Abrikosov vortices in a topological superconductor are an example of the latter. 4, 5 Fractionally charged excitations of the Laughlin fractional quantum Hall liquid are an example of the former. Anyons can arise in two ways: as localised excitations of an interacting quantum Hamiltonian 3 or as defects in an ordered system.

Anyons braid non-trivially: two counterclockwise exchanges do not leave the state of the system invariant, unlike in the cases of bosons or fermions. Topological quantum computation 1, 2 is an approach to fault-tolerant quantum computation in which the unitary quantum gates result from the braiding of certain topological quantum objects called ‘anyons’. We describe proposed schemes for carrying out braiding with MZMs as well as the necessary steps for implementing TQC. We also discuss fractional quantum Hall systems (the 5/2 state), which have been extensively studied in the context of non-Abelian anyons and TQC.

We discuss the experimental findings and their theoretical analyses, and provide a perspective on the extent to which the observations indicate the existence of anyonic MZMs in solid-state systems. Recent experimental work, following earlier theoretical predictions, has shown specific signatures consistent with the existence of Majorana modes localised at the ends of semiconductor nanowires in the presence of superconducting proximity effect. Well-separated MZMs should manifest non-Abelian braiding statistics suitable for unitary gate operations for TQC. We emphasise the theoretical prediction, experimental realisation and potential use of MZMs in future information processing devices through braiding-based topological quantum computation (TQC). We provide a current perspective on the rapidly developing field of Majorana zero modes (MZMs) in solid-state systems.

Braid society fill the gap