In this review, after providing the basic physical concept behind quantum annealing (or
adiabatic quantum computation), we present an overview of some recent theoretical as well …

This Colloquium gives an overview of recent theoretical and experimental progress in the
area of nonequilibrium dynamics of isolated quantum systems. There is particularly a focus …

The transverse field Ising and XY models (the simplest quantum spin models) provide the
organising principle for the rich variety of interconnected subjects which are covered in this …

We review recent theoretical work on two closely related issues: excitation of an isolated
quantum condensed matter system driven adiabatically across a continuous quantum phase …

Quantum annealing is a general strategy for solving difficult optimization problems with the
aid of quantum adiabatic evolution. Both analytical and numerical evidence suggests that …

The number of topological defects created in a system driven through a quantum phase
transition exhibits a power-law scaling with the driving time. This universal scaling law is the …

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 …

We introduce a scheme for the quantum simulation of many-body decoherence based on
the unitary evolution of a stochastic Hamiltonian. Modulating the strength of the interactions …

We study the dynamical response of a system to a sudden change of the tuning parameter λ
starting (or ending) at the quantum critical point. In particular, we analyze the scaling of the …

We discuss quantum annealing of the two-dimensional transverse-field Ising model on a D-
Wave device, encoded on L× L lattices with L≤ 32. Analyzing the residual energy and …