Theory of spin qubits in nanostructures

We review recent advances on the theory of spin qubits in nanostructures. We focus on four selected topics. First, we show how to form spin qubits in the new and promising material graphene. Afterwards, we discuss spin relaxation and decoherence in quantum dots. In particular, we demonstrate how charge fluctations in the surrounding environment cause spin decay via spin--orbit coupling. We then turn to a brief overview of how one can use electron-dipole spin resonance (EDSR) to perform single spin rotations in quantum dots using an oscillating electric field. The final topic we cover is the spin-spin coupling via spin-orbit interaction which is an alternative to the usual spin-spin coupling via the Heisenberg exchange interaction.