Quantum gates for the singlet-triplet $\mathrm{T}_+$ qubit

We theoretically show that hyperfine interactions can be harnessed for quantum gate operations in GaAs semiconductor quantum dots [1]. In the presence of an external magnetic field $B$, which splits the triplet states, the hyperfine interaction results in an avoided crossing between the spin singlet $\textrm{S}$ and spin triplet $\textrm{T}_{+}$, which form the basis of a new type of spin qubit. Coherent quantum control for this qubit is achieved through Landau-Zener-St\"uckelberg transitions at the S-T$_{+}$ avoided crossing [2]. A set of suitable transitions allows to build any single qubit gates on timescales shorter than the decoherence time $T_2^* \sim 16\mathrm{ns}$ [1]. We also show how to build a conditional two-qubit gate by capacitively coupling two S-T$_{+}$ qubits. \\[4pt] [1] H. Ribeiro, J. R. Petta, and G. Burkard, Phys. Rev. B 82, 115445 (2010). \newline [2] H. Ribeiro and G. Burkard, Phys. Rev. Lett. 102, 216802 (2009).