The one-dimensional p-wave superconductor proposed by Kitaev has long been a classic example for understanding topological phase transitions through various methods, such as examining the Berry phase, edge states of open chains, and, in particular, aspects from quantum entanglement of ground states. In order to understand the amount of information carried in the entanglement-related quantities, here we study topological phase transitions of the model with emphasis of using the deep learning approach. We feed different quantities, including Majorana correlation matrices (MCMs), entanglement spectra (ES) or entanglement eigenvectors (EE) originating from Block correlation matrices, into the deep neural networks for training, and investigate which one could be the most useful input format in this approach. We find that ES is information that is too compressed compared to MCM or EE. MCM and EE can provide us abundant information to recognize not only the topological phase transitions in the model but also phases of matter with different U (1) gauges, which is not reachable by using ES only.

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A combination of cloud-based deep learning (DL) algorithms with portable/wearable (P/W) devices has been developed as a smart heath care system to support automatic cardiac arrhythmias (CAs) classification using electrocardiography (ECG). However, long-term and continuous ECG monitoring is challenging because of limitations of batteries and transmission bandwidth of P/W devices while incorporated with consumer electronics (CE). A feasible approach to address this challenge is to decrease sampling rates. However, low sampling rates lead to lowresolution signals that hinder the CAs classification performance. In this study, we propose a DL-based ECG signal super-resolution framework (called SRECG) to enhance low-resolution ECG signals by jointly considering the accuracies when applied to the DLbased high-resolution multiclass classifier (HMC) of CAs. In our experiments, we downsampled the ECG signals from the CPSC2018 dataset and evaluated their HMC accuracies with and without the SRECG. Experimental results show that SRECG can well improve the HMC accuracies as compared to traditional interpolation methods. Moreover, approximately half of the CAs classification accuracies of HMC were maintained within the enhanced ECG signals by SRECG. The promising results confirm that SRECG can be suitably used to enhance low-resolution ECG signals from P/W devices with CE to improve their cloud-based HMC performances.

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Using machine learning (ML) to recognize different phases of matter and to infer the entire phase diagram has proven to be an effective tool given a large dataset. In our previous proposals, we have successfully explored phase transitions for topological phases of matter at low dimensions either in a supervised or an unsupervised learning protocol with the assistance of quantum information related quantities. In this work, we adopt our previous ML procedures to study quantum phase transitions of magnetism systems such as the XY and XXZ spin chains by using spin-spin correlation functions as the input data. We find that our proposed approach not only maps out the phase diagrams with accurate phase boundaries, but also indicates some new features that have not observed before. In particular, we define so-called relevant correlation functions to some corresponding phases that can always distinguish between those and their neighbors. Based on the unsupervised learning protocol we proposed [Phys. Rev. B 104, 165108 (2021)], the reduced latent representations of the inputs combined with the clustering algorithm show the connectedness or disconnectedness between neighboring clusters (phases), just corresponding to the continuous or disrupt quantum phase transition, respectively. This property reminds us of the behavior of order parameters. Moreover, in the Silhouette analysis we show that the ferromagnetic states in the XXZ model with various anisotropy parameters correspond to almost the same Silhouette value, while the critical or anti-ferromagnetic states behave quite differently. The analysis further indicates that the minima of Silhouette values are close to the phase transition points, showing strong positive correlation. These results again justify the usefulness of our proposed ML procedures and move a step toward understanding the relation between ML and quantum phase transitions from correlation function aspects.