Spintronic single-qubit gate based on a Π-shaped lateral quantum dot with spin-orbit interaction

In a quantum nanometric lateral quantum dot (QD) with a Pi geometry the spin properties of a single electron injected in the Coulomb blockade regime are modified by the spin-orbit interaction, resulting in a transformation of the qubit state carried by the spin. The Pi-shaped QD acts as a one-qubit spintronic quantum gate whose properties can be varied by tuning the Rashba parameter of the spin-orbit interaction, by changing the relative position of the junctions, as well as by modifying the length of the transverse legs. We discuss how a large class of transformations can be attained with already one Pi nanojunction or a few Pi nanojunctions in series.