IntroductionIn the past two decades, the rapid development of superconducting qubits has rendered them one of the most promising candidates for realizing large-scale quantum computers1,2,3,4,5,6. The transmon qubit, proposed in 2007, has become the most widely used superconducting qubit due to its simplicity and performance7,8. It consists of a Josephson junction and a shunt capacitor which reduces the sensitivity of the qubit to charge noise but keeps the qubit sufficiently anharmonic for reali...