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Title: Quantum Loop Topography for Machine Learning

Journal Article · · Physical Review Letters
 [1];  [1]
  1. Cornell Univ., Ithaca, NY (United States). Dept. of Physics; Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics
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Despite rapidly growing interest in harnessing machine learning in the study of quantum many-body systems, training neural networks to identify quantum phases is a nontrivial challenge. The key challenge is in efficiently extracting essential information from the many-body Hamiltonian or wave function and turning the information into an image that can be fed into a neural network. When targeting topological phases, this task becomes particularly challenging as topological phases are defined in terms of nonlocal properties. Here, we introduce quantum loop topography (QLT): a procedure of constructing a multidimensional image from the “sample” Hamiltonian or wave function by evaluating two-point operators that form loops at independent Monte Carlo steps. The loop configuration is guided by the characteristic response for defining the phase, which is Hall conductivity for the cases at hand. Feeding QLT to a fully connected neural network with a single hidden layer, we demonstrate that the architecture can be effectively trained to distinguish the Chern insulator and the fractional Chern insulator from trivial insulators with high fidelity. In addition to establishing the first case of obtaining a phase diagram with a topological quantum phase transition with machine learning, the perspective of bridging traditional condensed matter theory with machine learning will be broadly valuable.

Research Organization:
Cornell Univ., Ithaca, NY (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
SC0010313
OSTI ID:
1536508
Alternate ID(s):
OSTI ID: 1358297
Journal Information:
Physical Review Letters, Vol. 118, Issue 21; ISSN 0031-9007
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 175 works
Citation information provided by
Web of Science

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When does reinforcement learning stand out in quantum control? A comparative study on state preparation journal October 2019
Identifying topological order through unsupervised machine learning journal May 2019
Identifying quantum phase transitions using artificial neural networks on experimental data journal July 2019
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Machine learning in electronic-quantum-matter imaging experiments journal June 2019
Machine learning quantum phases of matter beyond the fermion sign problem journal August 2017
Machine learning inverse problem for topological photonics journal September 2018
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Learning epidemic threshold in complex networks by Convolutional Neural Network journal November 2019
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Quantum information processing with superconducting circuits: a review journal September 2017
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From DFT to machine learning: recent approaches to materials science–a review journal May 2019
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Machine Learning Based Localization and Classification with Atomic Magnetometers journal January 2018
Machine Learning Detection of Bell Nonlocality in Quantum Many-Body Systems journal June 2018
Experimental Simultaneous Learning of Multiple Nonclassical Correlations journal November 2019
Quantum information processing with superconducting circuits: a review text January 2016
Approximating quantum many-body wave-functions using artificial neural networks text January 2017
Machine Learning of Explicit Order Parameters: From the Ising Model to SU(2) Lattice Gauge Theory text January 2017
Self-Learning Monte Carlo Method: Continuous-Time Algorithm text January 2017
Machine Learning Topological Invariants with Neural Networks text January 2017
Machine learning based localization and classification with atomic magnetometers text January 2017
Machine learning out-of-equilibrium phases of matter text January 2017
Decoupling approximation robustly reconstructs directed dynamical networks text January 2017
Self-learning Monte Carlo with Deep Neural Networks text January 2018
Real space mapping of topological invariants using artificial neural networks text January 2018
Machine Learning of Frustrated Classical Spin Models. II. Kernel Principal Component Analysis text January 2018
Matrix Product Operators for Sequence to Sequence Learning text January 2018
Machine learning of phase transitions in the percolation and XY models text January 2018
Identifying topological order through unsupervised machine learning text January 2018
Deep Learning Topological Invariants of Band Insulators text January 2018
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A machine-learning solver for modified diffusion equations text January 2018
Quantum Neural Network States: A Brief Review of Methods and Applications text January 2018
Self-organizing maps as a method for detecting phase transitions and phase identification text January 2018
Extracting many-particle entanglement entropy from observables using supervised machine learning text January 2018
Reconstructing dynamical networks via feature ranking text January 2019
Multi-faceted machine learning of competing orders in disordered interacting systems text January 2019
Unsupervised Learning Eigenstate Phases of Matter text January 2019
All Optical Neural Network with Nonlinear Activation Functions text January 2019
Machine learning dynamical phase transitions in complex networks text January 2019
Learning epidemic threshold in complex networks by Convolutional Neural Network text January 2019
Hierarchy of energy scales in an O(3) symmetric antiferromagnetic quantum critical metal: a Monte Carlo study text January 2020

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71 CLASSICAL AND QUANTUM MECHANICS
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