Related papers: Quantum-inspired event reconstruction with Tensor …
The tensor network, as a facterization of tensors, aims at performing the operations that are common for normal tensors, such as addition, contraction and stacking. However, due to its non-unique network structure, only the tensor network…
Invariance has recently proven to be a powerful inductive bias in machine learning models. One such class of predictive or generative models are tensor networks. We introduce a new numerical algorithm to construct a basis of tensors that…
Situated as a language between computer science, quantum physics and mathematics, tensor network theory has steadily grown in popularity and can now be found in applications ranging across the entire field of quantum information processing.…
Modern approaches to generative modeling of continuous data using tensor networks incorporate compression layers to capture the most meaningful features of high-dimensional inputs. These methods, however, rely on traditional Matrix Product…
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…
We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction of the density matrix, which is highly demanding, or the contraction…
We investigate the global-symmetry projections applied to the tensor network states from the view point of the entanglement entropy and the mutual information. The projections to the translational invariant space and to the total-$S^z$-zero…
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…
Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…
Tensor networks and quantum computation are two of the most powerful tools for the simulation of quantum many-body systems. Rather than viewing them as competing approaches, here we consider how these two methods can work in tandem. We…
We present the Copupled Cluster (CC) method and the Density matrix Renormalization Grooup (DMRG) method in a unified way, from the perspective of recent developments in tensor product approximation. We present an introduction into recently…
Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost…
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…
Simulation of quantum systems is challenging due to the exponential size of the state space. Tensor networks provide a systematically improvable approximation for quantum states. 2D tensor networks such as Projected Entangled Pair States…
Matrix product states provide efficient classical descriptions of quantum systems that may be useful as reference states for quantum algorithms such as quantum phase estimation and quantum-selected configuration interaction. Shallow circuit…
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…
Quantum state tomography (QST) is a fundamental technique for estimating the state of a quantum system from measured data and plays a crucial role in evaluating the performance of quantum devices. However, standard estimation methods become…
We present a new approach to the design of deep networks for natural language processing (NLP), based on the general technique of Tensor Product Representations (TPRs) for encoding and processing symbol structures in distributed neural…
In this work, we firstly apply the Train-Tensor (TT) networks to construct a compact representation of the classical Multilayer Perceptron, representing a reduction of up to 95% of the coefficients. A comparative analysis between tensor…
We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network…