In this paper, we introduce a methodology that employs machine learning, specifically convolutional neural networks (CNNs), to discern the disorder landscape in the parameters of the disordered extended Hubbard model underlying the semiconductor quantum dot spin qubit architectures. Our approach, which we demonstrate with numerically simulated devices, takes advantage of currently used experimentally obtainable charge stability diagrams from neighboring quantum dot pairs, enabling the CNN to accurately identify disorder in each parameter of the extended Hubbard model. Remarkably, our CNN can process site-specific disorder in Hubbard parameters, including variations in hopping constants, on-site potentials (gate voltages), and both intrasite and intersite Coulomb terms. This advancement facilitates the prediction of spatially dependent disorder across all parameters simultaneously with high accuracy (
R2>0.994) and fewer parameter constraints, marking a significant improvement over previous methods that were focused only on analyzing on-site potentials at low coupling. Furthermore, our approach allows for the tuning of five or more quantum dots at a time, effectively addressing the often-overlooked issue of crosstalk. Not only does our method streamline the tuning process, potentially enabling fully automated adjustments, but it also introduces a ``no trust'' verification method to rigorously validate the neural network's predictions. Ultimately, this paper aims to lay the groundwork for generalizing our method to tackle a broad spectrum of physical problems.
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
2×2 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 (
R2≈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.
Spins in gated semiconductor quantum dots (QDs) are a promising platform for Hubbard model simulation inaccessible to computation. Precise control of the tunnel couplings by tuning voltages on metallic gates is vital for a successful QD-based simulator. However, the number of tunable voltages and the complexity of the relationships between gate voltages and the parameters of the resulting Hubbard models quickly increase with the number of quantum dots. As a consequence, it is not known if and how a particular gate geometry yields a target Hubbard model. To solve this problem, we propose a hybrid machine-learning approach using a combination of support vector machines (SVMs) and Bayesian optimization (BO) to identify combinations of voltages that realize a desired Hubbard model. SVM constrains the space of voltages by rejecting voltage combinations producing potentials unsuitable for tight-binding (TB) approximation. The target voltage combinations are then identified by BO in the constrained subdomain. For large QD arrays, we propose a scalable efficient iterative procedure using our SVM-BO approach, which optimises voltage subsets and utilises a two-QD SVM model for large systems. Our results use experimental gate lithography images and accurate integrals calculated with linear combinations of harmonic orbitals to train the machine learning algorithms.