Related papers: Global optimization of tensor renormalization grou…

We describe a simple real space renormalization group technique for two dimensional classical lattice models. The approach is similar in spirit to block spin methods, but at the same time it is fundamentally based on the theory of quantum…

We generalize the corner transfer matrix renormalization group, which consists of White's density matrix algorithm and Baxter's method of the corner transfer matrix, to three dimensional (3D) classical models. The renormalization group…

In the tensor-network framework, the expectation values of two-dimensional quantum states are evaluated by contracting a double-layer tensor network constructed from initial and final tensor-network states. The computational cost of…

Tensor networks (TNs) have become one of the most essential building blocks for various fields of theoretical physics such as condensed matter theory, statistical mechanics, quantum information, and quantum gravity. This review provides a…

We propose a tensor-network-based algorithm to study the classical Ising model on an infinitely large hyperbolic lattice with a regular 3D tesselation of identical dodecahedra. We reformulate the corner transfer matrix renormalization group…

The convergence of many numerical optimization techniques is highly dependent on the initial guess given to the solver. To address this issue, we propose a novel approach that utilizes tensor methods to initialize existing optimization…

This work presents a novel method for task optimization in industrial plants using quantum-inspired tensor network technology. This method obtains the best possible combination of tasks on a set of machines with directed constraints while…

The development of tensor renormalization group (TRG) algorithm in higher dimensions is an important and urgent task, as the TRG is expected to provide a way to overcome the sign problem in lattice quantum chromodynamics (QCD) calculations…

Tensor recovery has recently arisen in a lot of application fields, such as transportation, medical imaging and remote sensing. Under the assumption that signals possess sparse and/or low-rank structures, many tensor recovery methods have…

In the framework of tensor spaces, we consider orthogonalization kernels to generate an orthogonal basis of a tensor subspace from a set of linearly independent tensors. In particular, we experimentally study the loss of orthogonality of…

We discuss a renormalization procedure for random tensor networks, and show that the corresponding renormalization-group flow is given by the Hamiltonian vector flow of the canonical tensor model, which is a discretized model of quantum…

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…

Global covariance pooling in convolutional neural networks has achieved impressive improvement over the classical first-order pooling. Recent works have shown matrix square root normalization plays a central role in achieving…

We discuss the variational optimization of a unitary tensor-network circuit with different network structures. The ansatz is performed based on a generalization of well-developed multi-scale entanglement renormalization algorithm and also…

Tensor-network Born machines (TNBMs) are quantum-inspired generative models for learning data distributions. Using tensor-network contraction and optimization techniques, the model learns an efficient representation of the target…

Using the example of configurations generated with the worm algorithm for the two-dimensional Ising model, we propose renormalization group (RG) transformations, inspired by the tensor RG, that can be applied to sets of images. We relate…

Critical behavior of the Ising model is investigated at the center of large scale finite size systems, where the lattice is represented as the tiling of pentagons. The system is on the hyperbolic plane, and the recursive structure of the…

The tensor-entanglement renormalization group approach is applied to Hamiltonians that realize a class of topologically ordered states -- string-net condensed states. We analyze phase transitions between phases with and without string-net…

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…

Tensor network contractions are widely used in statistical physics, quantum computing, and computer science. We introduce a method to efficiently approximate tensor network contractions using low-rank approximations, where each intermediate…