scholarly journals Neural-Network Quantum States for Spin-1 Systems: Spin-Basis and Parameterization Effects on Compactness of Representations

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 879
Author(s):  
Michael Y. Pei ◽  
Stephen R. Clark
Keyword(s):  
Neural Network ◽  
Quantum Systems ◽  
Quantum States ◽  
Restricted Boltzmann Machines ◽  
New Approach ◽  
Single Spin ◽  
Gauge Equivalence ◽  
Tensor Network ◽  
The One ◽  
Spin Basis

Neural network quantum states (NQS) have been widely applied to spin-1/2 systems, where they have proven to be highly effective. The application to systems with larger on-site dimension, such as spin-1 or bosonic systems, has been explored less and predominantly using spin-1/2 Restricted Boltzmann Machines (RBMs) with a one-hot/unary encoding. Here, we propose a more direct generalization of RBMs for spin-1 that retains the key properties of the standard spin-1/2 RBM, specifically trivial product states representations, labeling freedom for the visible variables and gauge equivalence to the tensor network formulation. To test this new approach, we present variational Monte Carlo (VMC) calculations for the spin-1 anti-ferromagnetic Heisenberg (AFH) model and benchmark it against the one-hot/unary encoded RBM demonstrating that it achieves the same accuracy with substantially fewer variational parameters. Furthermore, we investigate how the hidden unit complexity of NQS depend on the local single-spin basis used. Exploiting the tensor network version of our RBM we construct an analytic NQS representation of the Affleck-Kennedy-Lieb-Tasaki (AKLT) state in the xyz spin-1 basis using only M=2N hidden units, compared to M∼O(N2) required in the Sz basis. Additional VMC calculations provide strong evidence that the AKLT state in fact possesses an exact compact NQS representation in the xyz basis with only M=N hidden units. These insights help to further unravel how to most effectively adapt the NQS framework for more complex quantum systems.

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.

QUANTUMNESS OF ENSEMBLE FROM NO-BROADCASTING PRINCIPLE

2006 ◽  
Vol 04 (01) ◽  
pp. 105-118 ◽  
Author(s):  
MICHAł HORODECKI ◽  
PAWEł HORODECKI ◽  
RYSZARD HORODECKI ◽  
MARCO PIANI
Keyword(s):  
Quantum Information ◽  
Information Content ◽  
Quantum Physics ◽  
Single Copy ◽  
Quantum Systems ◽  
Quantum States ◽  
New Approach ◽  
Permanence Property ◽  
The Status ◽  
The Difference

Quantum information, though not precisely defined, is a fundamental concept of quantum information theory which predicts many fascinating phenomena and provides new physical resources. A basic problem is to recognize the features of quantum systems responsible for those phenomena. One of these important features is that non-commuting quantum states cannot be broadcast: two copies cannot be obtained out of a single copy, not even reproduced marginally on separate systems. We focus on the difference in information content between one copy and two copies, which is a basic manifestation of the gap between quantum and classical information. We show that if the chosen information measure is the Holevo quantity, the difference between the information content of one copy and two copies is zero if and only if the states can be broadcast. We propose a new approach in defining measures of quantumness of ensembles based on the difference in information content between the original ensemble and the ensemble of duplicated states. We comment on the permanence property of quantum states and the recently introduced superbroadcasting operation. We also provide an appendix where we discuss the status of quantum information in quantum physics, based on the so-called isomorphism principle.

scholarly journals A NEW APPROACH TO CHARACTERIZE QUBIT CHANNELS

2008 ◽  
Vol 06 (supp01) ◽  
pp. 621-626 ◽  
Author(s):  
FILIPPO CARUSO ◽  
VITTORIO GIOVANNETTI
Keyword(s):  
Continuous Variable ◽  
Quantum Systems ◽  
Characteristic Functions ◽  
New Approach ◽  
Gaussian Channels ◽  
Grassmann Variables ◽  
The One ◽  
Do So

We analyze qubit channels by exploiting the possibility of representing two-level quantum systems in terms of characteristic functions. To do so, we use functions of non-commuting variables (Grassmann variables), defined in terms of generalized displacement operators, following an approach which resemble the one adopted for continuous–variable (Bosonic) systems. It allows us to introduce the notion of qubit Gaussian channels and to show that they share similar properties with the corresponding continuous–variable counterpart. Some examples of qubit channels are investigated using this approach.

New Approach for 3D Mesh Retrieval Using Artificial Neural Network and Histogram of Features

2018 ◽  
Vol 10 (2) ◽  
pp. 84-94 ◽  
Author(s):  
M. Pershina ◽  
V.S. Bouksim ◽  
K. Arhid ◽  
F.R. Zakani ◽  
M. Aboulfatah ◽  
...  
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
New Approach ◽  
3D Mesh ◽  
Artificial Neural

scholarly journals Application of Deep Learning in Fault Diagnosis of Rotating Machinery

Processes ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 919
Author(s):  
Wanlu Jiang ◽  
Chenyang Wang ◽  
Jiayun Zou ◽  
Shuqing Zhang
Keyword(s):  
Neural Network ◽  
Feature Extraction ◽  
Fault Diagnosis ◽  
Rotating Machinery ◽  
Generative Adversarial Networks ◽  
Extraction Ability ◽  
One Dimensional ◽  
Adversarial Networks ◽  
Diagnosis Model ◽  
The One

