Related papers: TNSPackage: A Fortran2003 library designed for ten…

Tensor networks are efficient for extremely high-dimensional representation, but their model selection, known as tensor network structure search (TN-SS), is a challenging problem. Although several works have targeted TN-SS, most existing…

Tensor methods have become a promising tool to solve high-dimensional problems in the big data era. By exploiting possible low-rank tensor factorization, many high-dimensional model-based or data-driven problems can be solved to facilitate…

Efficient methods to access the entanglement of a quantum many-body state, where the complexity generally scales exponentially with the system size $N$, have long a concern. Here we propose the Schmidt tensor network state (Schmidt TNS)…

We introduce a learning-based framework to optimize tensor programs for deep learning workloads. Efficient implementations of tensor operators, such as matrix multiplication and high dimensional convolution, are key enablers of effective…

Simulation of quantum systems is challenging due to the exponential size of the state space. Tensor networks provide a systematically improvable approximation for quantum states. 2D tensor networks such as Projected Entangled Pair States…

We introduce SeeMPS, a Python library dedicated to implementing tensor network algorithms based on the well-known Matrix Product States (MPS) and Quantized Tensor Train (QTT) formalisms. SeeMPS is implemented as a complete finite precision…

Tensor programs often need to process large tensors (vectors, matrices, or higher order tensors) that require a specialized storage format for their memory layout. Several such layouts have been proposed in the literature, such as the…

Neural Tensor Networks (NTNs), which are structured to encode the degree of relationship among pairs of entities, are used in Logic Tensor Networks (LTNs) to facilitate Statistical Relational Learning (SRL) in first-order logic. In this…

Tensor networks (TNs) are a central computational tool in quantum science and artificial intelligence. However, the lack of unified software interface across tensor-computing frameworks severely limits the portability of TN applications,…

Numerical simulations based on particle methods have been widely used in various fields including astrophysics. To date, simulation softwares have been developed by individual researchers or research groups in each field, with a huge amount…

Tree tensor network states (TTNS) decompose the system wavefunction to the product of low-rank tensors based on the tree topology, serving as the foundation of the multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) method. In…

We propose a generalized Lanczos method to generate the many-body basis states of quantum lattice models using tensor-network states (TNS). The ground-state wave function is represented as a linear superposition composed from a set of TNS…

From FORTRAN to NumPy, tensors have revolutionized how we express computation. However, tensors in these, and almost all prominent systems, can only handle dense rectilinear integer grids. Real world tensors often contain underlying…

Quantum many-body systems are challenging targets for computational physics due to their large degrees of freedom. The tensor networks, particularly Tensor Product States (TPS) and Projected Entangled Pair States (PEPS), effectively…

Deep neural networks (DNNs) frequently contain far more weights, represented at a higher precision, than are required for the specific task which they are trained to perform. Consequently, they can often be compressed using techniques such…

In the rapidly evolving field of quantum computing, tensor networks serve as an important tool due to their multifaceted utility. In this paper, we review the diverse applications of tensor networks and show that they are an important…

Although many active scientific codes use modern Fortran, most contemporary scientific software "libraries" are implemented in C and C++. Providing their numerical, algorithmic, or data management features to Fortran codes requires writing…

Tensor network (TN) methods are well established for computing partition functions in statistical mechanics, though this use has traditionally been limited to lattice models. We extend the scope of TN methodology to interacting particle…

Despite the omnipresence of tensors and tensor operations in modern deep learning, the use of tensor mathematics to formally design and describe neural networks is still under-explored within the deep learning community. To this end, we…

Tensors, or multidimensional arrays, are data structures that can naturally represent visual data of multiple dimensions. Inherently able to efficiently capture structured, latent semantic spaces and high-order interactions, tensors have a…