Learning Coulomb Diamonds in Large Quantum Dot Arrays

Abstract

We introduce an algorithm that is able to find the facets of Coulomb diamonds in quantum dot arrays. We simulate these arrays using the constant-interaction model, and rely only on onedimensional raster scans (rays) to learn a model of the device using regularized maximum likelihood estimation. This allows us to determine, for a given charge state of the device, which transitions exist and what the compensated gate voltages for these are. For smaller devices the simulator can also be used to compute the exact boundaries of the Coulomb diamonds, which we use to assess that our algorithm correctly finds the vast majority of transitions with high precision.

Bayesian autotuning of Hubbard model quantum simulators

“…Deep neural networks [39][40][41][42][43][44][45][46], image recognition [38,40,42,[47][48][49][50] and supervised classification [40,46,51] have been demonstrated to aid charge state characterization [41,42,48,49,51], coupling parameter tuning [37] and gate voltage optimization [36,41,43,46,49,52] in a single QD [43,49,51], double QDs [36-38, 42-44, 51], triple QDs and arrays of QDs [36,37,41,45,48]. Unsupervised statistical methods [52,53] and deterministic algorithms [36,[49][50][51] have also been used for double-QD tuning. ML also proven useful for compensating for cross-capacitance in devices [45], calibration of virtual gates in place of real ones [45,…”

“…Although scarcity of experimental data has been addressed in Refs [43,44] with synthetic data, many ML solutions for QD simulators suffer from crude theoretical assumptions. This includes the Thomas-Fermi approximation for electron density [44,54], the use of exponential fits to tunneling couplings [48] or constant interaction model with weak coupling and absent barrier gates [50], which limits their applicability to a wider range of designs and materials. Another limitation of the optimization techniques used in Refs [38,45] is the need for obtaining the gradients of gate voltages in the parameter search, which may be prone to vanishing gradient problem [55].…”