Related papers: Tensor chain and constraints in tensor networks

We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based…

We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017)]. By encoding the truth table of each vertex…

In this study, we introduce a novel family of tensor networks, termed constrained matrix product states (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures.…

Tensor networks provide an efficient approximation of operations involving high dimensional tensors and have been extensively used in modelling quantum many-body systems. More recently, supervised learning has been attempted with tensor…

One of the challenging problems in the condensed matter physics is to understand the quantum many-body systems, especially, their physical mechanisms behind. Since there are only a few complete analytical solutions of these systems, several…

Tensor networks are often used to accurately represent ground states of quantum spin chains. Two popular choices of such tensor network representations can be seen to implement linear maps that correspond, respectively, to euclidean time…

Strongly correlated layered 2D systems are of central importance in condensed matter physics, but their numerical study is very challenging. Motivated by the enormous successes of tensor networks for 1D and 2D systems, we develop an…

One of the most interesting directions in theoretical high-energy and condensed-matter physics is understanding dynamical properties of collective states of quantum field theories. The most elementary tool in this quest is retarded…

Tensor network states form a variational ansatz class widely used, both analytically and numerically, in the study of quantum many-body systems. It is known that if the underlying graph contains a cycle, e.g. as in projected entangled pair…

Tensor network methods have been a key ingredient of advances in condensed matter physics and have recently sparked interest in the machine learning community for their ability to compactly represent very high-dimensional objects. Tensor…

Tensor network methods provide an intuitive graphical language to describe quantum states, channels, open quantum systems and a class of numerical approximation methods that efficiently simulate certain many-body states in one spatial…

Tensor networks are a class of algorithms aimed at reducing the computational complexity of high-dimensional problems. They are used in an increasing number of applications, from quantum simulations to machine learning. Exploiting data…

Despite the omnipresence of tensors and tensor operations in modern deep learning, the use of tensor mathematics to formally design and describe neural networks is still under-explored within the deep learning community. To this end, we…

Tensor networks have proven to be a valuable tool, for instance, in the classical simulation of (strongly correlated) quantum systems. As the size of the systems increases, contracting larger tensor networks becomes computationally…

While tensor networks have their traditional application in simulating quantum systems, in the recent decade they have gathered interest as machine learning models. We combine the experience from both fields and derive how quantum…

Tensor networks such as matrix product states (MPS) and projected entangled pair states (PEPS) are commonly used to approximate quantum systems. These networks are optimized in methods such as DMRG or evolved by local operators. We provide…

Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…

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…

We consider the problem of designing an overlay network and routing mechanism that permits finding resources efficiently in a peer-to-peer system. We argue that many existing approaches to this problem can be modeled as the construction of…

We study tensor network states defined on an underlying graph which is sparsely connected. Generic sparse graphs are expander graphs with a high probability, and one can represent volume law entangled states efficiently with only polynomial…