Deep autoregressive models for the efficient variational simulation of many-body quantum systems

Abstract

Artificial Neural Networks were recently shown to be an efficient representation of highly-entangled many-body quantum states. In practical applications, neural-network states inherit numerical schemes used in Variational Monte Carlo, most notably the use of Markov-Chain Monte-Carlo (MCMC) sampling to estimate quantum expectations. The local stochastic sampling in MCMC caps the potential advantages of neural networks in two ways: (i) Its intrinsic computational cost sets stringent practical limits on the width and depth of the networks, and therefore limits their expressive capacity; (ii) Its difficulty in generating precise and uncorrelated samples can result in estimations of observables that are very far from their true value. Inspired by the state-of-the-art generative models used in machine learning, we propose a specialized Neural Network architecture that supports efficient and exact sampling, completely circumventing the need for Markov Chain sampling. We demonstrate our approach for two-dimensional interacting spin models, showcasing the ability to obtain accurate results on larger system sizes than those currently accessible to neural-network quantum states.

References in corpus (21)

• Adam: A Method for Stochastic Optimization
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Conditional Image Generation with PixelCNN Decoders
• A class of quantum many-body states that can be efficiently simulated
• Many-body quantum state tomography with neural networks
• The ALPS project release 1.3: open source software for strongly correlated systems
• The ALPS project release 2.0: Open source software for strongly correlated systems
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Quantum Entanglement in Neural Network States
• Reconstructing quantum states with generative models
• Symmetries and many-body excited states with neural-network quantum states
• Equivalence of restricted Boltzmann machines and tensor network states
• Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States
• Solving Statistical Mechanics Using Variational Autoregressive Networks
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Quantum Entanglement in Deep Learning Architectures
• Machine learning technique to find quantum many-body ground states of bosons on a lattice
• Chiral Topological Phases from Artificial Neural Networks
• Gradient optimization of finite projected entangled pair states
• Neural-network states for the classical simulation of quantum computing
• Fast Generation for Convolutional Autoregressive Models

Cited by in corpus (137)

