Related papers: Les Houches Lecture Notes on Tensor Networks

Tensor Network States are ans\"atze for the efficient description of quantum many-body systems. Their success for one dimensional problems, together with the fact that they do not suffer from the sign problem and can address the simulation…

With the increasing adoption of machine learning tools like neural networks across several domains, interesting connections and comparisons to concepts from other domains are coming to light. In this work, we focus on the class of Tensor…

The groundbreaking performance of deep neural networks (NNs) promoted a surge of interest in providing a mathematical basis to deep learning theory. Low-rank tensor decompositions are specially befitting for this task due to their close…

We provide a systematic approach to quantum mechanics from an information-theoretic perspective using the language of tensor networks. Our formulation needs only a single kind of object, so-called positive *-tensors. Physical models…

This book serves as an introductory yet thorough guide to tensor networks and their applications in quantum computation and quantum information, designed for advanced undergraduate and graduate-level readers. In Part I, foundational topics…

Tensor networks are a powerful formalism for transforming one set of degrees of freedom to another. They have been heavily used in analyzing the geometry of bulk/boundary correspondence in conformal field theories. Here we develop a…

This brief review introduces the reader to tensor network methods, a powerful theoretical and numerical paradigm spawning from condensed matter physics and quantum information science and increasingly exploited in different fields of…

We introduce the pro-tensor network, a categorification of the tensor network, as a fully rigorous yet graphically transparent framework for studying the collection of many many-body theories, which we dub many-many-body theory. We provide…

These are exciting times for quantum physics as new quantum technologies are expected to soon transform computing at an unprecedented level. Simultaneously network science is flourishing proving an ideal mathematical and computational…

We analyze the problem of high-order polynomial approximation from a many-body physics perspective, and demonstrate the descriptive power of entanglement entropy in capturing model capacity and task complexity. Instantiated with a…

It is a critical challenge to simultaneously gain high interpretability and efficiency with the current schemes of deep machine learning (ML). Tensor network (TN), which is a well-established mathematical tool originating from quantum…

A new renormalization group approach that maps lattice problems to tensor networks may hold the key to solving seemingly intractable models of strongly correlated systems in any dimension. A Physics Viewpoint on arXiv:0903.1069

Progress in the application of machine learning techniques to the prediction of solid-state and molecular materials properties has been greatly facilitated by the development state-of-the-art feature representations and novel deep learning…

In this paper we attempt to understand Lorentzian tensor networks, as a preparation for constructing tensor networks that can describe more exotic backgrounds such as black holes. To define notions of reference frames and switching of…

Tensor networks are a very powerful data structure tool originating from quantum system simulations. In recent years, they have seen increased use in machine learning, mostly in trainings with gradient-based techniques, due to their…

High-dimensional data arise naturally in many areas of science and engineering, including machine learning, signal processing, computational physics, and statistics. Such data are often represented as tensors, multi-dimensional…

Modern quantum optical systems such as photonic quantum computers and quantum imaging devices require great precision in their designs and implementations in the hope to realistically exploit entanglement and reach a real quantum advantage.…

Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools---called tensor network methods---form the backbone of modern numerical methods…

Tensor networks have found a wide use in a variety of applications in physics and computer science, recently leading to both theoretical insights as well as practical algorithms in machine learning. In this work we explore the connection…

Tensor Network (TN) decompositions have emerged as an indispensable tool in Big Data analytics owing to their ability to provide compact low-rank representations, thus alleviating the ``Curse of Dimensionality'' inherent in handling…