Related papers: Machine learning topological phases in real space

Topology is an important degree of freedom in characterizing electronic systems. Recently, it also brings new theoretical frontiers and many potential applications in photonics. However, the verification of the topological nature is highly…

Geared as an invitation for undergraduates, beginning graduate students, we present a pedagogical introduction to one-dimensional topological phases -- in particular the Su-Schrieffer-Heeger model. In the process, we delve upon ideas of…

In order to perform complex actions in human environments, an autonomous robot needs the ability to understand the environment, that is, to gather and maintain spatial knowledge. Topological map is commonly used for representing large…

Topological phases feature robust edge states that are protected against the effects of defects and disorder. The robustness of these states presents opportunities to design technologies that are tolerant to fabrication errors and resilient…

Nowadays, Machine Learning and Deep Learning methods have become the state-of-the-art approach to solve data classification tasks. In order to use those methods, it is necessary to acquire and label a considerable amount of data; however,…

Topological materials have potential applications for quantum technologies. Non-interacting topological materials, such as e.g., topological insulators and superconductors, are classified by means of fundamental symmetry classes. It is…

We demonstrate how to explore phase diagrams with automated and unsupervised machine learning to find regions of interest for possible new phases. In contrast to supervised learning, where data is classified using predetermined labels, we…

Topological insulator lie at the forefront of condensed matter physics. However strong disorder can destroy the topological states and make all states become localized. In this paper, we investigate the competition between topology and…

Higher-order topological phases give rise to new bulk and boundary physics, as well as new classes of topological phase transitions. While the realization of higher-order topological phases has been confirmed in many platforms by detecting…

Much attention has been devoted to the use of machine learning to approximate physical concepts. Yet, due to challenges in interpretability of machine learning techniques, the question of what physics machine learning models are able to…

Machine learning has recently emerged as a promising approach for studying complex phenomena characterized by rich datasets. In particular, data-centric approaches lend to the possibility of automatically discovering structures in…

Programmable quantum simulators such as superconducting quantum processors and ultracold atomic lattices represent rapidly developing emergent technology that may one day qualitatively outperform existing classical computers. Yet, apart…

Machine learning has made important headway in helping to improve the treatment of quantum many-body systems. A domain of particular relevance are correlated inhomogeneous systems. What has been missing so far is a general, scalable…

Multi-band insulating Bloch Hamiltonians with internal or spatial symmetries, such as particle-hole or inversion, may have topologically disconnected sectors of trivial atomic-limit (momentum-independent) Hamiltonians. We present a…

We explore the physics of topological lattice models in c-QED architectures for arbitrary coupling strength, and the use of the cavity transmission as a topological marker. For this, we develop an approach combining the input-output…

The gap between our ability to collect interesting data and our ability to analyze these data is growing at an unprecedented rate. Recent algorithmic attempts to fill this gap have employed unsupervised tools to discover structure in data.…

We analyze the computational aspects of detecting topological order in a quantum many-body system. We contrast the widely used topological entanglement entropy with a recently introduced operational definition for topological order based on…

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of…

Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set…

We describe a quantum-assisted machine learning (QAML) method in which multivariate data is encoded into quantum states in a Hilbert space whose dimension is exponentially large in the length of the data vector. Learning in this space…