Andreev spin qubits based on the helical edge states of magnetically doped two-dimensional topological insulators

We show that Andreev spin qubits can be realized in a Josephson junction based on the helical edge states of a two-dimensional topological insulator (quantum spin Hall system) proximized by superconducting films, in the presence of magnetic doping. We demonstrate that the electrical dipole transitions between the Andreev spin states induced by the magnetic doping can be harnessed to optically manipulate the Andreev spin qubit by microwave radiation pulses. We numerically simulate the realization of NOT and Hadamard quantum logic gates, and discuss implementations in realistic setups.