Related papers: Tensor Network Methods for Invariant Theory

Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…

Tensor methods have become a promising tool to solve high-dimensional problems in the big data era. By exploiting possible low-rank tensor factorization, many high-dimensional model-based or data-driven problems can be solved to facilitate…

In recent years, deep learning techniques have shown great success in various tasks related to inverse problems, where a target quantity of interest can only be observed through indirect measurements by a forward operator. Common approaches…

We argue first that translational invariant Matrix Product can be interpreted as a stationary sea of particles. Next, rather than starting from some local Hamiltonian with random potentials, we consider fluctuations of the local tensors of…

A polynomial is presented that models a topological knot in a unique manner. It distinguishes all types of knots including the orientation and has a group theory interpretation. The topologies may be labeled via a number, which upon a base…

This paper studies rotational virtual knot theory and its relationship with quantum link invariants. Every quantum link invariant for classical knots and links extends to an invariant of rotational virtual knots and links. The paper sets up…

Tensor networks have been successfully applied in simulation of quantum physical systems for decades. Recently, they have also been employed in classical simulation of quantum computing, in particular, random quantum circuits. This paper…

Tensor networks are a popular and computationally efficient approach to simulate general quantum systems on classical computers and, in a broader sense, a framework for dealing with high-dimensional numerical problems. This paper presents a…

Modeling joint probability distributions over sequences has been studied from many perspectives. The physics community developed matrix product states, a tensor-train decomposition for probabilistic modeling, motivated by the need to…

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…

Group equivariant neural networks have been explored in the past few years and are interesting from theoretical and practical standpoints. They leverage concepts from group representation theory, non-commutative harmonic analysis and…

When studying interacting systems, computing their statistical properties is a fundamental problem in various fields such as physics, applied mathematics, and machine learning. However, this task can be quite challenging due to the…

Random tensor networks are a powerful toy model for understanding the entanglement structure of holographic quantum gravity. However, unlike holographic quantum gravity, their entanglement spectra are flat. It has therefore been argued that…

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…

We show that general string-net condensed states have a natural representation in terms of tensor product states (TPS) . These TPS's are built from local tensors. They can describe both states with short-range entanglement (such as the…

Higher order tensor inversion is possible for even order. We have shown that a tensor group endowed with the Einstein (contracted) product is isomorphic to the general linear group of degree $n$. With the isomorphic group structures, we…

A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although…

In this paper, we construct a tensor network representation of quantum causal histories, as a step towards directly representing states in quantum gravity via bulk tensor networks. Quantum causal histories are quantum extensions of causal…

We analyze the problem of high-order polynomial approximation from a many-body physics perspective, and demonstrate the descriptive power of entanglement entropy in capturing model capacity and task complexity. Instantiated with a…

Distinguishing sets of quantum states shared by two parties using only local operations and classical communication measurements is a fundamental topic in quantum communication and quantum information theory. We introduce a graph-theoretic…