Open AccessAutoencoder-aided analysis of low-dimensional Hilbert spaces
Author(s) -
Giedrius Žlabys,
Mantas Račiūnas,
Egidijus Anisimovas
Publication year - 2022
Publication title -
lithuanian journal of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.269
H-Index - 16
eISSN - 2424-3647
pISSN - 1648-8504
DOI - 10.3952/physics.v61i4.4639
Subject(s) - hilbert space , subspace topology , autoencoder , ground state , feed forward , quantum , mathematics , quantum state , computer science , algorithm , statistical physics , topology (electrical circuits) , physics , mathematical analysis , quantum mechanics , artificial intelligence , deep learning , combinatorics , engineering , control engineering
Keywords: feedforward autoencoder, low-dimensional Hilbert spaces, numerical ground-state estimationWe 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.