Abstract
AbstractWe provide a current perspective on the rapidly developing field of Majorana zero modes (MZMs) in solid-state systems. We emphasise the theoretical prediction, experimental realisation and potential use of MZMs in future information processing devices through braiding-based topological quantum computation (TQC). Well-separated MZMs should manifest non-Abelian braiding statistics suitable for unitary gate operations for TQC. 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. 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. 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 describe proposed schemes for carrying out braiding with MZMs as well as the necessary steps for implementing TQC.
Highlights
Topological quantum computation[1,2] is an approach to faulttolerant quantum computation in which the unitary quantum gates result from the braiding of certain topological quantum objects called ‘anyons’
Not all anyons are directly useful in topological quantum computation (TQC); only non-Abelian anyons are useful, which does not include the anyonic excitations that are believed to occur in most odd-denominator fractional quantum Hall states
Perhaps the simplest realisation of a non-Abelian anyon is a quasiparticle or defect supporting a Majorana zero mode (MZM). (The zero mode here refers to the zero-energy midgap excitations that these localised quasiparticles typically correspond to in a lowdimensional topological superconductor.) This is a real fermionic operator that commutes with the Hamiltonian
Summary
We provide a current perspective on the rapidly developing field of Majorana zero modes (MZMs) in solid-state systems. We emphasise the theoretical prediction, experimental realisation and potential use of MZMs in future information processing devices through braiding-based topological quantum computation (TQC). Well-separated MZMs should manifest non-Abelian braiding statistics suitable for unitary gate operations for TQC. 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. 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. We discuss fractional quantum Hall systems (the 5/2 state), which have been extensively studied in the context of non-Abelian anyons and TQC. Npj Quantum Information (2015) 1, 15001; doi:10.1038/npjqi.2015.1; published online 27 October 2015
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