Topological quantum computation has emerged as one of the most exciting approaches to
constructing a fault-tolerant quantum computer. The proposal relies on the existence of …

Quantum mechanics classifies all elementary particles as either fermions or bosons, and this
classification is crucial to the understanding of a variety of physical systems, such as lasers …

We examine the interplay of symmetry and topological order in 2+ 1-dimensional topological
quantum phases of matter. We present a precise definition of the topological symmetry …

In the fractional quantum Hall effect, quasiparticles are collective excitations that have a
fractional charge and show fractional statistics as they interchange positions. While the …

We show that an ordinary semiconducting thin film with spin-orbit coupling can, under
appropriate circumstances, be in a quantum topologically ordered state supporting exotic …

Quasiparticles with fractional charge and fractional statistics are key features of the fractional
quantum Hall effect. We discuss in detail the definitions of fractional charge and statistics …

Topological quantum computation is a computational paradigm based on topological
phases of matter, which are governed by topological quantum field theories. In this …

The dichotomy between fermions and bosons is at the root of many physical phenomena,
from metallic conduction of electricity to super-fluidity, and from the periodic table to coherent …

We investigate transitions between topologically ordered phases in two spatial dimensions
induced by the condensation of a bosonic quasiparticle. To this end, we formulate an …

The finding of physical realizations of topologically ordered states in experimental settings,
from condensed matter to artificial quantum systems, has been the main challenge en route …