Supervised machine learning of ultracold atoms with speckle disorder

Abstract

We analyze how accurately supervised machine learning techniques can predict the lowest energy levels of one-dimensional noninteracting ultracold atoms subject to the correlated disorder due to an optical speckle field. Deep neural networks with different numbers of hidden layers and neurons per layer are trained on large sets of instances of the speckle field, whose energy levels have been preventively determined via a high-order finite difference technique. The Fourier components of the speckle field are used as feature vector to represent the speckle-field instances. A comprehensive analysis of the details that determine the possible success of supervised machine learning tasks, namely the depth and the width of the neural network, the size of the training set, and the magnitude of the regularization parameter, is presented. It is found that ground state energies of previously unseen instances can be predicted with essentially arbitrary accuracy. First and second excited state energies can be predicted too, albeit with slightly lower accuracy and using more layers of hidden neurons.

9 pages, 8 figures

References in corpus (16)

• Many-Body Physics with Ultracold Gases
• Probing many-body dynamics on a 51-atom quantum simulator
• Theory of ultracold Fermi gases
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Learning phase transitions by confusion
• Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms
• Ab initio thermodynamics of liquid and solid water
• Boosting Docking-based Virtual Screening with Deep Learning
• Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials
• Symmetries and many-body excited states with neural-network quantum states
• Anderson localization in Bose-Einstein condensates
• One-dimensional Anderson localization in certain correlated random potentials
• Mobility edge for cold atoms in laser speckle potentials
• Deep Learning the Quantum Phase Transitions in Random Electron Systems: Applications to Three Dimensions
• Projective quantum Monte Carlo simulations guided by unrestricted neural network states
• Semiclassical spectral function and density of states in speckle potentials

Cited by in corpus (17)

• Deep learning the Hohenberg-Kohn maps of Density Functional Theory
• Correlator Convolutional Neural Networks: An Interpretable Architecture for Image-like Quantum Matter Data
• Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions
• Machine-learning enhanced dark soliton detection in Bose-Einstein condensates
• Single-exposure absorption imaging of ultracold atoms using deep learning
• Scalable neural networks for the efficient learning of disordered quantum systems
• Machine-learning assisted quantum control in random environment
• Protein Structured Reservoir computing for Spike-based Pattern Recognition
• Efficient Learning of a One-dimensional Density Functional Theory
• Replacing neural networks by optimal analytical predictors for the detection of phase transitions
• Optical lattice experiments at unobserved conditions and scales through generative adversarial deep learning
• Supervised learning of random quantum circuits via scalable neural networks
• Quantum Reservoir Computing for Speckle-Disorder Potentials
• Effects of auto-correlated disorder on the dynamics in the vicinity of the many-body localization transition
• Two dimensional Quantum droplets in random repulsive potential
• Deep learning density functionals for gradient descent optimization
• Deep learning nonlocal and scalable energy functionals for quantum Ising models