Related papers: Tensor chain and constraints in tensor networks

Various iterative reconstruction algorithms for inverse problems can be unfolded as neural networks. Empirically, this approach has often led to improved results, but theoretical guarantees are still scarce. While some progress on…

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…

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 adapt the bialgebra and Hopf relations to expose internal structure in the ground state of a Hamiltonian with $Z_2$ topological order. Its tensor network description allows for exact contraction through simple diagrammatic rewrite rules.…

We study criteria for and properties of boundary-to-boundary holography in a class of spin network states defined by analogy to projected entangled pair states (PEPS). In particular, we consider superpositions of states corresponding to…

We propose and analyse a general tensor-based framework for incorporating second order features into network measures. This approach allows us to combine traditional pairwise links with information that records whether triples of nodes are…

We use the framework of $\textit{fixed-point BCFT tensor networks}$ to present a microscopic CFT derivation of the correspondence between reflected entropy (RE) and entanglement wedge cross section (EW) in AdS$_3$/CFT$_2$, for both…

Modern quantum optical systems such as photonic quantum computers and quantum imaging devices require great precision in their designs and implementations in the hope to realistically exploit entanglement and reach a real quantum advantage.…

Once developed for quantum theory, tensor networks have been established as a successful machine learning paradigm. Now, they have been ported back to the quantum realm in the emerging field of quantum machine learning to assess problems…

The problem of the distributed recovery of jointly sparse signals has attracted much attention recently. Let us assume that the nodes of a network observe different sparse signals with common support; starting from linear, compressed…

We introduce a new coarse-graining algorithm, tensor network skeletonization, for the numerical computation of tensor networks. This approach utilizes a structure-preserving skeletonization procedure to remove short-range correlations…

The development of efficient machine learning models for molecular systems representation is becoming crucial in scientific research. We introduce TensorNet, an innovative O(3)-equivariant message-passing neural network architecture that…

Tensor networks, a model that originated from quantum physics, has been gradually generalized as efficient models in machine learning in recent years. However, in order to achieve exact contraction, only tree-like tensor networks such as…

In problems involving approximation, completion, denoising, dimension reduction, estimation, interpolation, modeling, order reduction, regression, etc, we argue that the near-universal practice of assuming that a function, matrix, or tensor…

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…

Message-passing neural networks (MPNN) have shown extremely high efficiency and accuracy in predicting the physical properties of molecules and crystals, and are expected to become the next-generation material simulation tool after the…

Markov chains that describe interacting subsystems suffer, on the one hand, from state space explosion but lead, on the other hand, to highly structured matrices. In this work, we propose a novel tensor-based algorithm to address such…

This paper introduces the tensor representation of a network, here tensors are the primitive structures of the network. In view of tensor chains, two binary operations on tensor sets are defined: chain addition and reducing. Based on the…

Neural network (NN) designed for challenging machine learning tasks is in general a highly nonlinear mapping that contains massive variational parameters. High complexity of NN, if unbounded or unconstrained, might unpredictably cause…

In this work, we present tensor-based linear and nonlinear models for hyperspectral data classification and analysis. By exploiting principles of tensor algebra, we introduce new classification architectures, the weight parameters of which…