Related papers: Concatenated tensor network states
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…
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…
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…
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…
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…
Entanglement is a fundamental feature of quantum mechanics, playing a crucial role in quantum information processing. However, classifying entangled states, particularly in the mixed-state regime, remains a challenging problem, especially…
Matrix Product States can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system. We introduce a new family of states which extends this definition to two dimensions. Like in Matrix Product…
We show that any matrix product state (MPS) can be exactly represented by a recurrent neural network (RNN) with a linear memory update. We generalize this RNN architecture to 2D lattices using a multilinear memory update. It supports…
In this study, we introduce a novel family of tensor networks, termed constrained matrix product states (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures.…
In this article we present analytical results on the exact tensor network representations and correlation functions of the first examples of 2D ground states with quantum phase transitions between area law and extensive entanglement…
Tensor networks provide succinct representations of quantum many-body states and are an important computational tool for strongly correlated quantum systems. Their expressive and computational power is characterized by an underlying…
In the out-of-equilibrium evolution induced by a quench, fast degrees of freedom generate long-range entanglement that is hard to encode with standard tensor networks. However, local observables only sense such long-range correlations…
Complex networks structures have been extensively used for describing complex natural and technological systems, like the Internet or social networks. More recently complex network theory has been applied to quantum systems, where complex…
Tensor network methods have progressed from variational techniques based on matrix-product states able to compute properties of one-dimensional condensed-matter lattice models into methods rooted in more elaborate states such as projected…
Tensor network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum…
These lecture notes provide a brief overview of methods of entanglement theory applied to the study of quantum many-body systems, as well as of tensor network states capturing quantum states naturally appearing in condensed-matter systems.
Reliable methods for the classification and quantification of quantum entanglement are fundamental to understanding its exploitation in quantum technologies. One such method, known as Separable Neural Network Quantum States (SNNS), employs…
We introduce a new class of states for bosonic quantum fields which extend tensor network states to the continuum and generalize continuous matrix product states (cMPS) to spatial dimensions $d\geq 2$. By construction, they are Euclidean…
Tensor networks are efficient factorisations of high-dimensional tensors into a network of lower-order tensors. They have been most commonly used to model entanglement in quantum many-body systems and more recently are witnessing increased…
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…