# Machine Learning Topological States

@article{Deng2017MachineLT, title={Machine Learning Topological States}, author={Dong-Ling Deng and Xiaopeng Li and Sankar Das Sarma}, journal={Physical Review B}, year={2017}, volume={96}, pages={195145} }

Machine learning, the core of artificial intelligence and data science, is a very active field, with vast applications throughout science and technology. Recently, machine learning techniques have been adopted to tackle intricate quantum many-body problems and phase transitions. In this work, the authors construct exact mappings from exotic quantum states to machine learning network models. This work shows for the first time that the restricted Boltzmann machine can be used to study both…

## 169 Citations

Chiral topological phases from artificial neural networks

- Computer Science, Physics
- 2017

The authors harness the enormous flexibility of artificial neural networks to study exotic phases of quantum matter, known as chiral topological phases, that are particularly hard to investigate microscopically with more conventional computational methods.

Machine Learning Topological Phases with a Solid-State Quantum Simulator.

- Physics, MedicinePhysical review letters
- 2019

The convolutional neural networks-a class of deep feed-forward artificial neural networks with widespread applications in machine learning-can be trained to successfully identify different topological phases protected by chiral symmetry from experimental raw data generated with a solid-state quantum simulator.

Identifying quantum phase transitions using artificial neural networks on experimental data

- Computer Science, PhysicsNature Physics
- 2019

This work employs an artificial neural network and deep-learning techniques to identify quantum phase transitions from single-shot experimental momentum-space density images of ultracold quantum gases and obtains results that were not feasible with conventional methods.

Machine Learning Detection of Bell Nonlocality in Quantum Many-Body Systems.

- Physics, MedicinePhysical review letters
- 2018

Using reinforcement learning, it is demonstrated that RBM is capable of finding the maximum quantum violations of multipartite Bell inequalities with given measurement settings and builds a novel bridge between computer-science-based machine learning and quantum many-body nonlocality, which will benefit future studies in both areas.

Deep Learning of Matrix Product States

- Computer Science
- 2019

The conditions for translating RBMs into Matrix Product States (MPS) are established, showing that deep learning algorithms can be exploited as a powerful tool for an efficient representation of quantum states.

Identifying Product Order with Restricted Boltzmann Machines

- Mathematics, Physics
- 2017

Unsupervised machine learning via a restricted Boltzmann machine is an useful tool in distinguishing an ordered phase from a disordered phase. Here we study its application on the two-dimensional…

Applications of machine learning to studies of quantum phase transitions

- Computer Science
- 2019

It is concluded that the neural network is able to detect edge states when there is no disorder but unable to distinguish between edge states and Anderson localized states when disorder is introduced.

Machine Learning Spatial Geometry from Entanglement Features

- Mathematics, Physics
- 2017

This work is the first to successfully demonstrate the idea of spatial geometry emerging from learning, an idea proposed in a recent study of the holography duality in quantum gravity.

Quantum-inspired machine learning on high-energy physics data

- npj Quantum Information
- 2021

Tensor Networks, a numerical tool originally designed for simulating quantum many-body systems, have recently been applied to solve Machine Learning problems. Exploiting a tree tensor network, we…

Machine learning and the physical sciences

- Physics
- 2019

Machine learning (ML) encompasses a broad range of algorithms and modeling tools used for a vast array of data processing tasks, which has entered most scientific disciplines in recent years. This…

## References

SHOWING 1-10 OF 133 REFERENCES

Machine Learning Phases of Strongly Correlated Fermions

- Physics
- 2016

Machine learning offers an unprecedented perspective for the problem of classifying phases in condensed matter physics. We employ neural-network machine learning techniques to distinguish…

Machine learning phases of matter

- Physics, Computer Science
- 2016

It is shown that modern machine learning architectures, such as fully connected and convolutional neural networks, can identify phases and phase transitions in a variety of condensed-matter Hamiltonians.

Machine learning quantum phases of matter beyond the fermion sign problem

- Computer Science, PhysicsScientific Reports
- 2017

It is demonstrated that convolutional neural networks (CNN) can be optimized for quantum many-fermion systems such that they correctly identify and locate quantum phase transitions in such systems.

Learning Thermodynamics with Boltzmann Machines

- Physics, Computer ScienceArXiv
- 2016

A Boltzmann machine is developed that is capable of modeling thermodynamic observables for physical systems in thermal equilibrium and can faithfully reproduce the observables of the physical system.

Machine learning for many-body physics: efficient solution of dynamical mean-field theory

- Physics, Mathematics
- 2015

Machine learning methods for solving the equations of dynamical mean-field theory are developed. The method is demonstrated on the three dimensional Hubbard model. The key technical issues are…

An exact mapping between the Variational Renormalization Group and Deep Learning

- Computer Science, MathematicsArXiv
- 2014

This work constructs an exact mapping from the variational renormalization group, first introduced by Kadanoff, and deep learning architectures based on Restricted Boltzmann Machines (RBMs), and suggests that deep learning algorithms may be employing a generalized RG-like scheme to learn relevant features from data.

Solving the quantum many-body problem with artificial neural networks

- Computer Science, PhysicsScience
- 2017

A variational representation of quantum states based on artificial neural networks with a variable number of hidden neurons and a reinforcement-learning scheme that is capable of both finding the ground state and describing the unitary time evolution of complex interacting quantum systems.

Quantum Boltzmann Machine

- Physics, Computer Science
- 2016

This work proposes a new machine learning approach based on quantum Boltzmann distribution of a transverse-field Ising Hamiltonian that allows the QBM efficiently by sampling and discusses the possibility of using quantum annealing processors like D-Wave for QBM training and application.

Application of Quantum Annealing to Training of Deep Neural Networks

- Computer Science, PhysicsArXiv
- 2015

This work investigated an alternative approach that estimates model expectations of Restricted Boltzmann Machines using samples from a D-Wave quantum annealing machine, and found that the quantum sampling- based training approach achieves comparable or better accuracy with significantly fewer iterations of generative training than conventional CD-based training.

Discovering phase transitions with unsupervised learning

- Computer Science, Physics
- 2016

This work shows that unsupervised learning techniques can be readily used to identify phases and phases transitions of many-body systems by using principal component analysis to extract relevant low-dimensional representations of the original data and clustering analysis to identify distinct phases in the feature space.