In this review recent investigations are summarized of many-body quantum systems with
long-range interactions, which are currently realized in Rydberg atom arrays, dipolar …

Experimental progress in atomic, molecular, and optical platforms in the last decade has
stimulated strong and broad interest in the quantum coherent dynamics of many long-range …

Classical machine learning (ML) provides a potentially powerful approach to solving
challenging quantum many-body problems in physics and chemistry. However, the …

The Lie-Trotter formula, together with its higher-order generalizations, provides a direct
approach to decomposing the exponential of a sum of operators. Despite significant effort …

Continuously monitoring the environment of a quantum many-body system reduces the
entropy of (purifies) the reduced density matrix of the system, conditional on the outcomes of …

We review the mathematical speed limits on quantum information processing in many-body
systems. After the proof of the Lieb–Robinson Theorem in 1972, the past two decades have …

The competition between scrambling unitary evolution and projective measurements leads
to a phase transition in the dynamics of quantum entanglement. Here, we demonstrate that …

This tutorial article introduces the physics of quantum information scrambling in quantum
many-body systems. The goals are to understand how to precisely quantify the spreading of …

We consider quantum many-body dynamics under quantum measurements, where the
measurement-induced phase transitions (MIPs) occur when changing the frequency of the …

Laser-cooled and trapped atomic ions form an ideal standard for the simulation of interacting
quantum spin models. Effective spins are represented by appropriate internal energy levels …