Fine-tuning Neural Network Quantum States

Abstract

Recent progress in the design and optimization of neural-network quantum states (NQSs) has made them an effective method to investigate ground-state properties of quantum many-body systems. In contrast to the standard approach of training a separate NQS from scratch at every point of the phase diagram, we demonstrate that the optimization of a NQS at a highly expressive point of the phase diagram (i.e., close to a phase transition) yields features that can be reused to accurately describe a wide region across the transition. We demonstrate the feasibility of our approach on different systems in one and two dimensions by initially pretraining a NQS at a given point of the phase diagram, followed by fine-tuning only the output layer for all other points. Notably, the computational cost of the fine-tuning step is very low compared to the pretraining stage. We argue that the reduced cost of this paradigm has significant potential to advance the exploration of strongly-correlated systems using NQS, mirroring the success of fine-tuning in machine learning and natural language processing.

8 pages (including Appendix), 7 figures

References in corpus (28)

• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• The ITensor Software Library for Tensor Network Calculations
• Learning phase transitions by confusion
• Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
• Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
• Wave function optimization in the variational Monte Carlo method
• Numerical Evidence for Multiplicative Logarithmic Corrections from Marginal Operators
• Quantum many-body dynamics in two dimensions with artificial neural networks
• Direct evidence for a gapless $Z_2$ spin liquid by frustrating Néel antiferromagnetism
• Backflow Transformations via Neural Networks for Quantum Many-Body Wave-Functions
• NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems
• Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
• Fermionic Wave Functions from Neural-Network Constrained Hidden States
• Transformer variational wave functions for frustrated quantum spin 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
• Empowering deep neural quantum states through efficient optimization
• 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
• Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Models
• Unsupervised learning universal critical behavior via the intrinsic dimension
• Suppression of Dimer Correlations in the Two-Dimensional $J_1$-$J_2$ Heisenberg Model: an Exact Diagonalization Study
• Improved machine learning algorithm for predicting ground state properties
• Variational Monte Carlo with Large Patched Transformers
• Mapping of attention mechanisms to a generalized Potts model
• Quantum spin liquid phase in the Shastry-Sutherland model detected by an improved level spectroscopic method
• Highly resolved spectral functions of two-dimensional systems with neural quantum states
• Neural network approach to quasiparticle dispersions in doped antiferromagnets

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• Transformer Wave Function for two dimensional frustrated magnets: emergence of a Spin-Liquid Phase in the Shastry-Sutherland Model
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• Design principles of deep translationally-symmetric neural quantum states for frustrated magnets
• Many-Body Neural Network Wavefunction for a Non-Hermitian Ising Chain
• The toric code under antiferromagnetic isotropic Heisenberg interactions
• Optimizing Temperature Distributions for Training Neural Quantum States using Parallel Tempering
• Machine Learning Green's Functions of Strongly Correlated Hubbard Models
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