We review selected advances in the theoretical understanding of complex quantum many-
body systems with regard to emergent notions of quantum statistical mechanics. We cover …

Recent experimental developments in diverse areas—ranging from cold atomic gases to
light-driven semiconductors to microcavity arrays—move systems into the focus which are …

Artificial neural networks are the heart of machine learning algorithms and artificial
intelligence. Historically, the simplest implementation of an artificial neuron traces back to …

The study of open quantum systems–microscopic systems exhibiting quantum coherence
that are coupled to their environment–has become increasingly important in the past years …

In this article we provide a review of geometrical methods employed in the analysis of
quantum phase transitions and non-equilibrium dissipative phase transitions. After a …

The field of classical stochastic processes forms a major branch of mathematics. Stochastic
processes are, of course, also very well studied in biology, chemistry, ecology, geology …

The past few years have witnessed the concrete and fast spreading of quantum
technologies for practical computation and simulation. In particular, quantum computing …

Quantum computers hold the promise to solve certain problems exponentially faster than
their classical counterparts. Trapped atomic ions are among the physical systems in which …

Entangled states are a key resource in fundamental quantum physics, quantum
cryptography and quantum computation. Introduction of controlled unitary processes …

Logical qubits can be protected from decoherence by performing quantum error-correction
(QEC) cycles repeatedly. Algorithms for fault-tolerant QEC must be compiled to the specific …