Non-abelian statistics of Majorana modes and the applications to topological quantum computation

Abstract

Since their prediction as fundamental particles in 1937, Majorana fermions have drawn lots of interests in particle physics and dark matter. Their counterparts in condensed matter physics, Majorana zero-Modes (MZMs), have attracted remarkable attention in condensed matter for their potential in building a fault-tolerant quantum computer. Due to the relentless effort, lots of important progress has been made in Majorana physics in the past two decades, as introduced in several excellent review articles. This review focuses on the non-Abelian statistics of MZMs and their application to quantum computation. In the first section of this work, the theoretical progress in searching for MZM is briefly reviewed and the latest experimental progresses are summarized. We next introduce the basic concepts of non-Abelian statistics of MZMs and explain how they can be applied to quantum computation. We then discuss two key experiments to implementing quantum computers in the MZM platform: MZM braiding and MZM qubit readout. In this part, several representative proposals for the Majorana braiding and MZM qubit readout are elaborated. Finally, we introduce a latest concept, the symmetry-protected non-Abelian braiding of Majorana Kramers pairs in time-reversal invariant topological superconductors.