Related papers: Tensor Network States with Three-Site Correlators
Graph states play an important role in quantum information theory through their connection to measurement-based computing and error correction. Prior work has revealed elegant connections between the graph structure of these states and…
Tensor networks states allow to find the low energy states of local lattice Hamiltonians through variational optimization. Recently, a construction of such states in the continuum was put forward, providing a first step towards the goal of…
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…
Tensor networks developed in the context of condensed matter physics try to approximate order-$N$ tensors with a reduced number of degrees of freedom that is only polynomial in $N$ and arranged as a network of partially contracted smaller…
There has been a recent surge of interest in using machine learning to approximate density functional theory (DFT) in materials science. However, many of the most performant models are evaluated on large databases of computed properties of,…
Tensor networks are factorisations of high rank tensors into networks of lower rank tensors and have primarily been used to analyse quantum many-body problems. Tensor networks have seen a recent surge of interest in relation to supervised…
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…
We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network…
Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse of dimensionality is addressed by parametrizing the many-body state in terms of a network of partially contracted tensors.…
Variational tensor network optimization has become a powerful tool for studying classical statistical models in two dimensions. However, its application to three-dimensional systems remains limited, primarily due to the high computational…
We introduce Neural Tensor Network States ($\nu$TNS), a variational many-body wave-function ansatz that integrates deep neural networks with tensor-network architectures. In the $\nu$TNS framework, a neural network serves as a disentangler…
In this work, we introduce a Denser Feature Network (DenserNet) for visual localization. Our work provides three principal contributions. First, we develop a convolutional neural network (CNN) architecture which aggregates feature maps at…
Matrix product states (MPS), a tensor network designed for one-dimensional quantum systems, has been recently proposed for generative modeling of natural data (such as images) in terms of `Born machine'. However, the exponential decay of…
We develop a strategy for tensor network algorithms that allows to deal very efficiently with lattices of high connectivity. The basic idea is to fine-grain the physical degrees of freedom, i.e., decompose them into more fundamental units…
We devise a method based on the tensor-network formalism to calculate genuine multisite entanglement in ground states of infinite spin chains containing spin-1/2 or spin-1 quantum particles. The ground state is obtained by employing an…
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…
Calculation of observables with three-dimensional projected entangled pair states is generally hard, as it requires a contraction of complex multi-layer tensor networks. We utilize the multi-layer structure of these tensor networks to…
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…
This thesis is divided into two mainly independent parts: In the first part, we derive a criterion to determine when a translationally invariant Matrix Product State (MPS) has long range localizable entanglement, which indicates that the…
Tensor networks give simple representations of complex quantum states. They have proven useful in the study of condensed matter systems and conformal fields, and recently have provided toy models of AdS/CFT. Underlying the tensor network -…