Spintronic single-qubit gate based on a quantum ring with spin-orbit interaction

In a quantum ring connected with two external leads, the spin properties of an incoming electron are modified by the spin-orbit interaction, resulting in a transformation of the qubit state carried by the spin. The ring 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 the size of the ring. We show that a large class of unitary transformations can be attained with already one ring—or a few rings in series—including the important cases of the $Z$, $X$, and Hadamard gates. By choosing appropriate parameters the spin transformations can be made unitary, which corresponds to lossless gates.

Figure 1

The geometry of the device and the relevant wave functions in the different domains.

Figure 2

(a) Efficiency $\mid T_{\pi }\mid$ of the quantum gate with $\gamma =\pi$ as a function of the modulus of the half rotation angle $\theta =-\arctan \omega ∕\Omega$ and $ka$. The maximal value of $\mid \theta \mid$ corresponds to $\omega ∕\Omega =3.5$. (b) Cross section of the surface at $\mid \theta \mid =\pi ∕4$, where the transformation is essentially a Hadamard gate.

Figure 3

(Color online) Lines along which the ring acts as a $\gamma$ phase gate. Points on the curves show where the gates are lossless, i.e., $\mid T_{\gamma }\mid =1$.

Figure 4

Efficiency of a $\pi ∕2$ phase gate. Along the gray curve on the top $(ka-\omega ∕\Omega )$ plane the ring acts as a $\pi ∕2$ gate. The black lines on the same plane show where the efficiency $\mid T_{\pi ∕2}\mid$ equals unity; thus, at the crossing points of the black and gray lines this phase gate is unitary.