  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.
