Related papers: Deep learning for disordered topological insulator…
Neural network based machine learning is emerging as a powerful tool for obtaining phase diagrams when traditional regression schemes using local equilibrium order parameters are not available, as in many-body localized or topological…
Topological order in solid state systems is often calculated from the integration of an appropriate curvature function over the entire Brillouin zone. At topological phase transitions where the single particle spectral gap closes, the…
Recent realizations of exotic topological states in condensed matter and cold atoms have advanced the exploration for topological characteristics, such as invariant topological orders and band inversion. Here we construct a 1D optical…
Deep learning offers powerful tools for anticipating tipping points in complex systems, yet its potential for detecting flickering (noise-driven switching between coexisting stable states) remains unexplored. Flickering is a hallmark of…
In this paper we explore challenges in developing a topological framework in which machine learning can be used to robustly characterize global dynamics. Specifically, we focus on learning a useful discretization of the phase space of a…
Deep learning for predicting the electronic-structure Hamiltonian of quantum systems necessitates satisfying the covariance laws, among which achieving SO(3)-equivariance without sacrificing the non-linear expressive capability of networks…
Topological phases of matter possess intricate correlation patterns typically probed by entanglement entropies or entanglement spectra. In this work, we propose an alternative approach to assessing topologically induced edge states in free…
The high complexity of various inverse problems poses a significant challenge to model-based reconstruction schemes, which in such situations often reach their limits. At the same time, we witness an exceptional success of data-based…
We study one-dimensional disordered fermions that either undergo metal-insulator transitions or topological phase transitions to become trivial Anderson insulators. We focus on using entanglement to elucidate how the spatial, momentum, and…
We consider learning nonholonomic dynamical systems while discovering the constraints, and describe in detail the case of the rolling disk. A nonholonomic system is a system subject to nonholonomic constraints. Unlike holonomic constraints,…
Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…
We formulate an infinite hierarchy of continuous-variable separability criteria in terms of quasiprobability distributions and their derivatives evaluated at individual points in phase space. Our approach is equivalent to the…
The 2-dimensional Ising model on a square lattice is investigated with a variational autoencoder in the non-vanishing field case for the purpose of extracting the crossover region between the ferromagnetic and paramagnetic phases. The…
We study the properties of the entanglement spectrum in gapped non-interacting non-Hermitian systems, and its relation to the topological properties of the system Hamiltonian. Two different families of entanglement Hamiltonians can be…
We explore the use of Physics Informed Neural Networks to analyse nonlinear Hamiltonian Dynamical Systems with a first integral of motion. In this work, we propose an architecture which combines existing Hamiltonian Neural Network…
We show that quantum entanglement can provide an exponential advantage in learning properties of a bosonic continuous-variable (CV) system. The task we consider is estimating a probabilistic mixture of displacement operators acting on $n$…
Machine learning (ML) tools such as encoder-decoder deep convolutional neural networks (CNN) are able to extract relationships between inputs and outputs of large complex systems directly from raw data. For time-varying systems the…
This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient…
We provide a proof that entanglement of any density matrix which block diagonal in subspaces which are disjoint in terms of the Hilbert space of one of the two potentially entangled subsystems can simply be calculated as the weighted…
The potential for complex systems to exhibit tipping points in which an equilibrium state undergoes a sudden and often irreversible shift is well established, but prediction of these events using standard forecast modeling techniques is…