Related papers: Explicit tensor network representation for the gro…
We introduce a systematic mathematical language for describing fixed point models and apply it to the study to topological phases of matter. The framework is reminiscent of state-sum models and lattice topological quantum field theories,…
Tensor network states are capable of describing many-body systems with complex quantum entanglement, including systems with non-trivial topological order. In this paper, we study methods to calculate the topological properties of a tensor…
We show that quantum systems of extended objects naturally give rise to a large class of exotic phases - namely topological phases. These phases occur when the extended objects, called ``string-nets'', become highly fluctuating and…
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 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…
In this work, we study the representation space of contextualized embeddings and gain insight into the hidden topology of large language models. We show there exists a network of latent states that summarize linguistic properties of…
In the context of a quantum critical spin chain whose low energy physics corresponds to a conformal field theory (CFT), it was recently demonstrated [A. Milsted G. Vidal, arXiv:1805.12524] that certain classes of tensor networks used for…
We introduce a change of perspective on tensor network states that is defined by the computational graph of the contraction of an amplitude. The resulting class of states, which we refer to as tensor network functions, inherit the…
We present a unified framework to describe lattice gauge theories by means of tensor networks: this framework is efficient as it exploits the high amount of local symmetry content native of these systems describing only the gauge invariant…
We define a class of tensor network states for spin systems where the individual tensors are functionals of fields. The construction is based on the path integral representation of correlators of operators in quantum field theory. These…
Tensor network methods provide an intuitive graphical language to describe quantum states, channels, open quantum systems and a class of numerical approximation methods that efficiently simulate certain many-body states in one spatial…
A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems is…
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…
Multilayer networks have become increasingly ubiquitous across diverse scientific fields, ranging from social sciences and biology to economics and international relations. Despite their broad applications, the inferential theory for…
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 class of TNS and are used for the simulation of…
We study fermionic matrix product operator algebras and identify the associated algebraic data. Using this algebraic data we construct fermionic tensor network states in two dimensions that have non-trivial symmetry-protected or intrinsic…
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 fundamental concept of applying the system methodology to network analysis declares that network architecture should take into account services and applications which this network provides and supports. This work introduces a formal…
We define a class of lattice models for two-dimensional topological phases with boundary such that both the bulk and the boundary excitations are gapped. The bulk part is constructed using a unitary tensor category $\calC$ as in the…
The string-net condensate is a new class of materials which exhibits the quantum topological order. In order to answer the important question, "how useful is the string-net condensate in quantum information processing?", we consider the…