相关论文: Tensor network states and algorithms in the presen…

Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a…

In this thesis we extend the formalism of tensor network algorithms to incorporate global internal symmetries. We describe how to both numerically protect the symmetry and exploit it for computational gain in tensor network simulations. Our…

The benefits of exploiting the presence of symmetries in tensor network algorithms have been extensively demonstrated in the context of matrix product states (MPSs). These include the ability to select a specific symmetry sector (e.g. with…

This paper is a manual with tips and tricks for programming tensor network algorithms with global $SU(2)$ symmetry. We focus on practical details that are many times overlooked when it comes to implementing the basic building blocks of…

In this thesis I develop a formalism whereby a tensor network may be understood in terms of a unitary braided tensor category, and represented in a particularly efficient manner corresponding to the exploitation of this mathematical…

We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of many-body quantum mechanics on a classical computer. The core setting of this anthology are lattice problems in low…

We propose a simple connection between matrix quantum mechanics and tensor networks. This allows us to imbue tensor networks with some interesting additional structure. The geometry of the graph describing the tensor network state is…

A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although…

The efficient simulation of complex quantum systems remains a central challenge due to the exponential growth of Hilbert space with system size. Tensor network methods have long been established as powerful approximation schemes, and their…

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…

We adapt the bialgebra and Hopf relations to expose internal structure in the ground state of a Hamiltonian with $Z_2$ topological order. Its tensor network description allows for exact contraction through simple diagrammatic rewrite rules.…

We introduce two-dimensional tensor network representations of finite groups carrying a 4-cocycle index. We characterize the associated gapped (2+1)D phases that emerge when these anomalous symmetries act on tensor network ground states. We…

We construct parametrized isometric tensor network states -- referred to as skeletons -- that allow us to explore phases of abelian topological order and can be efficiently implemented on quantum processors. We obtain stable finite…

Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…

Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an…

We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based…

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…

We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017)]. By encoding the truth table of each vertex…

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…

Due to the unfavorable scaling of tensor network methods with the refinement parameter M, new approaches are necessary to improve the efficiency of numerical simulations based on such states in particular for gapless, strongly entangled…