Related papers: TNSPackage: A Fortran2003 library designed for ten…
Tree tensor network states (TTNSs) combined with the density matrix renormalization group (DMRG) are emerging as powerful tools for vibrational and vibronic structure simulations in molecules with strong coupling and fluxionality. In this…
Numerical tensor calculus comprise basic tensor operations such as the entrywise addition and contraction of higher-order tensors. We present, TLib, flexible tensor framework with generic tensor functions and tensor classes that assists…
Tensor Networks (TNs) are a computational paradigm used for representing quantum many-body systems. Recent works have shown how TNs can also be applied to perform Machine Learning (ML) tasks, yielding comparable results to standard…
In the world of linear algebra computation, a well-established standard exists called BLAS(Basic Linear Algebra Subprograms). This standard has been crucial for the development of software using linear algebra operations. Its benefits…
Tensor networks (TNs) and neural networks (NNs) are two fundamental data modeling approaches. TNs were introduced to solve the curse of dimensionality in large-scale tensors by converting an exponential number of dimensions to polynomial…
Tensorizing a neural network involves reshaping some or all of its dense weight matrices into higher-order tensors and approximating them using low-rank tensor network decompositions. This technique has shown promise as a model compression…
We present a new variational tree tensor network state (TTNS) ansatz, the three-legged tree tensor network state (T3NS). Physical tensors are interspersed with branching tensors. Physical tensors have one physical index and at most two…
The tensor network, as a facterization of tensors, aims at performing the operations that are common for normal tensors, such as addition, contraction and stacking. However, due to its non-unique network structure, only the tensor network…
Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse of dimensionality is addressed by parametrizing the many-body state in terms of a network of partially contracted tensors.…
Sparse tensor networks are commonly used to represent contractions over sparse tensors. Tensor contractions are higher-order analogs of matrix multiplication. Tensor networks arise commonly in many domains of scientific computing and data…
Tensor network states (TNS) are a promising but numerically challenging tool for simulating two-dimensional (2D) quantum many-body problems. We introduce an isometric restriction of the TNS ansatz that allows for highly efficient…
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…
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…
Situated as a language between computer science, quantum physics and mathematics, tensor network theory has steadily grown in popularity and can now be found in applications ranging across the entire field of quantum information processing.…
Tensor networks (TNs) enable compact representations of large tensors through shared parameters. Their use in probabilistic modeling is particularly appealing, as probabilistic tensor networks (PTNs) allow for tractable computation of…
Matrix and tensor operations form the basis of a wide range of fields and applications, and in many cases constitute a substantial part of the overall computational complexity. The ability of general-purpose GPUs to speed up many of these…
This paper explores the application of tensor networks (TNs) to the simulation of material deformations within the framework of linear elasticity. Material simulations are essential computational tools extensively used in both academic…
In recent years, tree tensor network methods have proven capable of simulating quantum many-body and other high-dimensional systems. This work is a user guide to our Python library PyTreeNet. It includes code examples and exercises to…
Matrix product states (MPS), a tensor network designed for one-dimensional quantum systems, has been recently proposed for generative modeling of natural data (such as images) in terms of `Born machine'. However, the exponential decay of…
The interplay of quantum and classical simulation and the delicate divide between them is in the focus of massively parallelized tensor network state (TNS) algorithms designed for high performance computing (HPC). In this contribution, we…