Abstract
Leveraging the higher harmonics content of the Josephson potential in a superconducting circuit offers a promising route in the search for new qubits with increased protection against decoherence. In this work, we demonstrate how the flux tunability of a hybrid semiconductor-superconductor Josephson junction based on a single full-shell nanowire enables this possibility. Near one flux quantum, , we find that the qubit system can be tuned from a gatemon regime to a parity-protected regime with qubit eigenstates localized in phase space in the and minima of the Josephson potential (). Estimates of qubit coherence and relaxation times due to different noise sources are presented.