Kinetic samplers for neural quantum states

Abstract

Neural quantum states (NQS) are a novel class of variational many-body wave functions that are very flexible in approximating diverse quantum states. Optimization of an NQS ansatz requires sampling from the corresponding probability distribution defined by squared wave function amplitude. For this purpose we propose to use kinetic sampling protocols and demonstrate that in many important cases such methods lead to much smaller autocorrelation times than Metropolis-Hastings sampling algorithm while still allowing to easily implement lattice symmetries (unlike autoregressive models). We also use Uniform Manifold Approximation and Projection algorithm to construct two-dimensional isometric embedding of Markov chains and show that kinetic sampling helps attain a more homogeneous and ergodic coverage of the Hilbert space basis.

arXiv commentv2: 8 pages, 11 figures, UMAP analysis of typical NQS added, revtex; comments are welcome!

References in corpus (28)

• UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Spin-lattice coupling in frustrated antiferromagnets
• Computational Studies of Quantum Spin Systems
• Quantum Entanglement in Neural Network States
• Generalized Lanczos Algorithm for Variational Quantum Monte Carlo
• Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• 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
• Quantum Entanglement in Deep Learning Architectures
• 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
• 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
• Deep AutoRegressive Networks
• mVMC - Open-source software for many-variable variational Monte Carlo method
• Neural Gutzwiller-projected variational wave functions
• Neural network wave functions and the sign problem
• Helping restricted Boltzmann machines with quantum-state representation by restoring symmetry
• Sublattice Coding Algorithm and Distributed Memory Parallelization for Large-Scale Exact Diagonalizations of Quantum Many-Body Systems
• Hybrid convolutional neural network and PEPS wave functions for quantum many-particle states
• U(1) symmetric recurrent neural networks for quantum state reconstruction
• Iterative Retraining of Quantum Spin Models Using Recurrent Neural Networks
• lattice-symmetries: A package for working with quantum many-body bases
• Accelerated Sampling on Discrete Spaces with Non-Reversible Markov Processes
• A Bayesian Inference Framework for Compression and Prediction of Quantum States

Cited by in corpus (1)

• lattice-symmetries: A package for working with quantum many-body bases