Determination of the Lowest-Energy States for the Model Distribution of Trained Restricted Boltzmann Machines Using a 1000 Qubit D-Wave 2X Quantum Computer

2017 ◽  
Vol 29 (7) ◽  
pp. 1815-1837 ◽  
Author(s):  
Yaroslav Koshka ◽  
Dilina Perera ◽  
Spencer Hall ◽  
M. A. Novotny
Keyword(s):  
Quantum Computer ◽  
Energy State ◽  
Bias Field ◽  
Strength Parameter ◽  
Restricted Boltzmann Machines ◽  
Boltzmann Machines ◽  
Energy States ◽  
Further Development ◽  
D Wave

The possibility of using a quantum computer D-Wave 2X with more than 1000 qubits to determine the global minimum of the energy landscape of trained restricted Boltzmann machines is investigated. In order to overcome the problem of limited interconnectivity in the D-Wave architecture, the proposed RBM embedding combines multiple qubits to represent a particular RBM unit. The results for the lowest-energy (the ground state) and some of the higher-energy states found by the D-Wave 2X were compared with those of the classical simulated annealing (SA) algorithm. In many cases, the D-Wave machine successfully found the same RBM lowest-energy state as that found by SA. In some examples, the D-Wave machine returned a state corresponding to one of the higher-energy local minima found by SA. The inherently nonperfect embedding of the RBM into the Chimera lattice explored in this work (i.e., multiple qubits combined into a single RBM unit were found not to be guaranteed to be all aligned) and the existence of small, persistent biases in the D-Wave hardware may cause a discrepancy between the D-Wave and the SA results. In some of the investigated cases, introduction of a small bias field into the energy function or optimization of the chain-strength parameter in the D-Wave embedding successfully addressed difficulties of the particular RBM embedding. With further development of the D-Wave hardware, the approach will be suitable for much larger numbers of RBM units.

scholarly journals Comparison of quantum and classical methods for labels and patterns in Restricted Boltzmann Machines

2021 ◽  
Vol 2122 (1) ◽  
pp. 012007
Author(s):  
Vivek Dixit ◽  
Yaroslav Koshka ◽  
Tamer Aldwairi ◽  
M.A. Novotny
Keyword(s):  
Classification Accuracy ◽  
Quantum Computer ◽  
Quantum Effect ◽  
Low Energy ◽  
Data Reconstruction ◽  
Boltzmann Machine ◽  
Restricted Boltzmann Machines ◽  
Boltzmann Machines ◽  
Comparable Performance ◽  
D Wave

Abstract Classification and data reconstruction using a restricted Boltzmann machine (RBM) is presented. RBM is an energy-based model which assigns low energy values to the configurations of interest. It is a generative model, once trained it can be used to produce samples from the target distribution. The D-Wave 2000Q is a quantum computer which has been used to exploit its quantum effect for machine learning. Bars-and-stripes (BAS) and cybersecurity (ISCX) datasets were used to train RBMs. The weights and biases of trained RBMs were used to map onto the D-Wave. Classification as well as image reconstruction were performed. Classification accuracy of both datasets indicates comparable performance using D-Wave’s adiabatic annealing and classical Gibb’s sampling.

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 A 64 bit quantum dragon data-set for machine learning

2021 ◽  
Vol 2122 (1) ◽  
pp. 012005
Author(s):  
M.A. Novotný ◽  
Yaroslav Koshka ◽  
G. Inkoonv ◽  
Vivek Dixit
Keyword(s):  
Machine Learning ◽  
Finite Interval ◽  
Tight Binding ◽  
Tight Binding Model ◽  
Restricted Boltzmann Machines ◽  
Binding Model ◽  
Data Set ◽  
Boltzmann Machines ◽  
Electron Transmission ◽  
D Wave

Abstract Design and examples of a sixty-four bit quantum dragon data-set are presented. A quantum dragon is a tight-binding model for a strongly disordered nanodevice, but when connected to appropriate semi-infinite leads has complete electron transmission for a finite interval of energies. The labeled data-set contains records which are quantum dragons, which are not quantum dragons, and which are indeterminate. The quantum dragon data-set is designed to be difficult for trained humans and machines to label a nanodevice with regard to its quantum dragon property. The 64 bit record length allows the data-set to be utilized in restricted Boltzmann machines which fit well onto the D-Wave 2000Q quantum annealer architecture.

scholarly journals The Molecular Bases Study of the Inherited Diseases for the Health Maintenance of the Beef Cattle

Genes ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 678
Author(s):  
Elena Konovalova ◽  
Olga Romanenkova ◽  
Olga Kostyunina ◽  
Elena Gladyr
Keyword(s):  
Dna Analysis ◽  
Genetic Defects ◽  
Health Maintenance ◽  
Angus Cattle ◽  
Hereford Cattle ◽  
Pcr Rflp ◽  
Cattle Herds ◽  
Molecular Bases ◽  
Further Development

The article highlighted the problem of meat cattle genetic defects. The aim was the development of DNA tests for some genetic defects diagnostics, the determination of the animal carriers and their frequencies tracking in time. The 1490 DNA samples from the Aberdeen Angus (n = 701), Hereford (n = 385), Simmental (n = 286) and Belgian Blue (n = 118) cattle have been genotyped on the genetic defects by newly created and earlier developed DNA tests based on AS-PCR and PCR-RFLP methods. The Aberdeen Angus cattle genotyping has revealed 2.38 ± 0.31% AMC-cows and 1.67 ± 0.19 % AMC-bulls, 0.65 ± 0.07% DDC-cows and 0.90 ± 0.10% DDC-bulls. The single animals among the Hereford cattle were carriers of MSUD and CWH (on 0.27 ± 0.05%), ICM and HY (on 0.16 ± 0.03%). The Simmental cattle were free from OS. All Belgian Blue livestock were M1- and 0.84%-CMD1-carriers. The different ages Aberdeen Angus cattle genotyping has shown the tendency of the AMC- and DDC frequencies to increase in the later generations. The statistically significant increase of DDC of 1.17% in the cows’ population born in 2019 compared to those born in 2015 allows concluding the further development of the DNA analysis-based measures preventing the manifestation of the genetic anomalies in meat cattle herds is necessary.

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