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.

Review paper, 16 pages, 9 figures, 3 tables

References in corpus (13)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
• 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
• Algorithms for finite Projected Entangled Pair States
• Constructing neural stationary states for open quantum many-body systems
• Variational Monte Carlo Method Combined with Quantum-Number Projection and Multi-Variable Optimization
• Solving the Bose-Hubbard model with machine learning
• Machine learning technique to find quantum many-body ground states of bosons on a lattice
• 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
• Optimizing Design Choices for Neural Quantum States

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