• Machine learning and the physical sciences
• Information-theoretic bounds on quantum advantage in machine learning
• Recurrent Neural Network Wave Functions
• Exploring entanglement and optimization within the Hamiltonian Variational Ansatz
• Barren Plateaus in Variational Quantum Computing
• Differentiable Quantum Architecture Search
• NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems
• Machine Learning for Quantum Matter
• Ab-initio quantum chemistry with neural-network wavefunctions
• Asymptotically unbiased estimation of physical observables with neural samplers
• Efficient generative modeling of protein sequences using simple autoregressive models
• Neural tensor contractions and the expressive power of deep neural quantum states
• Transformer variational wave functions for frustrated quantum spin systems
• Neural network wave functions and the sign problem
• Variational Neural Annealing
• Reinforcement Learning for Many-Body Ground-State Preparation Inspired by Counterdiabatic Driving
• Efficient quantum state tomography with convolutional neural networks
• Exploring QCD matter in extreme conditions with Machine Learning
• Empowering deep neural quantum states through efficient optimization
• Autoregressive Transformer Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation
• Variational Benchmarks for Quantum Many-Body Problems
• Experimental quantum homodyne tomography via machine learning
• Efficient Tensor Network ansatz for high-dimensional quantum many-body problems
• Discovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networks
• High-accuracy variational Monte Carlo for frustrated magnets with deep neural networks
• Neural Error Mitigation of Near-Term Quantum Simulations
• Transformer Quantum State: A Multi-Purpose Model for Quantum Many-Body Problems
• Boosting Monte Carlo simulations of spin glasses using autoregressive neural networks
• Transfer learning for scalability of neural-network quantum states
• Accurate Computation of Quantum Excited States with Neural Networks
• Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Models
• Optimizing Design Choices for Neural Quantum States
• Unbiasing time-dependent Variational Monte Carlo by projected quantum evolution
• Riemannian geometry and automatic differentiation for optimization problems of quantum physics and quantum technologies
• Equivariant Flows: sampling configurations for multi-body systems with symmetric energies
• Neural-network quantum states for many-body physics
• Deep Learning-Enhanced Variational Monte Carlo Method for Quantum Many-Body Physics
• U(1) symmetric recurrent neural networks for quantum state reconstruction
• Direct sampling of projected entangled-pair states
• Gauge equivariant neural networks for quantum lattice gauge theories
• Tensor networks for unsupervised machine learning
• From Tensor Network Quantum States to Tensorial Recurrent Neural Networks
• Variational Monte Carlo with Large Patched Transformers
• Scaling of neural-network quantum states for time evolution
• Role of stochastic noise and generalization error in the time propagation of neural-network quantum states
• Dynamics with autoregressive neural quantum states: application to critical quench dynamics
• Expressive power of complex-valued restricted Boltzmann machines for solving non-stoquastic Hamiltonians
• Transformer Wave Function for two dimensional frustrated magnets: emergence of a Spin-Liquid Phase in the Shastry-Sutherland Model
• Generative models for sampling and phase transition indication in spin systems
• Variational autoencoder reconstruction of complex many-body physics
• Machine-learning-assisted Monte Carlo fails at sampling computationally hard problems
• Neural-network quantum states at finite temperature
• Group Convolutional Neural Networks Improve Quantum State Accuracy
• Protocol Discovery for the Quantum Control of Majoranas by Differentiable Programming and Natural Evolution Strategies
• Reconstructing complex states of a 20-qubit quantum simulator
• Population Control Bias and Importance Sampling in Full Configuration Interaction Quantum Monte Carlo
• Automatic Differentiable Monte Carlo: Theory and Application
• Iterative Retraining of Quantum Spin Models Using Recurrent Neural Networks
• A fast and efficient deep learning procedure for tracking droplet motion in dense microfluidic emulsions
• Dynamical large deviations of two-dimensional kinetically constrained models using a neural-network state ansatz
• Calculating Renyi Entropies with Neural Autoregressive Quantum States
• Simulating disordered quantum systems via dense and sparse restricted Boltzmann machines
• Lee-Yang theory of criticality in interacting quantum many-body systems
• Neural Network Evolution Strategy for Solving Quantum Sign Structures
• A Bayesian generative neural network framework for epidemic inference problems
• Phase diagram of the $J$-$J_d$ Heisenberg Model on the Maple-Leaf Lattice: Neural networks and density matrix renormalization group
• Highly resolved spectral functions of two-dimensional systems with neural quantum states
• Neural network approach to quasiparticle dispersions in doped antiferromagnets
• Phase diagram of quantum generalized Potts-Hopfield neural networks
• Variational Neural-Network Ansatz for Continuum Quantum Field Theory
• jVMC: Versatile and performant variational Monte Carlo leveraging automated differentiation and GPU acceleration
