Experimentally feasible scheme for a high-fidelity controlled-phase gate with general cat-state qubits

Abstract

We propose an efficient scheme for implementing the universal controlled-phase gate with logical qubits encoded in the superpositions of $2d$ circularly distributed coherent states ($d$ is a positive integer), which have the advantage of protecting quantum information against the $(d\ensuremath{-}1)$-photon loss errors. We first demonstrate explicitly how to engineer dispersive interaction between the microwave cavity modes and multilevel transmon ancilla in circuit quantum electro-dynamical (QED) system. With the cat-state qubits, we realize the two-qubit controlled phase gate, and its operation time scales as $1/d$. This means that it will be less susceptible to environmental disturbances if we employ larger $d$ to encode information. Finally, we employ the experimentally reachable parameters in circuit QED system to numerically study the influence of the photon loss, the qubit relaxation, and the Kerr nonlinearity. The average fidelity for a controlled-phase gate has reached 0.9955 for $d=8$ when the system imperfections are considered. The results demonstrate the great potential of our scheme for quantum computation in circuit QED system.