  We theoretically study the dephasing of an Andreev spin qubit (ASQ) due to
electric and magnetic noise. Using a tight-binding model, we calculate the
Andreev states formed in a Josephson junction where the link is a semiconductor
with strong spin-orbit interaction. As a result of both the spin-orbit
interaction and induced superconductivity, the local charge and spin of these
states varies as a function of externally controllable parameters: the phase
difference between the superconducting leads, an applied magnetic field, and
filling of the underlying semiconductor. Concomitantly, coupling to
fluctuations of the electric or magnetic environment will vary, which informs
the rate of dephasing. We qualitatively predict the dependence of dephasing on
the nature of the environment, magnetic field, phase difference between the
junction, and filling of the semiconductor. Comparing the simulated electric-
and magnetic-noise-induced dephasing rate to experiment suggests that the
dominant source of noise is magnetic. Moreover, by appropriately tuning these
external parameters, we find sweet-spots at which we predict an enhancement in
ASQ coherence times.
