Quantum phase gate on a single superconducting Λ-type three-level and two superconducting resonators

Quantum phase gate is a necessary quantum component for quantum coding and quantum computing. Compared with the traditional gate circuit, quantum phase gate has the characteristics of unitarity and reversibility. Therefore, we construct a model of mutual coupling between a single Λ -type three-level atom and two superconducting resonators, which is connected by a capacitor. By separately controlling the disconnection time and connection time of the two superconducting resonators in the model as well as by controlling the magnetic flux of the superconducting quantum interference device (SQUID) to make a certain transition energy level of the Λ -type three-level atom equal the relevant resonance energy level, the interaction between the two levels can be achieved and the system can be manipulated. Afterwards, we propose four control schemes for implementing the controlled-Z gate through a three-step operation, and two operation schemes for implementing swap gate through a four-step operation. At the same time, the numerical simulations of fidelity are implemented for the first operation scheme for controlling the Z-gate. The results of fidelity discussion show that the fidelity of this scheme is 96.67% through the running time of 20.83 ns, thus it proves that this scheme is theoretically feasible. The increase in the three attenuation parameters, i.e., attenuation rate, relaxation rate, and phase shift ratio, will reduce the fidelity of the system, while the increase in coupling strength will cut down the time of system operation, thus reducing the influence of attenuation parameters and improving the system fidelity.In this paper we present a quantum phase gate scheme in which two superconducting resonators and a Λ -type three-level atom are coupled with two capacitors. Since the experimental setup is simplified, it is important to reduce the coherence between devices. In addition, the solution has no restriction on the strength of the classic pulse principally, through which the system operates faster and the fidelity of the phase gate is improved effectively.