Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

Entanglement features of random neural network quantum states

Journal Article · · Physical Review. B
 [1];  [2];  [3];  [4];  [5]
  1. Univ. of Illinois at Urbana-Champaign, IL (United States); OSTI
  2. Stanford Univ., CA (United States). Stanford Inst. of Theoretical Physics (ITP); Stanford Univ., CA (United States)
  3. Stanford Univ., CA (United States). Stanford Inst. of Theoretical Physics (ITP); Univ. of California, Santa Barbara, CA (United States)
  4. Boston Univ., MA (United States)
  5. Stanford Univ., CA (United States). Stanford Inst. of Theoretical Physics (ITP)
+ Show Author Affiliations
Restricted Boltzmann machines (RBMs) are a class of neural networks that have been successfully employed as a variational ansatz for quantum many-body wave functions. Here, we develop an analytic method to study quantum many-body spin states encoded by random RBMs with independent and identically distributed complex Gaussian weights. By mapping the computation of ensemble-averaged quantities to statistical mechanics models, we are able to investigate the parameter space of the RBM ensemble in the thermodynamic limit. We discover qualitatively distinct wave functions by varying RBM parameters, which correspond to distinct phases in the equivalent statistical mechanics model. Notably, there is a regime in which the typical RBM states have near-maximal entanglement entropy in the thermodynamic limit, similar to that of Haar-random states. However, these states generically exhibit nonergodic behavior in the Ising basis, and do not form quantum state designs, making them distinguishable from Haar-random states.
Research Organization:
Univ. of California, Oakland, CA (United States)
Sponsoring Organization:
Gordon and Betty Moore Foundation; National Science Foundation (NSF); US Air Force Office of Scientific Research (AFOSR); USDOE Office of Science (SC), High Energy Physics (HEP)
Grant/Contract Number:
SC0019380
OSTI ID:
1979815
Journal Information:
Physical Review. B, Journal Name: Physical Review. B Journal Issue: 11 Vol. 106; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (47)

Average quantal behavior and thermodynamic isolation journal June 1993
Holographic duality from random tensor networks journal November 2016
Multilayer feedforward networks are universal approximators journal January 1989
Some new results on neural network approximation journal January 1993
Neural network with unbounded activation functions is universal approximator journal September 2017
Universality of deep convolutional neural networks journal March 2020
Efficient representation of quantum many-body states with deep neural networks journal September 2017
Constructing exact representations of quantum many-body systems with deep neural networks journal December 2018
Restricted Boltzmann machines in quantum physics journal June 2019
Distribution of Eigenvalues for some sets of Random Matrices journal April 1967
Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems journal March 2008
Machine learning for quantum matter journal January 2020
An area law for one-dimensional quantum systems journal August 2007
Entanglement of random vectors journal December 2006
Entanglement Negativity at Measurement-Induced Criticality journal July 2021
Area law for the entropy of low-energy states journal November 2009
Two-dimensional frustrated J 1 − J 2 model studied with neural network quantum states journal September 2019
Measurement-driven entanglement transition in hybrid quantum circuits journal October 2019
Theory of the phase transition in random unitary circuits with measurements journal March 2020
Measurement-induced criticality in random quantum circuits journal March 2020
Hybrid convolutional neural network and projected entangled pair states wave functions for quantum many-particle states journal January 2021
Entanglement transitions from restricted Boltzmann machines journal September 2021
Class of ansatz wave functions for one-dimensional spin systems and their relation to the density matrix renormalization group journal January 1997
Localization of interacting fermions at high temperature journal April 2007
Many-body localization and thermalization: Insights from the entanglement spectrum journal May 2016
Equivalence of restricted Boltzmann machines and tensor network states journal February 2018
Phase transitions in restricted Boltzmann machines with generic priors journal October 2017
Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States journal July 2008
Measuring Renyi Entanglement Entropy in Quantum Monte Carlo Simulations journal April 2010
Distribution of the Ratio of Consecutive Level Spacings in Random Matrix Ensembles journal February 2013
Symmetries and Many-Body Excitations with Neural-Network Quantum States journal October 2018
Quantum Entanglement in Deep Learning Architectures journal February 2019
Neural-Network Approach to Dissipative Quantum Many-Body Dynamics journal June 2019
Universal Entanglement of Typical States in Constrained Systems journal February 2020
Multifractality Meets Entanglement: Relation for Nonergodic Extended States journal May 2020
Quantum Many-Body Dynamics in Two Dimensions with Artificial Neural Networks journal September 2020
Variational Monte Carlo Calculations of A ≤ 4 Nuclei with an Artificial Neural-Network Correlator Ansatz journal July 2021
Average entropy of a subsystem journal August 1993
Thermodynamic Limit of Density Matrix Renormalization journal November 1995
Neural-network quantum states at finite temperature journal March 2020
Quantum Entanglement in Neural Network States journal May 2017
Measurement-Induced Phase Transitions in the Dynamics of Entanglement journal July 2019
Anderson transitions journal October 2008
Machine learning and the physical sciences journal December 2019
Solving the quantum many-body problem with artificial neural networks journal February 2017
Machine-Learning Quantum States in the NISQ Era journal March 2020
Machine Learning Technique to Find Quantum Many-Body Ground States of Bosons on a Lattice journal January 2018

Similar Records

Exact representations of many-body interactions with restricted-Boltzmann-machine neural networks
Journal Article · Thu Jan 07 19:00:00 EST 2021 · Physical Review. E · OSTI ID:1849340
Entanglement transitions from restricted Boltzmann machines
Journal Article · Wed Sep 29 20:00:00 EDT 2021 · Physical Review. B · OSTI ID:1824174
Entanglement transitions from holographic random tensor networks
Journal Article · Tue Oct 08 20:00:00 EDT 2019 · Physical Review B · OSTI ID:1569745

Related Subjects

36 MATERIALS SCIENCE
Physics
artificial neural networks
machine learning
many-body techniques
quantum entanglement