Using a high-fidelity numerical model to infer the shape of a few-hole Ge quantum dot

TL;DR

This paper develops a high-fidelity numerical model to accurately infer the shape of few-hole Ge quantum dots by analyzing magnetospectroscopy data, accounting for complex physical effects.

Contribution

It introduces a comprehensive modeling approach that includes the split-off band, surrounding layers, and hole interactions to determine quantum dot shape from experimental data.

Findings

Model accurately predicts effective g-factors for quantum dots.

Maximum-likelihood estimation successfully infers quantum dot shape.

Method aids in assessing variability for scalable quantum computing.

Abstract

The magnetic properties of hole quantum dots in Ge are sensitive to their shape due to the interplay between strong spin-orbit coupling and confinement. We show that the split-off band, surrounding SiGe layers, and hole-hole interactions have a strong influence on calculations of the effective $g$ factor of a lithographic quantum dot in a Ge/SiGe heterostructure. Comparing predictions from a model including these effects to raw magnetospectroscopy data, we apply maximum-likelihood estimation to infer the shape of a quantum dot with up to four holes. We expect that methods like this will be useful in assessing qubit-to-qubit variability critical to further scaling quantum computing technologies based on spins in semiconductors.