Revealing quantum chaos with machine learning

Abstract

Understanding properties of quantum matter is an outstanding challenge in science. In this paper, we demonstrate how machine-learning methods can be successfully applied for the classification of various regimes in single-particle and many-body systems. We realize neural network algorithms that perform a classification between regular and chaotic behavior in quantum billiard models with remarkably high accuracy. We use the variational autoencoder for autosupervised classification of regular/chaotic wave functions, as well as demonstrating that variational autoencoders could be used as a tool for detection of anomalous quantum states, such as quantum scars. By taking this method further, we show that machine learning techniques allow us to pin down the transition from integrability to many-body quantum chaos in Heisenberg XXZ spin chains. For both cases, we confirm the existence of universal W shapes that characterize the transition. Our results pave the way for exploring the power of machine learning tools for revealing exotic phenomena in quantum many-body systems.

arXiv comment12 pages, 12 figures

References in corpus (52)

• Auto-Encoding Variational Bayes
• Quantum Machine Learning
• Probing many-body dynamics on a 51-atom quantum simulator
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Chaotic Dirac billiard in graphene quantum dots
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Machine learning phases of matter
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Quantum many-body scars
• An atom-by-atom assembler of defect-free arbitrary 2d atomic arrays
• Many-body quantum state tomography with neural networks
• Learning phase transitions by confusion
• Discovering Phase Transitions with Unsupervised Learning
• Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
• Synthetic three-dimensional atomic structures assembled atom by atom
• Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders
• Emergence and Frustration of Magnetic Order with Variable-Range Interactions in a Trapped Ion Quantum Simulator
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Deep Anomaly Detection Using Geometric Transformations
• Machine learning quantum phases of matter beyond the fermion sign problem
• Periodic orbits, entanglement and quantum many-body scars in constrained models: matrix product state approach
• Long-lived dipolar molecules and Feshbach molecules in a 3D optical lattice
• Machine Learning Phases of Strongly Correlated Fermions
• Identifying Quantum Phase Transitions using Artificial Neural Networks on Experimental Data
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Mutual Information, Neural Networks and the Renormalization Group
• Many-body localization and delocalization in large quantum chains
• Machine learning vortices at the Kosterlitz-Thouless transition
• Machine Learning in Electronic Quantum Matter Imaging Experiments
• Poisson versus GOE statistics in integrable and non-integrable quantum hamiltonian
• Probing many-body localization with neural networks
• Quantum chaos: an introduction via chains of interacting spins-1/2
• Anomalous Behavior of Spin Systems with Dipolar Interactions
• Classifying Snapshots of the Doped Hubbard Model with Machine Learning
• Far from equilibrium quantum magnetism with ultracold polar molecules
• Machine learning of quantum phase transitions
• Duality in power-law localization in disordered one-dimensional systems
• Learning hard quantum distributions with variational autoencoders
• Probing hidden spin order with interpretable machine learning
• Accurate mapping of multilevel Rydberg atoms on interacting spin-$1/2$ particles for the quantum simulation of Ising models
• Efficient Representation of Topologically Ordered States with Restricted Boltzmann Machines
• Learning multiple order parameters with interpretable machines
• Statistical properties of eigenstate amplitudes in complex quantum systems
• Quantum Dynamics of the Square-Lattice Heisenberg Model
• Nodal portraits of quantum billiards: Domains, lines, and statistics
• VELC: A New Variational AutoEncoder Based Model for Time Series Anomaly Detection
• Speeding-up the decision making of a learning agent using an ion trap quantum processor
• Towards meaningful physics from generative models
• Quantum spin chains and random matrix theory
• A New Strategy in Applying the Learning Machine to Study Phase Transitions

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• Unsupervised Learning of Rydberg Atom Array Phase Diagram with Siamese Neural Networks
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• Conservation Laws and Spin System Modeling through Principal Component Analysis
• Unsupervised interpretable learning of topological indices invariant under permutations of atomic bands
• Chaotic and regular dynamics in the three-site Bose-Hubbard model
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• Long-Range Order and Quantum Criticality in Antiferromagnetic Chains with Long-Range Staggered Interactions
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