The field of mechanical fault diagnosis has entered the era of “big data”. However, existing diagnostic algorithms, relying on artificial feature extraction and expert knowledge are of poor extraction ability and lack self-adaptability in the mass data. In the fault diagnosis of rotating machinery, due to the accidental occurrence of equipment faults, the proportion of fault samples is small, the samples are imbalanced, and available data are scarce, which leads to the low accuracy rate of the intelligent diagnosis model trained to identify the equipment state. To solve the above problems, an end-to-end diagnosis model is first proposed, which is an intelligent fault diagnosis method based on one-dimensional convolutional neural network (1D-CNN). That is to say, the original vibration signal is directly input into the model for identification. After that, through combining the convolutional neural network with the generative adversarial networks, a data expansion method based on the one-dimensional deep convolutional generative adversarial networks (1D-DCGAN) is constructed to generate small sample size fault samples and construct the balanced data set. Meanwhile, in order to solve the problem that the network is difficult to optimize, gradient penalty and Wasserstein distance are introduced. Through the test of bearing database and hydraulic pump, it shows that the one-dimensional convolution operation has strong feature extraction ability for vibration signals. The proposed method is very accurate for fault diagnosis of the two kinds of equipment, and high-quality expansion of the original data can be achieved.

A new approach to bracket prediction in the NCAA Men’s Basketball Tournament based on a dual-proportion likelihood

2015 ◽  
Vol 11 (1) ◽  
Author(s):  
Ajay Andrew Gupta
Keyword(s):  
National Collegiate Athletic Association ◽  
Expert Knowledge ◽  
Probability Model ◽  
Expected Value ◽  
Division I ◽  
Prediction System ◽  
New Approach ◽  
Men's Basketball ◽  
Popular Interest ◽  
The One

AbstractThe widespread proliferation of and interest in bracket pools that accompany the National Collegiate Athletic Association Division I Men’s Basketball Tournament have created a need to produce a set of predicted winners for each tournament game by people without expert knowledge of college basketball. Previous research has addressed bracket prediction to some degree, but not nearly on the level of the popular interest in the topic. This paper reviews relevant previous research, and then introduces a rating system for teams using game data from that season prior to the tournament. The ratings from this system are used within a novel, four-predictor probability model to produce sets of bracket predictions for each tournament from 2009 to 2014. This dual-proportion probability model is built around the constraint of two teams with a combined 100% probability of winning a given game. This paper also performs Monte Carlo simulation to investigate whether modifications are necessary from an expected value-based prediction system such as the one introduced in the paper, in order to have the maximum bracket score within a defined group. The findings are that selecting one high-probability “upset” team for one to three late rounds games is likely to outperform other strategies, including one with no modifications to the expected value, as long as the upset choice overlaps a large minority of competing brackets while leaving the bracket some distinguishing characteristics in late rounds.

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.

CLASSICAL DIFFUSION AND QUANTAL LOCALIZATION OF A KICKED PARTICLE IN A WELL

1988 ◽  
Vol 02 (01) ◽  
pp. 103-120 ◽  
Author(s):  
AVRAHAM COHEN ◽  
SHMUEL FISHMAN
Keyword(s):  
Diffusion Coefficient ◽  
Classical Limit ◽  
Approximate Formula ◽  
Quantum Systems ◽  
Potential Well ◽  
Diffusive Growth ◽  
Classical Chaos ◽  
The One ◽  
Short Time ◽  
Infinite Potential Well

The classical and quantal behavior of a particle in an infinite potential well, that is periodically kicked is studied. The kicking potential is K|q|α, where q is the coordinate, while K and α are constants. Classically, it is found that for α > 2 the energy of the particle increases diffusively, for α < 2 it is bounded and for α = 2 the result depends on K. An approximate formula for the diffusion coefficient is presented and compared with numerical results. For quantum systems that are chaotic in the classical limit, diffusive growth of energy takes place for a short time and then it is suppressed by quantal effects. For the systems that are studied in this work the origin of the quantal localization in energy is related to the one of classical chaos.

SEPARABILITY: A NEW APPROACH FROM THE CONIC STRUCTURE OF POSITIVE OPERATORS

2011 ◽  
Vol 09 (supp01) ◽  
pp. 415-422
Author(s):  
D. SALGADO ◽  
J. L. SÁNCHEZ-GÓMEZ ◽  
M. FERRERO
Keyword(s):  
Pure State ◽  
Convex Combination ◽  
Quantum States ◽  
Necessary Condition ◽  
New Approach ◽  
Product Matrix ◽  
Separability Problem ◽  
Multipartite System ◽  
Arbitrary Dimensions ◽  
Bipartite Case

We exploit the cone structure of unnormalized quantum states to reformulate the separability problem. Firstly a convex combination of every quantum state ρ in terms of a state Cρ with the same rank and another one Eρ with lower rank is perfomed, with weights 1 − λρ and λρ, respectively. Secondly a scalar [Formula: see text] is computed. Then ρ is separable if, and only if, [Formula: see text]. The computation of [Formula: see text] has been undergone under the simplest choice for Cρ as a product matrix and Eρ being a pure state, valid for any bipartite and multipartite system in arbitrary dimensions. A necessary condition is also formulated when Eρ is not pure in the bipartite case.

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