Related papers: Entanglement renormalization for disordered system…
An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square…
The intuitiveness of the tensor network graphical language is becoming well known through its use in numerical simulations using methods from tensor network algorithms. Recent times have also seen rapid progress in developing equations of…
Deep Neural Networks have achieved remarkable success relying on the developing high computation capability of GPUs and large-scale datasets with increasing network depth and width in image recognition, object detection and many other…
We use TensorNetwork [C. Roberts et al., arXiv: 1905.01330], a recently developed API for performing tensor network contractions using accelerated backends such as TensorFlow, to implement an optimization algorithm for the Multi-scale…
We propose and study a renormalization group transformation that can be used also for models with strong quenched disorder, like spin glasses. The method is based on a mapping between disorder distributions, chosen such as to keep some…
The tensor-network renormalization group (TNRG) is an accurate numerical real-space renormalization group method for studying phase transitions in both quantum and classical systems. Continuous phase transitions, as an important class of…
The interplay of disorder and interactions is a challenging topic of condensed matter physics, where correlations are crucial and exotic phases develop. In one spatial dimension, a particularly successful method to analyze such problems is…
We discuss in detail algorithms for implementing tensor network renormalization (TNR) for the study of classical statistical and quantum many-body systems. Firstly, we recall established techniques for how the partition function of a 2D…
The infinite disorder fixed point of the random transverse-field Ising model is expected to control the critical behavior of a large class of random quantum and stochastic systems having an order parameter with discrete symmetry. Here we…
In recent years, tensor network renormalization (TNR) has emerged as an efficient and accurate method for studying (1+1)D quantum systems or 2D classical systems using real-space renormalization group (RG) techniques. One notable…
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…
We investigate the problem of stabilizing an unknown networked linear system under communication constraints and adversarial disturbances. We propose the first provably stabilizing algorithm for the problem. The algorithm uses a distributed…
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 certain analytically-tractable quantum chaotic systems, the calculation of out-of-time-order correlation functions, entanglement entropies after a quench, and other related dynamical observables, reduces to an effective theory of an…
We develop a strategy for tensor network algorithms that allows to deal very efficiently with lattices of high connectivity. The basic idea is to fine-grain the physical degrees of freedom, i.e., decompose them into more fundamental units…
We review current progress in the functional renormalization group treatment of disordered systems. After an elementary introduction into the phenomenology, we show why in the context of disordered systems a functional renormalization group…
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…
This paper demonstrates a method for tensorizing neural networks based upon an efficient way of approximating scale invariant quantum states, the Multi-scale Entanglement Renormalization Ansatz (MERA). We employ MERA as a replacement for…
Originating from condensed matter physics, tensor networks are compact representations of high-dimensional tensors. In this paper, the prowess of tensor networks is demonstrated on the particular task of one-class anomaly detection. We…
We show that numerical quasi-one-dimensional renormalization group allows accurate study of weakly coupled chains with modest computational effort. We perform a systematic comparison with exact diagonalization results in two and three-leg…