The Su-Schrieffer-Heeger (SSH) model serves as a canonical example of a one-dimensional topological insulator, yet its behavior under more complex, realistic conditions remains a fertile ground for research. This paper presents a comprehensive computational investigation into generalized SSH models, exploring the interplay between topology, quasi-periodic disorder, non-Hermiticity, and time-dependent driving. Using exact diagonalization and specialized numerical solvers, we map the system's phase space through its spectral properties and localization characteristics, quantified by the Inverse Participation Ratio (IPR). We demonstrate that while the standard SSH model exhibits topologically protected edge states, these are destroyed by a localization transition induced by strong Aubry-André-Harper (AAH) modulation. Further, we employ unsupervised machine learning (PCA) to autonomously classify the system's phases, revealing that strong localization can obscure underlying topological signatures. Extending the model beyond Hermiticity, we uncover the non-Hermitian skin effect, a dramatic localization of all bulk states at a boundary. Finally, we apply a periodic Floquet drive to a topologically trivial chain, successfully engineering a Floquet topological insulator characterized by the emergence of anomalous edge states at the boundaries of the quasi-energy zone. These findings collectively provide a multi-faceted view of the rich phenomena hosted in generalized 1D topological systems.

Non-Hermitian topological phases can produce some remarkable properties, compared with their Hermitian counterpart, such as the breakdown of conventional bulk-boundary correspondence and the non-Hermitian topological edge mode. Here, we introduce several algorithms with multi-layer perceptron (MLP), and convolutional neural network (CNN) in the field of deep learning, to predict the winding of eigenvalues non-Hermitian Hamiltonians. Subsequently, we use the smallest module of the periodic circuit as one unit to construct high-dimensional circuit data features. Further, we use the Dense Convolutional Network (DenseNet), a type of convolutional neural network that utilizes dense connections between layers to design a non-Hermitian topolectrical Chern circuit, as the DenseNet algorithm is more suitable for processing high-dimensional data. Our results demonstrate the effectiveness of the deep learning network in capturing the global topological characteristics of a non-Hermitian system based on training data.

We show how machine learning techniques can be applied for the classification of topological phases in leaky photonic lattices using limited measurement data. We propose an approach based solely on bulk intensity measurements, thus exempt from the need for complicated phase retrieval procedures. In particular, we design a fully connected neural network that accurately determines topological properties from the output intensity distribution in dimerized waveguide arrays with leaky channels, after propagation of a spatially localized initial excitation at a finite distance, in a setting that closely emulates realistic experimental conditions.

Majorana zero modes in superconductor-nanowire hybrid structures are a promising candidate for topologically protected qubits with the potential to be used in scalable structures. Currently, disorder in such Majorana wires is a major challenge, as it can destroy the topological phase and thus reduce the yield in the fabrication of Majorana devices. We study machine learning optimization of a gate array in proximity to a grounded Majorana wire, which allows us to reliably compensate even strong disorder. We propose a metric for optimization that is inspired by the topological gap protocol, and which can be implemented based on measurements of the non-local conductance through the wire.

In this Letter we supervisedly train neural networks to distinguish different topological phases in the context of topological band insulators. After training with Hamiltonians of one-dimensional insulators with chiral symmetry, the neural network can predict their topological winding numbers with nearly 100% accuracy, even for Hamiltonians with larger winding numbers that are not included in the training data. These results show a remarkable success that the neural network can capture the global and nonlinear topological features of quantum phases from local inputs. By opening up the neural network, we confirm that the network does learn the discrete version of the winding number formula. We also make a couple of remarks regarding the role of the symmetry and the opposite effect of regularization techniques when applying machine learning to physical systems.

A detailed characterization of phases of matter is at the forefront of research in condensed-matter and statistical physics. Although physicists have made incredible progress in the characterization of a wide variety of phases, the identification of novel topological phases remains challenging. Now, Yi Zhang and Eun-Ah Kim from Cornell University, New York [1], have taken a big-data approach to tackling this problem. In their work, thousands of microscopic "images" or "snapshots" of a phase, created using a special topography procedure, are fed into a machine-learning algorithm that is trained to decide whether these images come from a topological or a conventional phase of matter--exactly as modern computer vision algorithms are designed to tell cats from dogs in a picture. Traditionally, phases of matter are differentiated by their symmetry properties [2].