Approximating power of machine-learning ansatz for quantum many-body states

Artem Borin, Dmitry A. Abanin

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


An artificial neural network (ANN) with the restricted Boltzmann machine (RBM) architecture was recently proposed as a versatile variational quantum many-body wave function. In this work we provide physical insights into the performance of this ansatz. We uncover the connection between the structure of the RBM and perturbation series, which explains the excellent precision achieved by the RBM ansatz in certain simple models, demonstrated in G. Carleo and M. Troyer [Science 355, 602 (2017)SCIEAS0036-807510.1126/science.aag2302]. Based on this relation, we improve the numerical algorithm to achieve a better performance of the RBM in cases where local minima complicate the convergence to the global one. Furthermore, we study the performance of a sparse RBM for approximating ground states of random, translationally invariant models in one dimension, as well as random matrix-product states. We find that the error in approximating such states exhibits a broad distribution and shows a positive correlation with the entanglement properties of the targeted state.

Original languageEnglish (US)
Article number195141
JournalPhysical Review B
Issue number19
StatePublished - May 15 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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