Related papers: Visualization of Entanglement Geometry by Structur…

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…

The tensor network representation of the ground state of a Bethe chain is analytically obtained and studied in relation to its entanglement distribution. Block entanglement displays a maximum at the interplay between single- and…

In the tensor-network framework, the expectation values of two-dimensional quantum states are evaluated by contracting a double-layer tensor network constructed from initial and final tensor-network states. The computational cost of…

Tensor network states are an indispensable tool for the simulation of strongly correlated quantum many-body systems. In recent years, tree tensor network states (TTNS) have been successfully used for two-dimensional systems and to benchmark…

We review different descriptions of many--body quantum systems in terms of tensor product states. We introduce several families of such states in terms of known renormalization procedures, and show that they naturally arise in that context.…

We investigate the global-symmetry projections applied to the tensor network states from the view point of the entanglement entropy and the mutual information. The projections to the translational invariant space and to the total-$S^z$-zero…

We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the density matrix renormalization group…

Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…

In this article we present analytical results on the exact tensor network representations and correlation functions of the first examples of 2D ground states with quantum phase transitions between area law and extensive entanglement…

Despite the fundamental importance of quantum entanglement in many-body systems, our understanding is mostly limited to bipartite situations. Indeed, even defining appropriate notions of multipartite entanglement is a significant challenge…

We develop a method for visualizing the internal structure of multipartite entanglement in pure stabilizer states. Our algorithm graphically organizes the many-body correlations in a hierarchical structure. This provides a rich taxonomy…

Classifying states as entangled or separable is a fundamental, but expensive task. This paper presents a method, the forest algorithm, to improve the amount of resources needed to detect entanglement. Starting from 'optimized' methods for…

Network visualization is essential for many scientific, societal, technological and artistic domains. The primary goal is to highlight patterns out of nodes interconnected by edges that are easy to understand, facilitate communication and…

A novel method has been devised to compute the Local Integrals of Motion (LIOMs) for a one-dimensional many-body localized system. In this approach, a class of optimal unitary transformations is deduced in a tensor-network formalism to…

We discuss the variational optimization of a unitary tensor-network circuit with different network structures. The ansatz is performed based on a generalization of well-developed multi-scale entanglement renormalization algorithm and also…

The intuitiveness of the tensor network graphical language is becoming well known through its use in numerical simulations using methods from tensor network algorithms. Recent times have also seen rapid progress in developing equations of…

We study the entanglement structure of states dual to multiboundary wormhole geometries using tensor network models. Perfect and random tensor networks tiling the hyperbolic plane have been shown to provide good models of the entanglement…

An efficient scheme to compute the geometric entanglement per lattice site for quantum many-body systems on a periodic finite-size chain is proposed in the context of a tensor network algorithm based on the matrix product state…

We devise a deterministic algorithm to efficiently sample high-quality solutions of certain spin-glass systems that encode hard optimization problems. We employ tensor networks to represent the Gibbs distribution of all possible…

In this work, we study the tensor ring decomposition and its associated numerical algorithms. We establish a sharp transition of algorithmic difficulty of the optimization problem as the bond dimension increases: On one hand, we show the…