Topological quantum codes on surfaces with lattice defects

一个系统的秩序是由其组成部分相互间的组织方式决定的。这种顺序表征了物质的不同相，一个系统的量子相指的是它的基态。它的最低能态。该项目将在这样的二维系统中进行研究，并增加特征，即新兴粒子，它们可以在相互和自交换下拾取任何相位（统计），因此得名。这些是物质的拓扑相，也是2016年诺贝尔奖授予索利斯、科斯特利茨和霍尔丹的主题。移动任意子的集合，同时以特定的方式交叉它们的路径，这被称为编织它们的世界线，并产生可用于计算和其他形式的信息处理的逻辑门。这些系统研究的直接应用将是允许“释放更多硬件”的拓扑量子存储器，用于各种计算和模拟的拓扑量子计算机，以及使量子计算对实验量子设置中必然出现的局部扰动具有鲁棒性的纠错方案的构建。该博士项目将研究具有有趣工程缺陷的晶格系统中物质拓扑相的奇异性质，并将以促进可靠的容错量子计算的量子信息和计算方案为总体目标进行，同时也为使用量子信息工具进行基本凝聚态物质和拓扑量子物理的探索性工作提供基础。

The order of a system is dened by the way its constituents are organised with respect to each other. Such order characterises different phases of matter, with the quantum phase of a system referring to its ground state, ie. its lowest energy conguration. This project will conduct investigations in such two-dimensional systems, with added characteristics, namely emerging particles which can pick up any phases (statistics) under their mutual and self-exchange, hence their name. These are topological phases of matter, and were the subject of the 2016 Nobel Prize to Thouless, Kosterlitz, and Haldane. Moving a collection of anyons while intersecting their paths in specific ways is referred to as braiding their worldlines, and gives rise to logic gates that can be used for computation and other forms of information processing. Direct applications of studies of these systems would be topological quantum memories allowing to \free up more hardware", topological quantum computers for diverse calculations and simulations, and the construction of error-correcting schemes rendering quantum computation robust to local perturbations which are bound to arise in experimental quantum set-ups.This PhD project will study exotic properties of topological phases of matter, in lattice systems with interesting engineered defects, and will be conducted with the general aim of contributing to quantum informational and computational schemes towards reliable fault-tolerant quantum computation, while also providing a ground for exploratory work on fundamental condensed matter and topological quantum physics using quantum information tools.