Neural network enhanced hybrid quantum many-body dynamical distributions

Abstract

Computing dynamical distributions in quantum many-body systems represents one of the paradigmatic open problems in theoretical condensed matter physics. Despite the existence of different techniques both in real-time and frequency space, computational limitations often dramatically constrain the physical regimes in which quantum many-body dynamics can be efficiently solved. Here we show that the combination of machine learning methods and complementary many-body tensor network techniques substantially decreases the computational cost of quantum many-body dynamics. We demonstrate that combining kernel polynomial techniques and real-time evolution, together with deep neural networks, allows to compute dynamical quantities faithfully. Focusing on many-body dynamical distributions, we show that this hybrid neural-network many-body algorithm, trained with single-particle data only, can efficiently extrapolate dynamics for many-body systems without prior knowledge. Importantly, this algorithm is shown to be substantially resilient to numerical noise, a feature of major importance when using this algorithm together with noisy many-body methods. Ultimately, our results provide a starting point towards neural-network powered algorithms to support a variety of quantum many-body dynamical methods, that could potentially solve computationally expensive many-body systems in a more efficient manner.

arXiv comment11 pages, 7 figures

References in corpus (58)

• The density-matrix renormalization group in the age of matrix product states
• Machine learning and the physical sciences
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Many-body localization, thermalization, and entanglement
• Efficient simulation of one-dimensional quantum many-body systems
• Machine learning phases of matter
• Real time evolution using the density matrix renormalization group
• Atomic quantum gases in periodically driven optical lattices
• The Kernel Polynomial Method
• Floquet Time Crystals
• On the phase structure of driven quantum systems
• Quantum Time Crystals
• Learning phase transitions by confusion
• Dynamical quantum phase transitions: a review
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Time crystals: a review
• Time-evolving a matrix product state with long-ranged interactions
• Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
• Identifying topological order through unsupervised machine learning
• Deep autoregressive models for the efficient variational simulation of many-body quantum systems
• Symmetries and many-body excited states with neural-network quantum states
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Equivalence of restricted Boltzmann machines and tensor network states
• Quantum many-body dynamics in two dimensions with artificial neural networks
• Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems
• Variational neural network ansatz for steady states in open quantum systems
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Dynamical quantum phase transitions in random spin chains
• Constructing neural stationary states for open quantum many-body systems
• Time-step targetting methods for real-time dynamics using DMRG
• Machine Learning for Quantum Matter
• Full quantum distribution of contrast in interference experiments between interacting one dimensional Bose liquids
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• Chebyshev matrix product state approach for spectral functions
• NetKet: A Machine Learning Toolkit for Many-Body Quantum Systems
• Neural Network-based Classification of Crystal Symmetries from X-Ray Diffraction Patterns
• Machine Learning by Unitary Tensor Network of Hierarchical Tree Structure
• Solving frustrated quantum many-particle models with convolutional neural networks
• Chebyshev Matrix Product State Impurity Solver for the Dynamical Mean-Field Theory
• Artificial Neural Network Approach to the Analytic Continuation Problem
• Chiral Topological Phases from Artificial Neural Networks
• Chebyshev expansion for Impurity Models using Matrix Product States
• Order parameter statistics in the critical quantum Ising chain
• Analytic continuation via domain-knowledge free machine learning
• Automated tuning of double quantum dots into specific charge states using neural networks
• Unsupervised identification of topological order using predictive models
• Efficient Tensor Network ansatz for high-dimensional quantum many-body problems
• Real space mapping of topological invariants using artificial neural networks
• Hamiltonian Learning for Quantum Error Correction
• Driven quantum dynamics: will it blend?
• Automated discovery of characteristic features of phase transitions in many-body localization
• A machine learning approach to dynamical properties of quantum many-body systems
• Magnetization distribution in the transverse Ising chain with energy flux
• Topological spin excitations in Harper-Heisenberg spin chains
• Inducing a many-body topological state of matter through Coulomb-engineered local interactions
• Solitonic in-gap modes in a superconductor-quantum antiferromagnet interface
• Dynamical topological excitations in parafermion chains
• Many-body Majorana-like zero modes without gauge symmetry breaking

Cited by in corpus (2)

• Physics-informed neural networks for quantum control
• Designing quantum many-body matter with conditional generative adversarial networks