit.In this article,we first introduce the research background.Second,we introduced the relevant basic knowledge about Quantum mechanics,Quantum informatics and circuit QED including coherent states and Schr¨odinger cat-states,controlled-phase gates,Jaynes-Cummings models,etc.The main work of this paper is the method to implement a universal controlledphase gate of two cat-state qubits via two microwave resonators coupled to a superconducting transmon qutrit.This scheme has the following advantages:(i)?During the gate operation,the qutrit remains in the ground state;thus decoherence from the qutrit is greatly suppressed.(ii)? This proposal requires only two basic operations and neither classical pulse nor measurement is needed;therefore the gate realization is simple.(iii)?The proposal is quite general and can be applied to implement the proposed gate with two microwave resonators or two optical cavities coupled to a single three-level natural or artificial atom.Finaly,numerical simulations show that high-fidelity implementation of this gate is feasible with current circuit QED technology.