Solving frustrated quantum many-particle models with convolutional neural networks

Abstract

Recently, there has been significant progress in solving quantum many-particle problem via machine learning based on the restricted Boltzmann machine. However, it is still highly challenging to solve frustrated models via machine learning, which has not been demonstrated so far. In this work, we design a brand new convolutional neural network (CNN) to solve such quantum many-particle problems. We demonstrate, for the first time, of solving the highly frustrated spin-1/2 J${}_1$-J${}_2$ antiferromagnetic Heisenberg model on square lattices via CNN. The energy per site achieved by the CNN is even better than previous string-bond-state calculations. Our work therefore opens up a new routine to solve challenging frustrated quantum many-particle problems using machine learning.

References in corpus (33)

• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Machine learning phases of matter
• Discovering Phase Transitions with Unsupervised Learning
• Twisted Light Transmission over 143 kilometers
• Quantum Entanglement in Neural Network States
• Machine learning quantum phases of matter beyond the fermion sign problem
• Efficient Representation of Quantum Many-body States with Deep Neural Networks
• Active learning machine learns to create new quantum experiments
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
• Machine Learning Topological Invariants with Neural Networks
• Machine Learning Phases of Strongly Correlated Fermions
• Matching matched filtering with deep networks in gravitational-wave astronomy
• Equivalence of restricted Boltzmann machines and tensor network states
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Direct evidence for a gapless $Z_2$ spin liquid by frustrating Néel antiferromagnetism
• Deep learning and the Schrödinger equation
• Detection of phase transition via convolutional neural network
• Unsupervised Learning of Frustrated Classical Spin Models I: Principle Component Analysis
• Constructing gapless spin liquid state for the spin-1/2 J1-J2 Heisenberg model on a square lattice
• Solving the Bose-Hubbard model with machine learning
• Deep Learning the Quantum Phase Transitions in Random Two-Dimensional Electron Systems
• Tensor Networks in a Nutshell
• Application of machine learning algorithms to the study of noise artifacts in gravitational-wave data
• On the Phase Structure of the 3D Edwards Anderson Spin Glass
• A tensor product state approach to spin-1/2 square $J_1$-$J_2$ antiferromagnetic Heisenberg model: evidence for deconfined quantum criticality
• Ground-State Properties of Quantum Many-Body Systems: Entangled-Plaquette States and Variational Monte Carlo
• Deep Learning the Quantum Phase Transitions in Random Electron Systems: Applications to Three Dimensions
• First-principles modeling of multferroic RMn${}_2$O${}_5$
• Simulating two- and three-dimensional frustrated quantum systems with string-bond states
• Deep neural networks for direct, featureless learning through observation: the case of 2d spin models
• Efficient numerical method to calculate three-tangle of mixed states
• Marshall-Peierls sign rule for excited states of the frustrated J1-J2 Heisenberg antiferromagnet
• Replica exchange molecular dynamics optimization of tensor network states for quantum many-body systems

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• Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
• Restricted Boltzmann Machines for Quantum States with Nonabelian or Anyonic Symmetries
• Quantum Neural Network States: A Brief Review of Methods and Applications
• Transformer variational wave functions for frustrated quantum spin systems
• Machine Learning for Condensed Matter Physics
• Neural network wave functions and the sign problem
• Empowering deep neural quantum states through efficient optimization
• Helping restricted Boltzmann machines with quantum-state representation by restoring symmetry
• Transformer Quantum State: A Multi-Purpose Model for Quantum Many-Body Problems
• A simple linear algebra identity to optimize Large-Scale Neural Network Quantum States
• Extensive deep neural networks for transferring small scale learning to large scale systems
• Optimizing Design Choices for Neural Quantum States
• Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ansätze
• Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions
• Investigating ultrafast quantum magnetism with machine learning
• Hybrid convolutional neural network and PEPS wave functions for quantum many-particle states
• Deep Learning-Enhanced Variational Monte Carlo Method for Quantum Many-Body Physics
• Neural network setups for a precise detection of the many-body localization transition: finite-size scaling and limitations
• Purifying Deep Boltzmann Machines for Thermal Quantum States
• Role of stochastic noise and generalization error in the time propagation of neural-network quantum states
• Combined unitary and symmetric group approach applied to low-dimensional spin systems
• Transformer Wave Function for two dimensional frustrated magnets: emergence of a Spin-Liquid Phase in the Shastry-Sutherland Model
• Neural-network quantum states at finite temperature
• Machine Learning Quantum States -- Extensions to Fermion-Boson Coupled Systems and Excited-State Calculations
• Approximating power of machine-learning ansatz for quantum many-body states
• Correlation-Enhanced Neural Networks as Interpretable Variational Quantum States
• Automatic Differentiable Monte Carlo: Theory and Application
• Neural Network Evolution Strategy for Solving Quantum Sign Structures
• Simulating disordered quantum systems via dense and sparse restricted Boltzmann machines
• Fault-tolerant quantum algorithms for quantum molecular systems: A survey
• Gaussian Process States: A data-driven representation of quantum many-body physics
• Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems
• $2^{1296}$ Exponentially Complex Quantum Many-Body Simulation via Scalable Deep Learning Method
• Ground state search by local and sequential updates of neural network quantum states
• Neural Projected Quantum Dynamics: a systematic study
• Variational optimization of the amplitude of neural-network quantum many-body ground states
• Spin-1/2 kagome Heisenberg antiferromagnet: Machine learning discovery of the spinon pair density wave ground state
• The quantum Gaussian process state: A kernel-inspired state with quantum support data
• A Bayesian Inference Framework for Compression and Prediction of Quantum States
• Scalable variational Monte Carlo with graph neural ansatz
• Scalable Imaginary Time Evolution with Neural Network Quantum States
• Phase diagram reconstruction of the Bose-Hubbard model with a Restricted Boltzmann Machine wavefunction
• Unsupervised Machine Learning of Quenched Gauge Symmetries: A Proof-of-Concept Demonstration
• Neural network enhanced hybrid quantum many-body dynamical distributions
• Investigating Network Parameters in Neural-Network Quantum States
• Boltzmann machines and quantum many-body problems
• Non-stabilizerness of Neural Quantum States
• Time-dependent Neural Galerkin Method for Quantum Dynamics
• Quantum many-body solver using artificial neural networks and its applications to strongly correlated electron systems
• Exploring explicit coarse-grained structure in artificial neural networks
• Machine Learning Wavefunction
• Human-machine collaboration: ordering mechanism of rank-2 spin liquid on breathing pyrochlore lattice
• Neural-network quantum state study of the long-range antiferromagnetic Ising chain
• Solving Fermi-Hubbard-type Models by Tensor Representations of Backflow Corrections
• Supervised learning of an interacting 2D hard-core boson model of a weak topological insulator using correlation functions
• Improving neural network performance for solving quantum sign structure
• Accuracy of Restricted Boltzmann Machines for the one-dimensional $J_1-J_2$ Heisenberg model
• A hybrid method integrating Green's function Monte Carlo and projected entangled pair states
• Group Convolutional Neural Network for the Low-Energy Spectrum in the Quantum Dimer Model
• The toric code under antiferromagnetic isotropic Heisenberg interactions
• Learning a compass spin model with neural network quantum states
• Bridging the Gap between Deep Learning and Frustrated Quantum Spin System for Extreme-scale Simulations on New Generation of Sunway Supercomputer