马约拉纳零能模的非阿贝尔统计及其在拓扑量子计算的应用

自1937年被预言以来,马约拉纳费米子在粒子物理领域和暗物质领域就广受关注.它们在凝聚态物理中的"副本",马约拉纳零能模(Majorana zero mode,MZM),被指出可以通过拓扑超导实现,并由于满足非阿贝尔统计及可以用来实现容错的量子计算机而成为凝聚态领域最受关注的研究方向之一.尤其在近二十年中,马约拉纳零能模在理论和实验方面均取得了诸多重要进展,一些综述文章对此做了较详细介绍.本文将会重点回顾MZM的非阿贝尔统计性质以及它们在量子计算中的应用.文章的第一部分首先简单介绍了凝聚态系统中MZM的理论发展并概述了在人工异质结体系中寻找MZM的最新理论和实验进展.然后介绍了MZM非阿贝尔统计的基本概念,并讨论这一性质怎样应用到量子计算中.接下来重点讨论了利用MZM平台实现量子计算机的两个关键步骤:MZM非阿贝尔编织操作的实验实现方案和MZM量子比特的读取.在这一部分里,本文分别详细列举了现有的比较受关注的实现MZM编织操作和量子比特的读取实验装置.最后,文章介绍了在对称性保护的拓扑超导系统中实现马约拉纳的对称保护非阿贝尔统计的可能性.

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

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 faulttolerant 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.