Related papers: Simulating matrix models with tensor networks
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…
This review elaborates on the foundation, the advantages, and the prospects of tensor network representations for quantum states in vibrational spectroscopy. The focus is on the recently introduced matrix product state decomposition of…
Understanding the equilibrium properties and out of equilibrium dynamics of quantum field theories are key aspects of fundamental problems in theoretical particle physics and cosmology. However, their classical simulation is highly…
The theory of entanglement provides a fundamentally new language for describing interactions and correlations in many body systems. Its vocabulary consists of qubits and entangled pairs, and the syntax is provided by tensor networks. We…
Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular case of TNS and are used for the simulation of 1+1 dimensional…
Tensor networks are a powerful modeling framework developed for computational many-body physics, which have only recently been applied within machine learning. In this work we utilize a uniform matrix product state (u-MPS) model for…
Tensor network methods are a class of numerical tools and algorithms to study many-body quantum systems in and out of equilibrium, based on tailored variational wave functions. They have found significant applications in simulating lattice…
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 states are used to approximate ground states of local Hamiltonians on a lattice in D spatial dimensions. Different types of tensor network states can be seen to generate different geometries. Matrix product states (MPS) in…
This paper examines the use of tensor networks, which can efficiently represent high-dimensional quantum states, in language modeling. It is a distillation and continuation of the work done in (van der Poel, 2023). To do so, we will…
We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. Using a sequentially prepared quantum circuit representation of a matrix product state (MPS) that we…
Tensor network states provide successful descriptions of strongly correlated quantum systems with applications ranging from condensed matter physics to cosmology. Any family of tensor network states possesses an underlying entanglement…
Tensor network states are an indispensable tool for the simulation of strongly correlated quantum many-body systems. In recent years, tree tensor network states (TTNS) have been successfully used for two-dimensional systems and to benchmark…
Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks…
Tensor network methods are taking a central role in modern quantum physics and beyond. They can provide an efficient approximation to certain classes of quantum states, and the associated graphical language makes it easy to describe and…
Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools---called tensor network methods---form the backbone of modern numerical methods…
Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most…
Tensor networks are a powerful tool to simulate a variety of different physical models, including those that suffer from the sign problem in Monte Carlo simulations. The Hubbard model on the honeycomb lattice with non-zero chemical…
This book serves as an introductory yet thorough guide to tensor networks and their applications in quantum computation and quantum information, designed for advanced undergraduate and graduate-level readers. In Part I, foundational topics…
We describe a simple method to find the ground state energy without calculating the expectation value of the Hamiltonian in the time-evolving block decimation algorithm with tensor network states. For example, we consider quantum…