Related papers: Optimization at the boundary of the tensor network…

The success of tensor network approaches in simulating strongly correlated quantum systems crucially depends on whether the many body states that are relevant for the problem can be encoded in a local tensor network. Despite numerous…

We propose a new variational scheme based on the neural-network quantum states to simulate the stationary states of open quantum many-body systems. Using the high expressive power of the variational ansatz described by the restricted…

Given a microscopic lattice Hamiltonian for a topologically ordered phase, we describe a tensor network approach to characterize its emergent anyon model and, in a chiral phase, also its gapless edge theory. First, a tensor network…

The algebraic Bethe Ansatz is a prosperous and well-established method for solving one-dimensional quantum models exactly. The solution of the complex eigenvalue problem is thereby reduced to the solution of a set of algebraic equations.…

We establish a direct connection between general tensor networks and deep feed-forward artificial neural networks. The core of our results is the construction of neural-network layers that efficiently perform tensor contractions, and that…

Projected entangled pair states (PEPS) offer memory-efficient representations of some quantum many-body states that obey an entanglement area law, and are the basis for classical simulations of ground states in two-dimensional (2d)…

The fields of entanglement theory and tensor networks have recently emerged as central tools for characterising quantum phases of matter. In this article, we determine the entanglement structure of ground states of gapped symmetric quantum…

We present a detailed analysis of various tensor network parameterizations within the Complete Graph Tensor Network States (CGTNS) approach. We extend our 2-site CGTNS scheme by introducing 3-site correlators. For this we devise three…

In many physical scenarios, close relations between the bulk properties of quantum systems and theories associated to their boundaries have been observed. In this work, we provide an exact duality mapping between the bulk of a quantum spin…

We investigate robust linear consensus over networks under capacity-constrained communication. The capacity of each edge is encoded as an upper bound on the number of state variables that can be communicated instantaneously. When the edge…

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…

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.

Artificial neural networks have been recently introduced as a general ansatz to compactly represent many- body wave functions. In conjunction with Variational Monte Carlo, this ansatz has been applied to find Hamil- tonian ground states and…

Solving for the lowest energy eigenstate of the many-body Schrodinger equation is a cornerstone problem that hinders understanding of a variety of quantum phenomena. The difficulty arises from the exponential nature of the Hilbert space…

This paper accompanies with our recent work on quantum error correction (QEC) and entanglement spectrum (ES) in tensor networks (arXiv:1806.05007). We propose a general framework for planar tensor network state with tensor constraints as a…

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…

A tree tensor network variational method is proposed to simulate quantum many-body systems with global symmetries where the optimization is reduced to individual charge configurations. A computational scheme is presented, how to extract the…

Random tensor network states are toy models for holographic duality, which have entanglement properties determined by graph geometry. In this paper, we propose a generalization of the random tensor network states which describe an ensemble…

Efficient methods to access the entanglement of a quantum many-body state, where the complexity generally scales exponentially with the system size $N$, have long a concern. Here we propose the Schmidt tensor network state (Schmidt TNS)…

The tensor product representation of quantum states leads to a promising variational approach to study quantum phase and quantum phase transitions, especially topological ordered phases which are impossible to handle with conventional…