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Title: Backflow Transformations via Neural Networks for Quantum Many-Body Wave Functions

Journal Article · · Physical Review Letters
 [1];  [1]
  1. Univ. of Illinois at Urbana-Champaign, IL (United States)

Obtaining an accurate ground state wave function is one of the great challenges in the quantum many-body problem. In this Letter, we propose a new class of wave functions, neural network backflow (NNB). Here, the backflow approach, pioneered originally by Feynman and Cohen [Phys. Rev. 102, 1189 (1956)], adds correlation to a mean-field ground state by transforming the single-particle orbitals in a configuration-dependent way. NNB uses a feed-forward neural network to learn the optimal transformation via variational Monte Carlo calculations. NNB directly dresses a mean-field state, can be systematically improved, and directly alters the sign structure of the wave function. It generalizes the standard backflow [L. F. Tocchio et al., Phys. Rev. B 78, 041101(R) (2008)], which we show how to explicitly represent as a NNB. We benchmark the NNB on Hubbard models at intermediate doping, finding that it significantly decreases the relative error, restores the symmetry of both observables and single-particle orbitals, and decreases the double-occupancy density. Finally, we illustrate interesting patterns in the weights and bias of the optimized neural network.

Research Organization:
Univ. of Illinois at Urbana-Champaign, IL (United States)
Sponsoring Organization:
USDOE Office of Science (SC); USDOE
Grant/Contract Number:
SC0008692; FG02-12ER46875
OSTI ID:
1611137
Alternate ID(s):
OSTI ID: 1524471
Journal Information:
Physical Review Letters, Vol. 122, Issue 22; ISSN 0031-9007
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 60 works
Citation information provided by
Web of Science

References (80)

