Related papers: Tensor Network States for Vibrational Spectroscopy

Tensor Networks are non-trivial representations of high-dimensional tensors, originally designed to describe quantum many-body systems. We show that Tensor Networks are ideal vehicles to connect quantum mechanical concepts to machine…

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…

Exact many-body quantum problems are known to be computationally hard due to the exponential scaling of the numerical resources required. Since the advent of the Density Matrix Renormalization Group, it became clear that a successful…

Understanding quantum systems is of significant importance for assessing the performance of quantum hardware and software, as well as exploring quantum control and quantum sensing. An efficient representation of quantum states enables…

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…

The study of tensor network theory is an important field and promises a wide range of experimental and quantum information theoretical applications. Matrix product state is the most well-known example of tensor network states, which…

Quantum state tomography is an essential component of modern quantum technology. In application to continuous-variable harmonic-oscilator systems, such as the electromagnetic field, existing tomography methods typically reconstruct the…

Reconstructing quantum states is an important task for various emerging quantum technologies. The process of reconstructing the density matrix of a quantum state is known as quantum state tomography. Conventionally, tomography of arbitrary…

We characterize the variational power of quantum circuit tensor networks in the representation of physical many-body ground-states. Such tensor networks are formed by replacing the dense block unitaries and isometries in standard tensor…

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…

In the rapidly evolving field of quantum computing, tensor networks serve as an important tool due to their multifaceted utility. In this paper, we review the diverse applications of tensor networks and show that they are an important…

We introduce Neural Tensor Network States ($\nu$TNS), a variational many-body wave-function ansatz that integrates deep neural networks with tensor-network architectures. In the $\nu$TNS framework, a neural network serves as a disentangler…

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…

Matrix models, as quantum mechanical systems without explicit spatial dependence, provide valuable insights into higher-dimensional gauge and gravitational theories, especially within the framework of string theory, where they can describe…

Tensor networks are efficient representations of high-dimensional tensors which have been very successful for physics and mathematics applications. We demonstrate how algorithms for optimizing such networks can be adapted to supervised…

A brief pedagogical overview of recent advances in tensor network state methods are presented that have the potential to broaden their scope of application radically for strongly correlated molecular systems. These include global fermionic…

Tensor network states and methods have erupted in recent years. Originally developed in the context of condensed matter physics and based on renormalization group ideas, tensor networks lived a revival thanks to quantum information theory…

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 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…

Quantum state tomography (QST) aiming at reconstructing the density matrix of a quantum state plays an important role in various emerging quantum technologies. Recognizing the challenges posed by imperfect measurement data, we develop a…