Effects of spin-orbit interaction on quantum states in semiconducting dots and wires

We study effects of spin-orbit interaction on quantum states in multiple low-dimensional systems. In the first part we investigate coupling of hybrid qubit with other broadly used types of qubit like singlet-triplet or single spin qubit in quantum dots. In the second part we investigate effects of strong in-plane magnetic field on g-factor renormalization in lateral quantum dots in GaAs, exploiting the symmetry of the underlying lattice. In the third part we analyze the topological phase transition in Majorana nanowires and we show that edge spin along the direction of the external magnetic field can be used as a probe of this elusive transition.