Decoherence mechanisms in Andreev spin qubits

We theoretically study the dephasing of an Andreev spin qubit interacting with nuclear spins. Using a tight-binding model, we calculate the Andreev states formed in a Josephson junction mediated by a semiconductor with large strong spin-orbit interaction. Because of both the spin-orbit interaction and the superconducting boundary, the local spin of these states varies as a function of the phase difference between the superconducting leads. Consequently, coupling to fluctuations of the magnetic environment is renormalized which informs the rate of dephasing. We qualitative predict the dependence of dephasing on the nature of the environment and phase difference between the junction.