相关论文: Charged String Tensor Networks

We characterize the variational power of quantum circuit tensor networks in the representation of physical many-body ground-states. Such tensor networks are formed by replacing the dense block unitaries and isometries in standard tensor…

Tensorial neural networks (TNNs) combine the successes of multilinear algebra with those of deep learning to enable extremely efficient reduced-order models of high-dimensional problems. Here, I describe a deep neural network architecture…

The string-net condensate is a new class of materials which exhibits the quantum topological order. In order to answer the important question, "how useful is the string-net condensate in quantum information processing?", we consider the…

Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks…

Tensor network techniques are becoming increasingly popular tools to solve partial differential equations within the so-called quantics representation. Their popularity stems from the fact that their spatial resolution depends only…

We describe the use of tensor networks to numerically determine wave functions of interacting two-dimensional fermionic models in the continuum limit. We use two different tensor network states: one based on the numerical continuum limit of…

Recent progress in applying complex network theory to problems in quantum information has resulted in a beneficial crossover. Complex network methods have successfully been applied to transport and entanglement models while information…

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…

Near-term quantum devices generally suffer from shallow circuit depth and hence limited expressivity due to noise and decoherence. To address this, we propose tensor-network-assisted parametrized quantum circuits, which concatenate a…

Geometrical constructions using flexible cords have been known since the earliest days of recorded mathematics. In this paper we introduce rigorous definitions for two classes of string networks. A taut network is one in which all cords are…

Classically simulating quantum circuits is crucial when developing or testing quantum algorithms. Due to the underlying exponential complexity, efficient data structures are key for performing such simulations. To this end, tensor networks…

Many complex networks are only a part of larger systems, where a number of coexisting topologies interact and depend on each other. We introduce a layered model to facilitate the description and analysis of such systems. As an example of…

Tensors, or multidimensional arrays, are data structures that can naturally represent visual data of multiple dimensions. Inherently able to efficiently capture structured, latent semantic spaces and high-order interactions, tensors have a…

In many real-world networks, nodes have class labels, attributes, or variables that affect the network's topology. If the topology of the network is known but the labels of the nodes are hidden, we would like to select a small subset of…

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…

Modern transportation network modeling increasingly involves the integration of diverse methodologies including sensor-based forecasting, reinforcement learning, classical flow optimization, and demand modeling that have traditionally been…

Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…

In this paper, we present a density estimation framework based on tree tensor-network states. The proposed method consists of determining the tree topology with Chow-Liu algorithm, and obtaining a linear system of equations that defines the…

Graph classification is an important learning task for graph-structured data. Graph neural networks (GNNs) have recently gained growing attention in graph learning and have shown significant improvements in many important graph problems.…

Complex systems that consist of different kinds of entities that interact in different ways can be modeled by multilayer networks. This paper uses the tensor formalism with the Einstein tensor product to model this type of networks. Several…