Related papers: Thesis: Tensor networks for dynamic spacetimes
We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not…
Tensor Networks (TN) are approximations of high-dimensional tensors designed to represent locally entangled quantum many-body systems efficiently. This study provides a comprehensive comparison between classical TNs and TN-inspired quantum…
Random tensor networks (RTNs) have proved to be fruitful tools for modelling the AdS/CFT correspondence. Due to their flat entanglement spectra, when discussing a given boundary region $R$ and its complement $\bar R$, standard RTNs are most…
Tensor networks are an efficient platform to represent interesting quantum states of matter as well as to compute physical observables and information-theoretic quantities. We present a general protocol to construct fixed-point tensor…
The cosmological horizon has an associated entropy suggesting that it might encode a quantum mechanical system on its surface. This has motivated extending the principles of the anti-de Sitter (AdS) space/ conformal field theory (CFT)…
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…
A concrete model of extracting the physics from the bulk of a gravitational universe is important to the study of quantum gravity and its possible relationship with experiments. Such a model can be constructed in the AdS/CFT correspondence…
Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…
Tensor networks (TNs) and neural networks (NNs) are two fundamental data modeling approaches. TNs were introduced to solve the curse of dimensionality in large-scale tensors by converting an exponential number of dimensions to polynomial…
Tensor networks, originally designed to address computational problems in quantum many-body physics, have recently been applied to machine learning tasks. However, compared to quantum physics, where the reasons for the success of tensor…
We propose a new statistical model suitable for machine learning of systems with long distance correlations such as natural languages. The model is based on directed acyclic graph decorated by multi-linear tensor maps in the vertices and…
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…
Tensor networks are a compressed format for multi-dimensional data. One-dimensional tensor networks -- often referred to as tensor trains (TT) or matrix product states (MPS) -- are increasingly being used as a numerical ansatz for continuum…
Tensor networks are a very powerful data structure tool originating from quantum system simulations. In recent years, they have seen increased use in machine learning, mostly in trainings with gradient-based techniques, due to their…
The AdS/CFT correspondence is an explicit realization of the holographic principle relating a theory of gravity in a volume of space to a lower dimensional quantum field theory on its boundary. By exploiting elements of quantum error…
Compared to sequential learning models, graph-based neural networks exhibit some excellent properties, such as ability capturing global information. In this paper, we investigate graph-based neural networks for text classification problem.…
The p-adic AdS/CFT correspondence relates a CFT living on the p-adic numbers to a system living on the Bruhat-Tits tree. Modifying our earlier proposal for a tensor network realization of p-adic AdS/CFT, we prove that the path integral of a…
Accurate representation to an academic network is of great significance to academic relationship mining like predicting scientific impact. A Latent Factorization of Tensors (LFT) model is one of the most effective models for learning the…
An asymptotically AdS geometry connecting two or more boundaries is given by a entangled state, that can be expanded in the product basis of the Hilbert spaces of each CFT living on the boundaries. We derive a prescription to compute this…
Large-scale Dynamic Networks (LDNs) are becoming increasingly important in the Internet age, yet the dynamic nature of these networks captures the evolution of the network structure and how edge weights change over time, posing unique…