Flux-tunable parity-protected qubit based on a single full-shell nanowire Josephson junction

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, $\Phi\approx \Phi_0=h/2e$, 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 $0$ and $\pi$ minima of the Josephson potential ($\cos 2\varphi_0$). Estimates of qubit coherence and relaxation times due to different noise sources are presented.