Quantum random sampling is the leading proposal for demonstrating a computational
advantage of quantum computers over classical computers. Recently the first large-scale …

After many years of development of the basic tools, quantum simulation with ultracold atoms
has now reached the level of maturity at which it can be used to investigate complex …

Quantum phase transitions (QPTs) involve transformations between different states of matter
that are driven by quantum fluctuations. These fluctuations play a dominant part in the …

With the rapid development of quantum technologies, a pressing need has emerged for a
wide array of tools for the certification and characterization of quantum devices. Such tools …

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 …

How do closed quantum many-body systems driven out of equilibrium eventually achieve
equilibration? And how do these systems thermalize, given that they comprise so many …

Kibble-Zurek theory models the dynamics of spontaneous symmetry breaking, which plays
an important role in a wide variety of physical contexts, ranging from cosmology to …

We review the recent progress in the understanding of the relaxation of isolated near-
integrable quantum many-body systems. Focusing on prethermalization and universal …

The many-body physics at quantum phase transitions shows a subtle interplay between
quantum and thermal fluctuations, emerging in the low-temperature limit. In this review, we …

Phase transitions are ubiquitous in our three-dimensional world. By contrast, most
conventional transitions do not occur in infinite uniform low-dimensional systems because of …