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