scholarly journals Learning a compass spin model with neural network quantum states

2021 ◽  
Author(s):  
Eric Zou ◽  
Erik Long ◽  
Erhai Zhao
Keyword(s):  
Neural Network ◽  
Ground States ◽  
Spin Model ◽  
Quantum Spin ◽  
Quantum States ◽  
Stochastic Gradient Descent ◽  
Tuning Parameter ◽  
Honeycomb Lattice ◽  
Restricted Boltzmann Machines ◽  
Boltzmann Machines

Abstract Neural network quantum states provide a novel representation of the many-body states of interacting quantum systems and open up a promising route to solve frustrated quantum spin models that evade other numerical approaches. Yet its capacity to describe complex magnetic orders with large unit cells has not been demonstrated, and its performance in a rugged energy landscape has been questioned. Here we apply restricted Boltzmann machines and stochastic gradient descent to seek the ground states of a compass spin model on the honeycomb lattice, which unifies the Kitaev model, Ising model and the quantum 120-degree model with a single tuning parameter. We report calculation results on the variational energy, order parameters and correlation functions. The phase diagram obtained is in good agreement with the predictions of tensor network ansatz, demonstrating the capacity of restricted Boltzmann machines in learning the ground states of frustrated quantum spin Hamiltonians. The limitations of the calculation are discussed. A few strategies are outlined to address some of the challenges in machine learning frustrated quantum magnets.

scholarly journals Adaptive hyperparameter updating for training restricted Boltzmann machines on quantum annealers

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Guanglei Xu ◽  
William S. Oates
Keyword(s):  
Neural Network ◽  
Maximum Likelihood ◽  
Image Reconstruction ◽  
Image Recognition ◽  
Shannon Entropy ◽  
Reconstruction Error ◽  
Likelihood Method ◽  
Restricted Boltzmann Machines ◽  
Boltzmann Machines ◽  
D Wave

AbstractRestricted Boltzmann Machines (RBMs) have been proposed for developing neural networks for a variety of unsupervised machine learning applications such as image recognition, drug discovery, and materials design. The Boltzmann probability distribution is used as a model to identify network parameters by optimizing the likelihood of predicting an output given hidden states trained on available data. Training such networks often requires sampling over a large probability space that must be approximated during gradient based optimization. Quantum annealing has been proposed as a means to search this space more efficiently which has been experimentally investigated on D-Wave hardware. D-Wave implementation requires selection of an effective inverse temperature or hyperparameter ($$\beta $$ β ) within the Boltzmann distribution which can strongly influence optimization. Here, we show how this parameter can be estimated as a hyperparameter applied to D-Wave hardware during neural network training by maximizing the likelihood or minimizing the Shannon entropy. We find both methods improve training RBMs based upon D-Wave hardware experimental validation on an image recognition problem. Neural network image reconstruction errors are evaluated using Bayesian uncertainty analysis which illustrate more than an order magnitude lower image reconstruction error using the maximum likelihood over manually optimizing the hyperparameter. The maximum likelihood method is also shown to out-perform minimizing the Shannon entropy for image reconstruction.

scholarly journals Neural network operations and Susuki–Trotter evolution of neural network states

2018 ◽  
Vol 16 (08) ◽  
pp. 1840008 ◽  
Author(s):  
Nahuel Freitas ◽  
Giovanna Morigi ◽  
Vedran Dunjko
Keyword(s):  
Neural Network ◽  
Optimization Techniques ◽  
Quantum States ◽  
Stochastic Methods ◽  
Many Body ◽  
Boltzmann Machines ◽  
Quantum Operations ◽  
Model Complex ◽  
Network States ◽  
Hidden Nodes

It was recently proposed to leverage the representational power of artificial neural networks, in particular Restricted Boltzmann Machines, in order to model complex quantum states of many-body systems [G. Carleo and M. Troyer, Science 355(6325) (2017) 602.]. States represented in this way, called Neural Network States (NNSs), were shown to display interesting properties like the ability to efficiently capture long-range quantum correlations. However, identifying an optimal neural network representation of a given state might be challenging, and so far this problem has been addressed with stöchastic optimization techniques. In this work, we explore a different direction. We study how the action of elementary quantum operations modifies NNSs. We parametrize a family of many body quantum operations that can be directly applied to states represented by Unrestricted Boltzmann Machines, by just adding hidden nodes and updating the network parameters. We show that this parametrization contains a set of universal quantum gates, from which it follows that the state prepared by any quantum circuit can be expressed as a Neural Network State with a number of hidden nodes that grows linearly with the number of elementary operations in the circuit. This is a powerful representation theorem (which was recently obtained with different methods) but that is not directly useful, since there is no general and efficient way to extract information from this unrestricted description of quantum states. To circumvent this problem, we propose a step-wise procedure based on the projection of Unrestricted quantum states to Restricted quantum states. In turn, two approximate methods to perform this projection are discussed. In this way, we show that it is in principle possible to approximately optimize or evolve Neural Network States without relying on stochastic methods such as Variational Monte Carlo, which are computationally expensive.

