Rotation gate for a three-level superconducting quantum interference device qubit with resonant interaction

We show a way to realize an arbitrary rotation gate in a three-level superconducting quantum interference device (SQUID) qubit using resonant interaction. In this approach, the two logical states of the qubit are represented by the two lowest levels of the SQUID and a higher-energy intermediate level is utilized for the gate manipulation. By considering spontaneous decay from the intermediate level during the gate operation, we present a formula for calculating average fidelity over all possible initial states. Finally, based on realistic system parameters, we show that an arbitrary rotation gate can be achieved with a high fidelity in a SQUID