• Neural network backflow for ab-initio quantum chemistry
• A learning by confusion approach to characterize phase transitions
• Continuous-mixture Autoregressive Networks for efficient variational calculation of many-body systems
• Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems
• Ground state search by local and sequential updates of neural network quantum states
• Mapping out phase diagrams with generative classifiers
• A Non-stochastic Optimization Algorithm for Neural-network Quantum States
• Neural Projected Quantum Dynamics: a systematic study
• Spin-1/2 kagome Heisenberg antiferromagnet: Machine learning discovery of the spinon pair density wave ground state
• Wave function network description and Kolmogorov complexity of quantum many-body systems
• Artificial-intelligence-based surrogate solution of dissipative quantum dynamics: physics-informed reconstruction of the universal propagator
• Neural networks in quantum many-body physics: a hands-on tutorial
• A Bayesian Inference Framework for Compression and Prediction of Quantum States
• Scalable variational Monte Carlo with graph neural ansatz
• Autoregressive neural Slater-Jastrow ansatz for variational Monte Carlo simulation
• Deep reinforcement learning for preparation of thermal and prethermal quantum states
• Scalable Imaginary Time Evolution with Neural Network Quantum States
• Continuous-time dynamics and error scaling of noisy highly-entangling quantum circuits
• Impact of conditional modelling for a universal autoregressive quantum state
• Empirical Sample Complexity of Neural Network Mixed State Reconstruction
• Exponentially improved efficient machine learning for quantum many-body states with provable guarantees
• The autoregressive neural network architecture of the Boltzmann distribution of pairwise interacting spins systems
• Accelerating equilibrium spin-glass simulations using quantum annealers via generative deep learning
• Phase diagram reconstruction of the Bose-Hubbard model with a Restricted Boltzmann Machine wavefunction
• Numerically exact mimicking of quantum gas microscopy for interacting lattice fermions
• Transformer Wave Function for Quantum Long-Range models
• Unsupervised Learning of Rydberg Atom Array Phase Diagram with Siamese Neural Networks
• Lee-Yang theory of quantum phase transitions with neural network quantum states
• Noise-Agnostic Quantum Error Mitigation with Data Augmented Neural Models
• Generative Neural Samplers for the Quantum Heisenberg Chain
• Realizing highly entangled states in asymmetrically coupled three NV centers at room temperature
• Neural network enhanced hybrid quantum many-body dynamical distributions
• Spacetime Neural Network for High Dimensional Quantum Dynamics
• Rayleigh-Gauss-Newton optimization with enhanced sampling for variational Monte Carlo
• Approximately-symmetric neural networks for quantum spin liquids
• Network-Initialized Monte Carlo Based on Generative Neural Networks
• Which transformer architecture fits my data? A vocabulary bottleneck in self-attention
• Solving Quantum Statistical Mechanics with Variational Autoregressive Networks and Quantum Circuits
• Sparse Autoregressive Neural Networks for Classical Spin Systems
• Liouville Space Neural Network Representation of Density Matrices
• Coarse-grained spectral projection (CGSP): a deep learning-assisted approach to quantum unitary dynamics
• Variational Neural and Tensor Network Approximations of Thermal States
• Broken-Symmetry Ground States of the Heisenberg model on the Pyrochlore Lattice
• Time-dependent variational principle for open quantum systems with artificial neural networks
• Unveiling the nonclassicality within quasi-distribution representations through deep learning
• Building imaginary-time thermal field theory with artificial neural networks
• Efficient Optimization of Variational Autoregressive Networks with Natural Gradient
• Improving neural network performance for solving quantum sign structure
• Many-body mobility edges in 1D and 2D revealed by convolutional neural networks
• Physics-informed Transformers for Electronic Quantum States
• NNQS-AFQMC: Neural network quantum states enhanced fermionic quantum Monte Carlo
• Seeding neural network quantum states with tensor network states
• Many-Body Neural Network Wavefunction for a Non-Hermitian Ising Chain
• Kinetic samplers for neural quantum states
• Universal Performance Gap of Neural Quantum States Applied to the Hofstadter-Bose-Hubbard Model
• Accuracy of Restricted Boltzmann Machines for the one-dimensional $J_1-J_2$ Heisenberg model
• Artificial intelligence for representing and characterizing quantum systems
• Nonequilibrium thermodynamics of self-supervised learning
• Worldline algorithm by oracle-guided variational autoregressive network
• Variational decision diagrams for quantum-inspired machine learning applications
• Emulating ultrafast dissipative quantum dynamics with deep neural networks
• Magnetic correlations in the $SU(3)$ triangular-lattice $t$-$J$ model at finite doping
• Neural quantum states for entanglement depth certification from randomized Pauli measurements
• The toric code under antiferromagnetic isotropic Heisenberg interactions
• Weakly-supervised learning on Schrodinger equation
• Overcoming barriers to scalability in variational quantum Monte Carlo