scholarly journals Approximating Ground States by Neural Network Quantum States

Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 82 ◽  
Author(s):  
Ying Yang ◽  
Chengyang Zhang ◽  
Huaixin Cao
Keyword(s):  
Neural Network ◽  
Tensor Product ◽  
Relative Error ◽  
Ground State ◽  
Ground States ◽  
Quantum States ◽  
The Neural Network

Motivated by the Carleo’s work (Science, 2017, 355: 602), we focus on finding the neural network quantum statesapproximation of the unknown ground state of a given Hamiltonian H in terms of the best relative error and explore the influences of sum, tensor product, local unitary of Hamiltonians on the best relative error. Besides, we illustrate our method with some examples.

scholarly journals Learnability scaling of quantum states: Restricted Boltzmann machines

2019 ◽  
Vol 100 (19) ◽  
Author(s):  
Dan Sehayek ◽  
Anna Golubeva ◽  
Michael S. Albergo ◽  
Bohdan Kulchytskyy ◽  
Giacomo Torlai ◽  
...  
Keyword(s):  
Quantum States ◽  
Restricted Boltzmann Machines ◽  
Boltzmann Machines

scholarly journals Topological hardcore bosons on the honeycomb lattice

2016 ◽  
Vol 94 (9) ◽  
pp. 814-820
Author(s):  
S.A. Owerre
Keyword(s):  
Spin Model ◽  
Quantum Spin ◽  
Quantum Gases ◽  
Xy Model ◽  
Honeycomb Lattice ◽  
Edge States ◽  
Topological Properties ◽  
Quantum Spin Systems ◽  
System Maps ◽  
Quantum Spin Model

This paper presents a connection between the topological properties of hardcore bosons and that of magnons in quantum spin magnets. We utilize the Haldane-like hardcore bosons on the honeycomb lattice as an example. We show that this system maps to a spin-1/2 quantum XY model with a next-nearest-neighbour Dzyaloshinsky–Moriya interaction. We obtain the magnon excitations of the quantum spin model and compute the edge states, Berry curvature, and thermal and spin Nernst conductivities. Because of the mapping from spin variables to bosons, the hardcore bosons possess the same nontrivial topological properties as those in quantum spin systems. These results are important in the study of magnetic excitations in quantum magnets and they are also useful for understanding the control of ultracold bosonic quantum gases in honeycomb optical lattices, which is experimentally accessible.

scholarly journals Restricted Boltzmann Machines for Quantum States with Non-Abelian or Anyonic Symmetries

2020 ◽  
Vol 124 (9) ◽  
Author(s):  
Tom Vieijra ◽  
Corneel Casert ◽  
Jannes Nys ◽  
Wesley De Neve ◽  
Jutho Haegeman ◽  
...  
Keyword(s):  
Quantum States ◽  
Restricted Boltzmann Machines ◽  
Boltzmann Machines

scholarly journals Anomaly Detection of Wind Turbines Based on Deep Small-World Neural Network

2020 ◽  
Vol 10 (4) ◽  
pp. 1243 ◽  
Author(s):  
Meng Li ◽  
Shuangxin Wang ◽  
Shanxiang Fang ◽  
Juchao Zhao
Keyword(s):  
Neural Network ◽  
Anomaly Detection ◽  
Wind Turbines ◽  
Small World ◽  
Value Theory ◽  
False Alarms ◽  
Learning Networks ◽  
Restricted Boltzmann Machines ◽  
Boltzmann Machines ◽  
Early Failures

Accurate and efficient condition monitoring is the key to enhance the reliability and security of wind turbines. In recent years, an intelligent anomaly detection method based on deep learning networks has been receiving increasing attention. Since accurately labeled data are usually difficult to obtain in real industries, this paper proposes a novel Deep Small-World Neural Network (DSWNN) on the basis of unsupervised learning to detect the early failures of wind turbines. During network construction, a regular auto-encoder network with multiple restricted Boltzmann machines is first constructed and pre-trained by using unlabeled data of wind turbines. After that, the trained network is transformed into a DSWNN model by randomly add-edges method, where the network parameters are fine-tuned by using minimal amounts of labeled data. In order to guard against the changes and disturbances of wind speed and reduce false alarms, an adaptive threshold based on extreme value theory is presented as the criterion of anomaly judgment. The DSWNN model is excellent in depth mining data characteristics and accurate measurement error. Last, two failure cases of wind turbine anomaly detection are given to demonstrate its validity and accuracy of the proposed methodology contrasted with the deep belief network and deep neural network.

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