Solitonic Andreev spin qubits from Andreev states in Corbino Josephson junctions

We study a type of solitonic Andreev bound state (ABS) in a Corbino-geometry Josephson junction created on a two-dimensional electron gas (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 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, nonholonomic SASQ dynamics, and other aspects of qubit operation are also analyzed.