In the past two decades, the density matrix renormalization group (DMRG) has emerged as
an innovative new method in quantum chemistry relying on a theoretical framework very …

During the last years, low‐rank tensor approximation has been established as a new tool in
scientific computing to address large‐scale linear and multilinear algebra problems, which …

Tensor networks have in recent years emerged as the powerful tools for solving the large-
scale optimization problems. One of the most popular tensor network is tensor train (TT) …

The treatment of high‐dimensional problems such as the Schrödinger equation can be
approached by concepts of tensor product approximation. We present general techniques …

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

We propose algorithms for the solution of high-dimensional symmetrical positive definite
(SPD) linear systems with the matrix and the right-hand side given and the solution sought in …

Effectively compressing and optimizing tensor networks requires reliable methods for fixing
the latent degrees of freedom of the tensors, known as the gauge. Here we introduce a new …

Hierarchical tensors can be regarded as a generalisation, preserving many crucial features,
of the singular value decomposition to higher-order tensors. For a given tensor product …

Quantum state preparation is a vital routine in many quantum algorithms, including solution
of linear systems of equations, Monte Carlo simulations, quantum sampling, and machine …

Tensors arise naturally in high-dimensional problems in chemistry, financial mathematics,
and many other areas. The numerical treatment of such problems is difficult due to the curse …