Autoencoder-aided analysis of low-dimensional Hilbert spaces

Abstract

Keywords: feedforward autoencoder, low-dimensional Hilbert spaces, numerical ground-state estimation We study the applicability of feedforward autoencoders in determining the ground state of a quantum system from a noisy signal provided in a form of random superpositions sampled from a low-dimensional subspace of the system’s Hilbert space. The proposed scheme relies on a minimum set of assumptions: the presence of a finite number of orthogonal states in the samples and a weak statistical dominance of the targeted ground state. The provided data is compressed into a two-dimensional feature space and subsequently analyzed to determine the optimal approximation to the true ground state. The scheme is applicable to single- and many-particle quantum systems as well as in the presence of magnetic frustration.