Singlet-Doublet Transitions of a Quantum Dot Josephson Junction Detected in a Transmon Circuit

We realize a hybrid superconductor-semiconductor transmon device in which the Josephson effect is controlled by gate-defined quantum dot an InAs/Al nanowire. Microwave spectroscopy of transmon's transition spectrum allows us to probe ground state parity as function gate voltages, external magnetic flux, and field applied parallel The measured phase diagram agreement with that predicted single-impurity Anderson model superconducting leads. Through continuous time monitoring circuit we furthermore resolve quasiparticle dynamics junction across boundaries. Our results can facilitate realization semiconductor-based $0-\pi$ qubits Andreev qubits.