Related papers: Entanglement bipartitioning and tree tensor networ…

We apply a series of projection techniques on top of tensor networks to compute energies of ground state wave functions with higher accuracy than tensor networks alone with minimal additional cost. We consider both matrix product states as…

Strongly correlated layered 2D systems are of central importance in condensed matter physics, but their numerical study is very challenging. Motivated by the enormous successes of tensor networks for 1D and 2D systems, we develop an…

Tensor network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum…

Extending corresponding results for matrix product states [Verstraete and Cirac, PRB 73, 094423 (2006); Schuch et al. PRL 100, 030504 (2008)], it is shown how the approximation error of tree tensor network states (TTNS) can be bounded using…

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost…

Tensor network states provide successful descriptions of strongly correlated quantum systems with applications ranging from condensed matter physics to cosmology. Any family of tensor network states possesses an underlying entanglement…

Tensor Networks (TNs) are a computational paradigm used for representing quantum many-body systems. Recent works have shown how TNs can also be applied to perform Machine Learning (ML) tasks, yielding comparable results to standard…

In this work, we present the tree tensor network Nystr\"om (TTNN), an algorithm that extends recent research on streamable tensor approximation, such as for Tucker and tensor-train formats, to the more general tree tensor network format,…

Tensor networks are powerful factorization techniques which reduce resource requirements for numerically simulating principal quantum many-body systems and algorithms. The computational complexity of a tensor network simulation depends on…

Quantum machine learning researchers often rely on incorporating Tensor Networks (TN) into Deep Neural Networks (DNN) and variational optimization. However, the standard optimization techniques used for training the contracted trainable…

Tensor networks are a compressed format for multi-dimensional data. One-dimensional tensor networks -- often referred to as tensor trains (TT) or matrix product states (MPS) -- are increasingly being used as a numerical ansatz for continuum…

Discrete-time quantum walks provide a natural framework for quantum transport on complex networks. On regular structures, coin-walker entanglement has been widely used to characterize quantum transport and to support quantum algorithmic…

These lecture notes provide a brief overview of methods of entanglement theory applied to the study of quantum many-body systems, as well as of tensor network states capturing quantum states naturally appearing in condensed-matter systems.

We introduce a tree tensor network (TTN) impurity solver that enables highly efficient and accurate real-time simulations of quantum impurity models. By decomposing a noninteracting bath Hamiltonian into a Cayley tree, the method provides a…

Entanglement-based networks (EBNs) enable general-purpose quantum communication by combining entanglement and its swapping in a sequence that addresses the challenges of achieving long distance communication with high fidelity associated…

The topology of classical networks is determined by physical links between nodes, and after a network request the links are used to establish the desired connections. Quantum networks offer the possibility to generate different kinds of…

Spin chains can be used to describe a wide range of platforms for quantum computation and quantum information. They enable the understanding, demonstration, and modeling of numerous useful phenomena, such as high fidelity transfer of…

Quantum networks are composed of quantum nodes that interact coherently by way of quantum channels and open a broad frontier of scientific opportunities. For example, a quantum network can serve as a `web' for connecting quantum processors…

We prove a conjecture of W.~Hackbusch in a bigger generality than in our previous article. Here we consider Tensor Train (TT) model with an arbitrary number of leaves and a corresponding "almost binary tree" for Hierarchical Tucker (HT)…

In this paper, we propose new learning algorithms for approximating high-dimensional functions using tree tensor networks in a least-squares setting. Given a dimension tree or architecture of the tensor network, we provide an algorithm that…