The theory of entanglement provides a fundamentally new language for describing
interactions and correlations in many-body systems. Its vocabulary consists of qubits and …

A review is given on the foundations and applications of non-Hermitian classical and
quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra …

Modern quantum machine learning (QML) methods involve variationally optimizing a
parameterized quantum circuit on a training data set, and subsequently making predictions …

Originally developed in the context of condensed-matter physics and based on
renormalization group ideas, tensor networks have been revived thanks to quantum …

The thermodynamic description of many-particle systems rests on the assumption of
ergodicity, the ability of a system to explore all allowed configurations in the phase space …

Tensor networks provide extremely powerful tools for the study of complex classical and
quantum many-body problems. Over the past two decades, the increment in the number of …

Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum
many-body systems in and out of equilibrium. In particular, the one-dimensional matrix …

Machine learning, one of today's most rapidly growing interdisciplinary fields, promises an
unprecedented perspective for solving intricate quantum many-body problems …

We review the dynamics after quantum quenches in integrable quantum spin chains. We
give a pedagogical introduction to relaxation in isolated quantum systems, and discuss the …

Parameterized quantum circuits are a promising technology for achieving a quantum
advantage. An important application is the variational simulation of time evolution of …