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A restricted Boltzmann machine (RBM) is a generative model that could be used in effectively balancing a cybersecurity dataset because the synthetic data a RBM generates follows the probability distribution of the training data. RBM training can be performed using contrastive divergence (CD) and quantum annealing (QA). QA-based RBM training is fundamentally different from CD and requires samples from a quantum computer. We present a real-world application that uses a quantum computer. Specifically, we train a RBM using QA for cybersecurity applications. The D-Wave 2000Q has been used to implement QA. RBMs are trained on the ISCX data, which ismore » a benchmark dataset for cybersecurity. For comparison, RBMs are also trained using CD. CD is a commonly used method for RBM training. Our analysis of the ISCX data shows that the dataset is imbalanced. We present two different schemes to balance the training dataset before feeding it to a classifier. The first scheme is based on the undersampling of benign instances. The imbalanced training dataset is divided into five sub-datasets that are trained separately. A majority voting is then performed to get the result. Our results show the majority vote increases the classification accuracy up from 90.24% to 95.68%, in the case of CD. For the case of QA, the classification accuracy increases from 74.14% to 80.04%. In the second scheme, a RBM is used to generate synthetic data to balance the training dataset. We show that both QA and CD-trained RBM can be used to generate useful synthetic data. Balanced training data is used to evaluate several classifiers. Among the classifiers investigated, K-Nearest Neighbor (KNN) and Neural Network (NN) perform better than other classifiers. They both show an accuracy of 93%. Our results show a proof-of-concept that a QA-based RBM can be trained on a 64-bit binary dataset. The illustrative example suggests the possibility to migrate many practical classification problems to QA-based techniques. Further, we show that synthetic data generated from a RBM can be used to balance the original dataset.« less

The first-principles density functional theory has been used to study Ga/In-substituted strontium hexaferrite (SrFe12O19). Based on the calculation of the substitution energy of Ga and In in SrFe12O19 and the formation probability analysis, we conclude that in SrFe12−xGaxO19 the substituted Ga atoms prefer to occupy the 12k, 2a, and 4f1 sites, while In atoms in SrFe12−xInxO19 occupy the 12k, 4f2, and 4f1 sites. We used the site occupation probabilities to calculate the magnetic properties of the substituted SrFe12O19. It was found that as the fraction of Ga atoms in SrFe12−xGaxO19 increases, the saturation magnetization (Ms) as well as magnetic anisotropymore » energy (MAE) decrease, while the anisotropy field (Ha) increases. In the case of SrFe12−xInxO19, Ms, MAE, and Ha decrease with an increase of the concentration of In atoms.« less