Quantum Entanglement in Neural Network States journal May 2017
Equivalence of restricted Boltzmann machines and tensor network states journal February 2018
Backflow correlations in the Hubbard model: An efficient tool for the study of the metal-insulator transition and the large- U limit journal May 2011
Effects of backflow correlation in the three-dimensional electron gas: Quantum Monte Carlo study journal September 1998
Unifying neural-network quantum states and correlator product states via tensor networks journal February 2018
Static and dynamical properties of doped Hubbard clusters journal May 1992
Solving frustrated quantum many-particle models with convolutional neural networks journal September 2018
Machine Learning Technique to Find Quantum Many-Body Ground States of Bosons on a Lattice journal January 2018
Constructing exact representations of quantum many-body systems with deep neural networks journal December 2018
Criticality, the Area Law, and the Computational Power of Projected Entangled Pair States journal June 2006
Entanglement Renormalization journal November 2007
Symmetries and Many-Body Excitations with Neural-Network Quantum States journal October 2018
Efficient representation of topologically ordered states with restricted Boltzmann machines journal April 2019
Approximation by superpositions of a sigmoidal function journal December 1989
Many-Body Problem with Strong Forces journal June 1955
Ground-state properties of quantum many-body systems: entangled-plaquette states and variational Monte Carlo journal August 2009
Green's Function Monte Carlo Method for Liquid He 3 journal March 1981
Machine learning topological states journal November 2017
Density matrix formulation for quantum renormalization groups journal November 1992
Complete-graph tensor network states: a new fermionic wave function ansatz for molecules journal October 2010
Itinerant ferromagnetic phase of the Hubbard model journal February 2011
Simulation of Quantum Many-Body Systems with Strings of Operators and Monte Carlo Tensor Contractions journal January 2008
The Theory of Complex Spectra journal November 1929
Solving the quantum many-body problem with artificial neural networks journal February 2017
Structure of the Ground State of a Fermion Fluid journal September 1981
Stripe order in the underdoped region of the two-dimensional Hubbard model journal November 2017
Striped Spin Liquid Crystal Ground State Instability of Kagome Antiferromagnets journal November 2013
Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms journal December 2015
Quantum Monte Carlo study of the Ne atom and the Ne+ ion journal June 2006
Generalized transfer matrix states from artificial neural networks journal April 2019
Chiral topological phases from artificial neural networks journal May 2018
Method to Solve Quantum Few-Body Problems with Artificial Neural Networks journal July 2018
Simple Variational Wave Functions for Two-Dimensional Heisenberg Spin-½ Antiferromagnets journal June 1988
Efficient representation of quantum many-body states with deep neural networks journal September 2017
Role of backflow correlations for the nonmagnetic phase of the t – t ′ Hubbard model journal July 2008
Quantum Monte Carlo of nitrogen: Atom, dimer, atomic, and molecular solids journal April 1994
Theory of Superconductivity journal December 1957
Fermion Monte Carlo algorithms and liquid He 3 journal March 1989
Nonlinear Network Description for Many-Body Quantum Systems in Continuous Space journal May 2018
Metal-insulator transition and strong-coupling spin liquid in the t–t ′ Hubbard model journal January 2009
Neural-Network Quantum States, String-Bond States, and Chiral Topological States journal January 2018
Learning hard quantum distributions with variational autoencoders journal June 2018
Restricted Boltzmann machine learning for solving strongly correlated quantum systems journal November 2017
Many-body wavefunctions for normal liquid He 3 journal September 2006
Approximating quantum many-body wave functions using artificial neural networks journal January 2018
Variational ground states of two-dimensional antiferromagnets in the valence bond basis journal September 2007
Energy Spectrum of the Excitations in Liquid Helium journal June 1956
Interaction-induced Fermi-surface renormalization in the t 1 − t 2 Hubbard model close to the Mott-Hubbard transition journal May 2010
Spin-liquid and magnetic phases in the anisotropic triangular lattice: The case of κ − ( ET ) 2 X journal August 2009
Efficient Classical Simulation of Slightly Entangled Quantum Computations journal October 2003
Effects of three-body and backflow correlations in the two-dimensional electron gas journal October 1993
Iterative backflow renormalization procedure for many-body ground-state wave functions of strongly interacting normal Fermi liquids journal March 2015
Neural-network quantum state tomography journal February 2018
Approximation by superpositions of a sigmoidal function journal December 1992
Complete-graph tensor network states: A new fermionic wave function ansatz for molecules text January 2010
Learning hard quantum distributions with variational autoencoders text January 2018
Constructing exact representations of quantum many-body systems with deep neural networks text January 2018
Theory of Superconductivity journal May 1965
The Theory of Complex Spectra journal October 1930
Symmetries and Many-Body Excitations with Neural-Network Quantum States text January 2018
The Theory of Complex Spectra journal April 1932
Inhomogeneous backflow transformations in quantum Monte Carlo calculations text January 2008
Iterative backflow renormalization procedure for many-body ground state wave functions of strongly interacting normal Fermi liquids text January 2015
Machine Learning Topological States text January 2016
Stripe order in the underdoped region of the two-dimensional Hubbard model text January 2017
Quantum Entanglement in Neural Network States text January 2017
Approximating quantum many-body wave-functions using artificial neural networks text January 2017
Machine learning technique to find quantum many-body ground states of bosons on a lattice text January 2017
Unifying Neural-network Quantum States and Correlator Product States via Tensor Networks text January 2017
Neural-Network Quantum States, String-Bond States, and Chiral Topological States text January 2017
Chiral Topological Phases from Artificial Neural Networks text January 2017
Nonlinear Network description for many-body quantum systems in continuous space text January 2017
Method to solve quantum few-body problems with artificial neural networks text January 2018
Solving frustrated quantum many-particle models with convolutional neural networks text January 2018
Generalized Transfer Matrix States from Artificial Neural Networks text January 2018
Efficient Representation of Topologically Ordered States with Restricted Boltzmann Machines text January 2018
Backflow Correlations for the Electron Gas and Metallic Hydrogen text January 2003
Entanglement renormalization text January 2005
Effects of Backflow Correlation in the Three-Dimensional Electron Gas: Quantum Monte Carlo Study text January 1998
Efficient classical simulation of slightly entangled quantum computations text January 2003

Cited By (1)