During the last ten years, superconducting circuits have passed from being interesting
physical devices to becoming contenders for near-future useful and scalable quantum …

Low-rank tensor representations can provide highly compressed approximations of
functions. These concepts, which essentially amount to generalizations of classical …

Tensor completion recovers missing entries of multiway data. The missing of entries could
often be caused during the data acquisition and transformation. In this paper, we provide an …

The global (patch-wise) geometry map, which describes the computational domain, is a new
feature in isogeometric analysis. This map has a global tensor structure, inherited from the …

Sparse tensors appear in many large-scale applications with multidimensional and sparse
data. While multidimensional sparse data often need to be processed on manycore …

Tensor contractions constitute a key computational ingredient of numerical multi-linear
algebra. However, as the order and dimension of tensors grow, the time and space …

Randomized algorithms are efficient techniques for big data tensor analysis. In this tutorial
paper, we review and extend a variety of randomized algorithms for decomposing large …

Multi-configurational time-dependent Hartree (MCTDH) based approaches are efficient,
accurate, and versatile methods for high-dimensional quantum dynamics simulations …

The Matsubara Green's function that is used to describe temperature-dependent behavior is
expressed on a numerical grid. While such a grid usually has a couple of hundred points for …

We introduce novel algorithmic solutions for hybrid CPU-multiGPU tensor network state
algorithms utilizing non-Abelian symmetries building on AI-motivated state-of-the-art …