Predicting spin-orbit coupling in hole spin qubit arrays with vision-transformer-based neural networks on a generalized Hubbard model

TL;DR

This paper presents a neural network method to accurately predict spin-orbit coupling strength in hole spin qubit arrays from charge stability diagrams, even with unknown system parameters.

Contribution

The study introduces a neural network trained on simulated data to determine SOC strength and other Hubbard model parameters from charge diagrams, enhancing qubit array characterization.

Findings

Neural network predicts SOC strength with R^2 ≈ 0.94.

Method accurately estimates Hubbard model parameters.

Approach enables automated qubit array analysis.

Abstract

We introduce a neural-network-based machine learning method to predict the effective spin-orbit coupling (SOC) strength in hole quantum dot arrays from standard charge stability diagrams. Specifically, we study a $2\times 2$ Ge hole quantum dot array described by a generalized spin-orbit coupled Hubbard model that incorporates random site- and bond-dependent disorder in all system parameters, including onsite potentials, Coulomb interaction strengths, interdot tunneling amplitudes, as well as the direction and angle of the SOC-induced spin rotations accompanying interdot tunneling. We train the neural network on numerically simulated charge stability diagrams from nearest-neighbor pairs of quantum dots for different chemical potentials and out-of-plane magnetic fields, and show that this enables us to predict the SOC-induced spin-flip tunneling amplitudes -- and, thus, the effective SOC strength -- with high fidelity ($R^2\approx 0.94$) even when all other Hubbard model parameters are unknown. Furthermore, our neural network can also predict the other Hubbard model parameters with high fidelity, demonstrating that neural-network-based approaches can be a powerful tool for the automated characterization of hole spin qubit arrays.