Related papers: Renormalization of tensor networks using graph ind…
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…
With the advances in data acquisition technology, tensor objects are collected in a variety of applications including multimedia, medical and hyperspectral imaging. As the dimensionality of tensor objects is usually very high,…
The Density Matrix Renormalization Group (DMRG) method scales exponentially in the system width for models in two dimensions, but remains one of the most powerful methods for studying 2D systems with a sign problem. Reviewing past…
The renormalization group (RG) constitutes a fundamental framework in modern theoretical physics. It allows the study of many systems showing states with large-scale correlations and their classification in a relatively small set of…
Tensor network algorithms have been remarkably successful solving a variety of problems in quantum many-body physics. However, algorithms to optimize two-dimensional tensor networks known as PEPS lack many of the aspects that make the…
We study a renormalization group (RG) map for tensor networks that include two-dimensional lattice spin systems such as the Ising model. Numerical studies of such RG maps have been quite successful at reproducing the known critical…
We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the density matrix renormalization group…
Limited data and low dose constraints are common problems in a variety of tomographic reconstruction paradigms which lead to noisy and incomplete data. Over the past few years sinogram denoising has become an essential pre-processing step…
We make Kadanoff's block idea into a reliable three-dimensional (3D) real space renormalization group (RG) method. Kadanoff's idea, expressed in spin representation, offers a qualitative intuition for clarifying scaling behavior in…
In this paper, we perform a comprehensive study of the renormalization group (RG) method on thermal tensor networks (TTN). By Trotter-Suzuki decomposition, one obtains the 1+1D TTN representing the partition function of 1D quantum lattice…
This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are…
As quantum technologies develop, we acquire control of an ever-growing number of quantum systems. Unfortunately, current tools to detect relevant quantum properties of quantum states, such as entanglement and Bell nonlocality, suffer from…
Network embedding is a very important method for network data. However, most of the algorithms can only deal with static networks. In this paper, we propose an algorithm Recurrent Neural Network Embedding (RNNE) to deal with dynamic…
Tensor completion estimates missing components by exploiting the low-rank structure of multi-way data. The recently proposed methods based on tensor train (TT) and tensor ring (TR) show better performance in image recovery than classical…
In the tensor network approach to statistical physics, properties of the critical point of a 2D lattice model are encoded by a four-legged tensor which is a fixed point of an RG map. The traditional way to find the fixed point tensor…
We present a conceptually clear and algorithmically useful framework for parameterizing the costs of tensor network contraction. Our framework is completely general, applying to tensor networks with arbitrary bond dimensions, open legs, and…
We propose a hybrid quantum-classical algorithm for approximating the ground state of two-dimensional quantum systems using an isometric tensor network ansatz, which maps naturally to quantum circuits. Inspired by the density matrix…
The widely used density matrix renormalization group (DRMG) method often fails to converge in systems with multiple length scales, such as lattice discretizations of continuum models and dilute or weakly doped lattice models. The local…
We develop the tensor renormalization group (TRG) algorithm for statistical systems with open boundaries, which allows us to investigate not only the bulk but also the boundary property, such as the surface magnetization. We demonstrate…
Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…