Empowering deep neural quantum states through efficient optimization

Abstract

Computing the ground state of interacting quantum matter is a long-standing challenge, especially for complex two-dimensional systems. Recent developments have highlighted the potential of neural quantum states to solve the quantum many-body problem by encoding the many-body wavefunction into artificial neural networks. However, this method has faced the critical limitation that existing optimization algorithms are not suitable for training modern large-scale deep network architectures. Here, we introduce a minimum-step stochastic-reconfiguration optimization algorithm, which allows us to train deep neural quantum states with up to $10^6$ parameters. We demonstrate our method for paradigmatic frustrated spin-1/2 models on square and triangular lattices, for which our trained deep networks approach machine precision and yield improved variational energies compared to existing results. Equipped with our optimization algorithm, we find numerical evidence for gapless quantum-spin-liquid phases in the considered models, an open question to date. We present a method that captures the emergent complexity in quantum many-body problems through the expressive power of large-scale artificial neural networks.

References in corpus (53)

• The density-matrix renormalization group in the age of matrix product states
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Stochastic series expansion method with operator-loop update
• Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model
• Quantum Natural Gradient
• Generalized Lanczos Algorithm for Variational Quantum Monte Carlo
• Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model
• Spin liquid nature in the Heisenberg $J_1$-$J_2$ triangular antiferromagnet
• Spin liquid phase of the $S=\frac{1}{2}$ $J_1-J_2$ Heisenberg model on the triangular lattice
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
• Green Function Monte Carlo with Stochastic Reconfiguration
• Deep autoregressive models for the efficient variational simulation of many-body quantum systems
• Symmetries and many-body excited states with neural-network quantum states
• Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States
• Effects of Backflow Correlation in the Three-Dimensional Electron Gas: Quantum Monte Carlo Study
• Competing Spin Liquid States in the Spin-$1/2$ Heisenberg Model On Triangular Lattice
• Direct evidence for a gapless $Z_2$ spin liquid by frustrating Néel antiferromagnetism
• 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
• Dirac Spin Liquid on the Spin-1/2 Triangular Heisenberg Antiferromagnet
• NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems
• Gapless spin-liquid phase in an extended spin 1/2 triangular Heisenberg model
• Neural Quantum States of frustrated magnets: generalization and sign structure
• Constructing gapless spin liquid state for the spin-1/2 J1-J2 Heisenberg model on a square lattice
• Chiral Spin Liquid and Quantum Criticality in Extended $S=1/2$ Heisenberg Models on the Triangular Lattice
• Ab-initio quantum chemistry with neural-network wavefunctions
• Global phase diagram and quantum spin liquids in spin-1/2 triangular antiferromagnet
• Solving frustrated quantum many-particle models with convolutional neural networks
• Fermionic Wave Functions from Neural-Network Constrained Hidden States
• Neural Gutzwiller-projected variational wave functions
• Path-Integral Renormalization Group Method for Numerical Study on Ground States of Strongly Correlated Electronic Systems
• 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
• Neural network wave functions and the sign problem
• Empowering deep neural quantum states through efficient optimization
• Gapless spin liquid ground state of spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices
• Symmetry fractionalization in the topological phase of the spin-$\frac{1}{2}$ $J_1$-$J_2$ triangular Heisenberg model
• Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape
• High-accuracy variational Monte Carlo for frustrated magnets with deep neural networks
• A simple linear algebra identity to optimize Large-Scale Neural Network Quantum States
• Optimizing Design Choices for Neural Quantum States
• Finite temperature electronic simulations beyond the Born-Oppenheimer approximation
• Spectral function of the $J_1-J_2$ Heisenberg model on the triangular lattice
• 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
• Determinant-free fermionic wave function using feed-forward neural networks
• Neural Network Evolution Strategy for Solving Quantum Sign Structures
• lattice-symmetries: A package for working with quantum many-body bases
• Nature of quantum spin liquids of the S=1/2 Heisenberg antiferromagnet on the triangular lattice: A parallel DMRG study
• jVMC: Versatile and performant variational Monte Carlo leveraging automated differentiation and GPU acceleration
• $2^{1296}$ Exponentially Complex Quantum Many-Body Simulation via Scalable Deep Learning Method
• Ground state search by local and sequential updates of neural network quantum states
• Broken-Symmetry Ground States of the Heisenberg model on the Pyrochlore Lattice

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• Comparing Symmetrized Determinant Neural Quantum States for the Hubbard Model
• Basis dependence of Neural Quantum States for the Transverse Field Ising Model
• Generalized Lanczos method for systematic optimization of neural-network quantum states
• Application of Langevin Dynamics to Advance the Quantum Natural Gradient Optimization Algorithm
• High-precision ground state parameters of the two-dimensional spin-1/2 Heisenberg model on the square lattice
• Magnetic correlations in the $SU(3)$ triangular-lattice $t$-$J$ model at finite doping
• Hybrid between biologically and quantum-inspired many-body states