Unsupervised identification of topological order using predictive models

Abstract

Machine-learning driven models have proven to be powerful tools for the identification of phases of matter. In particular, unsupervised methods hold the promise to help discover new phases of matter without the need for any prior theoretical knowledge. While for phases characterized by a broken symmetry, the use of unsupervised methods has proven to be successful, topological phases without a local order parameter seem to be much harder to identify without supervision. Here, we use an unsupervised approach to identify topological phases and transitions out of them. We train artificial neural nets to relate configurational data or measurement outcomes to quantities like temperature or tuning parameters in the Hamiltonian. The accuracy of these predictive models can then serve as an indicator for phase transitions. We successfully illustrate this approach on both the classical Ising gauge theory as well as on the quantum ground state of a generalized toric code.

12 pages, 13 figures

References in corpus (21)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Machine learning phases of matter
• Ground state overlap and quantum phase transitions
• Learning phase transitions by confusion
• Discovering Phase Transitions with Unsupervised Learning
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders
• Identifying topological order through unsupervised machine learning
• Topological order, emergent gauge fields, and Fermi surface reconstruction
• Entanglement and topological entropy of the toric code at finite temperature
• Kernel methods for interpretable machine learning of order parameters
• A quantum topological phase transition at the microscopic level
• Fidelity analysis of topological quantum phase transitions
• Hamiltonian Learning for Quantum Error Correction
• Scaling dimension of fidelity susceptibility in quantum phase transitions
• Divergence of predictive model output as indication of phase transitions
• Interplay of Topological Order and Spin Glassiness in the Toric Code under Random Magnetic Fields
• Self-organizing maps as a method for detecting phase transitions and phase identification
• Generation of ice states through deep reinforcement learning

Cited by in corpus (52)

• Provably efficient machine learning for quantum many-body problems
• Unsupervised machine learning and band topology
• Machine Learning for Quantum Matter
• Realizing Quantum Convolutional Neural Networks on a Superconducting Quantum Processor to Recognize Quantum Phases
• Topological quantum phase transitions retrieved through unsupervised machine learning
• Review: Quantum Metrology and Sensing with Many-Body Systems
• Unsupervised machine learning of topological phase transitions from experimental data
• Unsupervised machine learning of quantum phase transitions using diffusion maps
• Unsupervised Learning of Non-Hermitian Topological Phases
• Towards Novel Insights in Lattice Field Theory with Explainable Machine Learning
• Interpreting machine learning of topological quantum phase transitions
• Machine learning discovery of new phases in programmable quantum simulator snapshots
• Quantum Phase Recognition via Quantum Kernel Methods
• Scalable Hamiltonian learning for large-scale out-of-equilibrium quantum dynamics
• Analyzing non-equilibrium quantum states through snapshots with artificial neural networks
• Generative models for sampling and phase transition indication in spin systems
• Phase Detection with Neural Networks: Interpreting the Black Box
• Interpretable and unsupervised phase classification
• Designing quantum many-body matter with conditional generative adversarial networks
• A supervised learning algorithm for interacting topological insulators based on local curvature
• Hessian-based toolbox for reliable and interpretable machine learning in physics
• Unsupervised learning of topological phase diagram using topological data analysis
• Replacing neural networks by optimal analytical predictors for the detection of phase transitions
• Mapping out phase diagrams with generative classifiers
• Quasiparticles as Detector of Topological Quantum Phase Transitions
• Engineering Topological Phases Guided by Statistical and Machine Learning Methods
• Learning entanglement breakdown as a phase transition by confusion
• Statistical learning of engineered topological phases in the kagome superlattice of AV${}_3$Sb${}_5$
• Exponentially improved efficient machine learning for quantum many-body states with provable guarantees
• Error-tolerant quantum convolutional neural networks for symmetry-protected topological phases
• Learning phase transitions from regression uncertainty: A new regression-based machine learning approach for automated detection of phases of matter
• Adversarial Machine Learning Phases of Matter
• Variational Tensor Neural Networks for Deep Learning
• Neural network enhanced hybrid quantum many-body dynamical distributions
• Unsupervised Learning of Rydberg Atom Array Phase Diagram with Siamese Neural Networks
• A simple framework for contrastive learning phases of matter
• Deep Learning of Phase Transitions for Quantum Spin Chains from Correlation Aspects
• Unsupervised interpretable learning of topological indices invariant under permutations of atomic bands
• Learning by Confusion: The Phase Diagram of the Holstein Model
• Transfer learning from Hermitian to non-Hermitian quantum many-body physics
• Automatic Learning of Topological Phase Boundaries
• Machine learning classification of two-dimensional vortex configurations
• Characterizing out-of-distribution generalization of neural networks: application to the disordered Su-Schrieffer-Heeger model
• Quaternion-based machine learning on topological quantum systems
• Deep learning of topological phase transitions from entanglement aspects for two-dimensional chiral p-wave superconductors
• Quantum Convolutional Neural Network for Phase Recognition in Two Dimensions
• Learning interactions between Rydberg atoms
• Classifying topological neural network quantum states via diffusion maps
• Quantum circuit complexity and unsupervised machine learning of topological order
• Supervised learning of an interacting 2D hard-core boson model of a weak topological insulator using correlation functions
• Deep learning of topological phase transitions from entanglement aspects: An unsupervised way
• Quantum Phase Recognition via Quantum Attention Mechanism