Related papers: Algorithms for tensor network renormalization
In this thesis, we present a novel method combining energy-based finite-size scaling with tensor network renormalization (TNR) to study phase transitions in lattice models. This approach effectively calculates running coupling constants and…
We address the problem of implementing bottleneck layers from classical pre-trained neural networks on a quantum computer, with the goal of exploring intrinsically quantum ansatz for representing large linear layers within hybrid…
Although quantum machine learning has shown great promise, the practical application of quantum computers remains constrained in the noisy intermediate-scale quantum era. To take advantage of quantum machine learning, we investigate the…
In the machine learning fields, Recurrent Neural Network (RNN) has become a popular architecture for sequential data modeling. However, behind the impressive performance, RNNs require a large number of parameters for both training and…
We propose an entanglement-based algorithm of the tensor-network strong-disorder renormalization group (tSDRG) method for quantum spin systems with quenched randomness. In contrast to the previous tSDRG algorithm based on the energy…
We establish several relations between quantum error correction (QEC) and tensor network (TN) methods of quantum many-body physics. We exhibit correspondences between well-known families of QEC codes and TNs, and demonstrate a formal…
Tensor networks are the main building blocks in a wide variety of computational sciences, ranging from many-body theory and quantum computing to probability and machine learning. Here we propose a parallel algorithm for the contraction of…
Tensor Network States (TNS) offer an efficient representation for the ground state of quantum many body systems and play an important role in the simulations of them. Numerous TNS are proposed in the past few decades. However, due to the…
Low-rank tensor models have been applied in accelerating dynamic magnetic resonance imaging (dMRI). Recently, a new tensor nuclear norm based on t-SVD has been proposed and applied to tensor completion. Inspired by the different properties…
Deep neural network architectures often consist of repetitive structural elements. We introduce an approach that reveals these patterns and can be broadly applied to the study of deep learning. Similarly to how a power strip helps untangle…
We analyze classical dimer models on the square and triangular lattice using a tensor network representation of the dimers. The correlation functions are numerically calculated using the recently developed "Tensor renormalization group"…
Recurrent Neural Network (RNN) are a popular choice for modeling temporal and sequential tasks and achieve many state-of-the-art performance on various complex problems. However, most of the state-of-the-art RNNs have millions of parameters…
In this paper we review basic and emerging models and associated algorithms for large-scale tensor networks, especially Tensor Train (TT) decompositions using novel mathematical and graphical representations. We discus the concept of…
Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…
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…
Recurrent Neural Networks (RNNs) produce state-of-art performance on many machine learning tasks but their demand on resources in terms of memory and computational power are often high. Therefore, there is a great interest in optimizing the…
Variational quantum algorithms are practical approaches to prepare ground states, but their potential for quantum advantage remains unclear. Here, we use differentiable 2D tensor networks (TN) to optimize parameterized quantum circuits that…
It is a critical challenge to simultaneously gain high interpretability and efficiency with the current schemes of deep machine learning (ML). Tensor network (TN), which is a well-established mathematical tool originating from quantum…
Tensor networks are powerful factorization techniques which reduce resource requirements for numerically simulating principal quantum many-body systems and algorithms. The computational complexity of a tensor network simulation depends on…
The most common method for DNN pruning is hard thresholding of network weights, followed by retraining to recover any lost accuracy. Recently developed smart pruning algorithms use the DNN response over the training set for a variety of…