Investigation of bi-particle states in gate-array-controlled quantum-dot systems aided by machine learning techniques

TL;DR

This paper explores using machine learning to efficiently predict many-electron states in quantum dot systems, reducing computational effort while accurately identifying spectral properties and state transitions.

Contribution

It introduces machine learning models to predict eigenvalues and eigenfunctions in quantum dot systems, offering a faster alternative to traditional diagonalization methods.

Findings

ML models can accurately predict many-electron eigenvalues

Linear classifier detects singlet-triplet transitions effectively

ML approaches reduce computational costs significantly

Abstract

Quantum computing architectures require an accurate and efficient description in terms of many-electron states. Recent implementations include quantum dot arrays, where the ground state of a multi q-bit system can be altered by voltages applied to the top gates. An extensive investigation concerning the spectra of the many-electron systems under multiple operation conditions set by external voltages typically requires a relatively large number of Hamiltonian diagonalizations, where the Coulomb interaction is considered in an exact manner. Instead of making exhaustive calculations using high throughput computing, we approach this problem by augmenting numerical diagonalizations with machine learning techniques designed to predict the many-electron eigenvalues and eigenfunctions. To this end, we employ and compare the results from linear regression methods such as multivariate least squares (MLS) as well as non-linear techniques based on kernel ridge regression (KRR), Gaussian process regression (GPR) and artificial neural networks (ANNs). The input feature vectors are assembled from readily available information comprised from a binary representation of the potential and the strength of the Coulomb interaction. Furthermore, employing a linear classifier, we establish a rule for detecting a singlet-triplet transition which may arise for certain potential configurations.