Magic angle for barrier-controlled double quantum dots

TL;DR

This paper reveals that the exchange interaction in barrier-controlled double quantum dot qubits is insensitive to certain impurity directions at a specific 'magic' angle, enabling reduced cross-talk in scalable quantum computing layouts.

Contribution

It identifies the 'magic angle' at approximately 54.7° where impurity effects are minimized, providing a new design principle for scalable quantum dot qubit arrays.

Findings

Exchange interaction is insensitive to impurities at the magic angle.

Aligning double dots at the magic angle reduces qubit cross-talk.

The phenomenon is explained through Coulomb interaction expansion and tunnel coupling dependence.

Abstract

We show that the exchange interaction of a singlet-triplet spin qubit confined in double quantum dots, when being controlled by the barrier method, is insensitive to a charged impurity lying along certain directions away from the center of the double-dot system. These directions differ from the polar axis of the double dots by the magic angle, equaling $\arccos\left(1/\sqrt{3}\right)\approx 54.7^\circ$, a value previously found in atomic physics and nuclear magnetic resonance. This phenomenon can be understood from an expansion of the additional Coulomb interaction created by the impurity, but also relies on the fact that the exchange interaction solely depends on the tunnel coupling in the barrier-control scheme. Our results suggest that for a scaled-up qubit array, when all pairs of double dots rotate their respective polar axes from the same reference line by the magic angle, cross-talks between qubits can be eliminated, allowing clean single-qubit operations. While our model is a rather simplified version of actual experiments, our results suggest that it is possible to minimize unwanted couplings by judiciously designing the layout of the qubits.