From Higher-Order Topological Superconductors to Topological Quantum Codes.

从高阶拓扑超导体到拓扑量子码。

• 批准号: 2126016
• 金额: --
• 依托单位: University of Cambridge
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2018
• 资助国家: 英国
• 起止时间: 2018 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2126016
• 关键词: Higher; Order; Topological; Superconductors; Quantum

The discovery of a new class of materials known as topological insulators has been cause for great excitement over the past decade owing to the possibility of realising novel phenomena such as insulating materials with highly conducting surfaces. The key to these surprising properties lies in the topology of these systems, that is, global, quantised, characteristics of the bulk material that are insensitive to local imperfections such as defects and impurities. The theoretical advancements in describing such materials have allowed for the topological classification of a further class of many-body systems, namely topological superconductors (TSCs).While the classification of TSCs is now fairly established, much current attention has shifted to a new subclass of TSCs known as higher-order TSCs. These systems display even more exotic properties deriving from spatial symmetries. Under certain circumstances, one may predict the existence of exotic corner-bound zero-energy objects that lead to a nonlocally supported ground state degeneracy. Novel examples indicate that, for certain forms of interactions, such systems may also support topologically ordered phases closely related to topological quantum codes. Such codes form one of the most promising schemes for quantum error correction and may lead to quantum computers robust against most relevant sources of disturbances.The goal of this project is to develop a classification of higher-order TSCs and, based on this, to investigate the connection between interacting higher-order TSCs and topological quantum codes. We will build on, and develop further, existing theoretical frameworks for characterising topological materials and correlated forms of topological order. We plan to support our formal theoretical findings with numerical simulations.

在过去的十年中，一类新材料的发现被称为拓扑绝缘体，这是由于实现新现象的可能性，例如具有高导电表面的绝缘材料。这些令人惊讶的特性的关键在于这些系统的拓扑结构，即，整体的，量化的，对局部缺陷（如缺陷和杂质）不敏感的散装材料的特性。描述这种材料的理论进步已经允许对另一类多体系统进行拓扑分类，即拓扑超导体（TSCs）。虽然TSCs的分类现在已经相当确定，但目前的注意力已经转移到一个新的TSCs子类，称为高阶TSCs。这些系统显示出更多来自空间对称性的奇异性质。在某些情况下，人们可以预言存在奇异的角束缚零能量物体，导致非局部支持的基态简并。新的例子表明，对于某些形式的相互作用，这样的系统也可能支持拓扑有序的相位密切相关的拓扑量子代码。这类编码是量子纠错的最有前途的方案之一，并且可能导致量子计算机对大多数相关干扰源的鲁棒性。本项目的目标是开发高阶TSC的分类，并在此基础上，研究相互作用的高阶TSC和拓扑量子编码之间的联系。我们将建立在，并进一步发展，现有的理论框架的特点拓扑材料和相关形式的拓扑秩序。我们计划用数值模拟来支持我们的正式理论研究结果。