Solitonic Andreev spin qubits from Andreev states in Corbino Josephson junctions

We study a novel type of solitonic Andreev bound state (ABS) in a Corbino-geometry Josephson junction created on a 2DEG. The Josephson junction is subjected to a weak magnetic flux that induces a fluxoid mismatch between the inner disk and outer ring superconductors. The mismatch produces a Josephson vortex (phase soliton) that binds unconventional spinful but chargeless ABSs, analogous to Jackiw-Rebbi solitonic states. The position around the Josephson junction of the trapped ABSs can be controlled externally by a junction phase bias. As the solitonic ABSs are shuttled around the Josephson junction, the 2DEG spin-orbit coupling induces a geometric precession of their spin. We argue that these solitonic ABSs constitute a natural candidate for a novel type of superconducting Andreev spin qubit, dubbed solitonic Andreev spin qubit (SASQ), that combines features of Andreev spin qubits and geometric spin qubits. Holonomic single-qubit SASQ operations are induced through soliton shuttling, with the resulting SU(2) trajectories densely covering the qubit Bloch sphere. Effects of disorder, non-holonomic SASQ dynamics and other aspects of qubit operation are also analyzed.