Charge and spin control of Andreev states in semiconducting Josephson junctions

Andreev spin qubits are known to be supported in Josephson junctions mediated by quasi-one-dimensional semiconductors with strong spin-orbit interaction. We theoretically study the Andreev state spectrum as a function of applied magnetic field, phase difference, and filling of the underlying semiconductor, all of which can be controlled in situ in experiments. ​Additionally, we show that one can control the effective charge and spin of the Andreev states by changing these experimental knobs. Consequently, we find a dependence of the coherence time as a function of magnetic field, phase difference and filling. We show that this dependence can be used to identify the dominant noise sources in Andreev spin qubits and tune to sweet spots to protect against them.