Related papers: Computing vibrational energy levels by solving lin…
This paper proposes a novel formulation of the tensor completion problem to impute missing entries of data represented by tensors. The formulation is introduced in terms of tensor train (TT) rank which can effectively capture global…
Finding the rank of a tensor is a problem that has many applications. Unfortunately it is often very difficult to determine the rank of a given tensor. Inspired by the heuristics of convex relaxation, we consider the nuclear norm instead of…
This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks…
Higher-order tensor datasets arise commonly in recommendation systems, neuroimaging, and social networks. Here we develop probable methods for estimating a possibly high rank signal tensor from noisy observations. We consider a generative…
Tensor cores, along with tensor processing units, represent a new form of hardware acceleration specifically designed for deep neural network calculations in artificial intelligence applications. Tensor cores provide extraordinary…
We consider a variational problem for the two-dimensional (2D) Heisenberg and XY models, using a trial state which is constructed as a 2D product of local weights. Variational energy is calculated by use of the the corner transfer matrix…
The CP tensor decomposition is used in applications such as machine learning and signal processing to discover latent low-rank structure in multidimensional data. Computing a CP decomposition via an alternating least squares (ALS) method…
We investigate the low-rank tensor recovery problem using a relaxation of the nuclear p-norm by theta bodies. We provide algebraic descriptions of the norms and compute their Gr\"obner bases. Moreover, we develop geometric properties of…
We present a novel analysis of the dynamics of tensor power iterations in the overcomplete regime where the tensor CP rank is larger than the input dimension. Finding the CP decomposition of an overcomplete tensor is NP-hard in general. We…
A new physical implementation for quantum computation is proposed. The vibrational modes of molecules are used to encode qubit systems. Global quantum logic gates are realized using shaped femtosecond laser pulses which are calculated…
The tensor rank decomposition, also known as canonical polyadic(CP) or simply tensor decomposition, has a long history in multilinear algebra. However, computing a rank decomposition becomes particularly challenging when the rank lies…
The article describes a new approach to obtaining the energy-momentum tensor of electromagnetic field in medium without the use of Maxwell's equations and Poynting theorem. The energy-momentum tensor has new qualities and consequences. Its…
We introduce a framework for the calculation of ground and excited state energies of bosonic systems suitable for near-term quantum devices and apply it to molecular vibrational anharmonic Hamiltonians. Our method supports generic reference…
Tensors, especially higher-order tensors, are typically represented in low-rank formats to preserve the main information of the high-dimensional data while saving memory space. In practice, only a small fraction elements in high-dimensional…
This paper introduces a new multivariate convolutional sparse coding based on tensor algebra with a general model enforcing both element-wise sparsity and low-rankness of the activations tensors. By using the CP decomposition, this model…
Estimating vibrational entropy is a significant challenge in thermodynamics and statistical mechanics due to its reliance on quantum mechanical properties. This paper introduces a quantum algorithm designed to estimate vibrational entropy…
An iterative method we previously proposed to compute nuclear strength functions is developed to allow it to accurately calculate properties of individual nuclear states. The approach is based on the quasi-particle-random-phase…
Machine learning has revolutionized the high-dimensional representations for molecular properties such as potential energy. However, there are scarce machine learning models targeting tensorial properties, which are rotationally covariant.…
An overview of theories related to vibrational energy relaxation (VER) in proteins is presented. VER of a selected mode in cytochrome c is studied using two theoretical approaches. One is the equilibrium simulation approach with quantum…
Fabrication process variations can significantly influence the performance and yield of nano-scale electronic and photonic circuits. Stochastic spectral methods have achieved great success in quantifying the impact of process variations,…