Harnessing the GaAs quantum dot nuclear spin bath for quantum control

We theoretically demonstrate that nuclear spins can be harnessed to coherently control two-electron spin states in a double quantum dot. Hyperfine interactions lead to an avoided crossing between the spin singlet state and the ms = +1 triplet state, T_+ . We show that a coherent superposition of singlet and triplet states can be achieved using finite-time Landau-Zener-St\"uckelberg interferometry. In this system the coherent rotation rate is set by the Zeeman energy, resulting in ~1 nanosecond single spin rotations. We analyze the coherence of this spin qubit by considering the coupling to the nuclear spin bath and show that T_2^* ~ 16 ns, in good agreement with experimental data. Our analysis further demonstrates that efficient single qubit and two qubit control can be achieved using Landau-Zener-St\"uckelberg interferometry.