Boltzmann machines and quantum many-body problems

Abstract

Analyzing quantum many-body problems and elucidating the entangled structure of quantum states is a significant challenge common to a wide range of fields. Recently, a novel approach using machine learning was introduced to address this challenge. The idea is to "embed" nontrivial quantum correlations (quantum entanglement) into artificial neural networks. Through intensive developments, artificial neural network methods are becoming new powerful tools for analyzing quantum many-body problems. Among various artificial neural networks, this topical review focuses on Boltzmann machines and provides an overview of recent developments and applications.

arXiv commentReview paper, 16 pages, 9 figures, 3 tables

References in corpus (68)

• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Quantum Spin Liquid States
• Fermionic quantum computation
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Deep neural network solution of the electronic Schrödinger equation
• Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
• Quantum Natural Gradient
• Quantum Entanglement in Neural Network States
• Generalized Lanczos Algorithm for Variational Quantum Monte Carlo
• Efficient Representation of Quantum Many-body States with Deep Neural Networks
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Machine Learning Topological States
• Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
• Symmetries and many-body excited states with neural-network quantum states
• Fermionic neural-network states for ab-initio electronic structure
• Equivalence of restricted Boltzmann machines and tensor network states
• Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States
• Quantum many-body dynamics in two dimensions with artificial neural networks
• Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems
• Variational neural network ansatz for steady states in open quantum systems
• Solving Many-Electron Schrödinger Equation Using Deep Neural Networks
• Approximating quantum many-body wave-functions using artificial neural networks
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Algorithms for finite Projected Entangled Pair States
• Quantum Entanglement in Deep Learning Architectures
• Direct evidence for a gapless $Z_2$ spin liquid by frustrating Néel antiferromagnetism
• Constructing neural stationary states for open quantum many-body systems
• Critical level crossings and gapless spin liquid in the square-lattice spin-$1/2$ $J_1$-$J_2$ Heisenberg antiferromagnet
• Backflow Transformations via Neural Networks for Quantum Many-Body Wave-Functions
• Constructing exact representations of quantum many-body systems with deep neural networks
• Variational Monte Carlo Method Combined with Quantum-Number Projection and Multi-Variable Optimization
• Neural Quantum States of frustrated magnets: generalization and sign structure
• Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
• Solving the Bose-Hubbard model with machine learning
• Machine learning technique to find quantum many-body ground states of bosons on a lattice
• Solving frustrated quantum many-particle models with convolutional neural networks
• Restricted Boltzmann Machines for Quantum States with Nonabelian or Anyonic Symmetries
• Ground-State Properties of Quantum Many-Body Systems: Entangled-Plaquette States and Variational Monte Carlo
• mVMC - Open-source software for many-variable variational Monte Carlo method
• Fermionic Wave Functions from Neural-Network Constrained Hidden States
• Neural Gutzwiller-projected variational wave functions
• Chiral Topological Phases from Artificial Neural Networks
• Gapless quantum spin liquid and global phase diagram of the spin-1/2 $J_1$-$J_2$ square antiferromagnetic Heisenberg model
• Gapless spin liquid and valence-bond solid in the $J_1-J_2$ Heisenberg model on the square lattice: insights from singlet and triplet excitations
• Quenches near Ising quantum criticality as a challenge for artificial neural networks
• Neural network wave functions and the sign problem
• Discovering Quantum Phase Transitions with Fermionic Neural Networks
• Unifying Neural-network Quantum States and Correlator Product States via Tensor Networks
• Neural network representation of tensor network and chiral states
• Variational Benchmarks for Quantum Many-Body Problems
• Helping restricted Boltzmann machines with quantum-state representation by restoring symmetry
• Efficient Representation of Topologically Ordered States with Restricted Boltzmann Machines
• High-accuracy variational Monte Carlo for frustrated magnets with deep neural networks
• Phases of two-dimensional spinless lattice fermions with first-quantized deep neural-network quantum states
• Optimizing Design Choices for Neural Quantum States
• Solving Quasiparticle Band Spectra of Real Solids using Neural-Network Quantum States
• A machine learning approach to dynamical properties of quantum many-body systems
• Purifying Deep Boltzmann Machines for Thermal Quantum States
• Determinant-free fermionic wave function using feed-forward neural networks
• Latent Heat Calculation of the 3D q=3, 4, and 5 Potts models by Tensor Product Variational Approach
• Neural-network quantum states at finite temperature
• Machine Learning Quantum States -- Extensions to Fermion-Boson Coupled Systems and Excited-State Calculations
• Neural Network Operations and Susuki-Trotter evolution of Neural Network States
• The quantum Gaussian process state: A kernel-inspired state with quantum support data
• Neural-network Quantum States for Spin-1 systems: spin-basis and parameterization effects on compactness of representations

Cited by in corpus (4)

• A simple linear algebra identity to optimize Large-Scale Neural Network Quantum States
• Quantum many-body solver using artificial neural networks and its applications to strongly correlated electron systems
• Predicting sampling advantage of stochastic Ising Machines for Quantum Simulations
• Generalized Lanczos method for systematic optimization of neural-network quantum states