New Routes from Topological Materials to Quantum Computing

近年来，拓扑学的概念在室温下的真实的材料中得到了显著的应用。 存在一种全新的“拓扑材料”，它们是在其表面上具有稳健金属态的半导体。 就像一个球不可能在没有剧烈转变的情况下变形成甜甜圈一样，这些拓扑材料不可能在没有相变的情况下被剥夺其迷人的特性。 除了这些拓扑材料，理论家们还预测了“分形”拓扑相，其中包含了与原始自由度完全不同的涌现粒子。 这些相包含称为任意子的粒子，它们既不是玻色子也不是费米子。 这些成分对于拓扑量子计算是必不可少的，拓扑量子计算涉及将这些任意子相互移动（“编织”）以实现计算操作。 这种非局域行为对不完美性具有鲁棒性，使这些系统成为量子计算的一个有前途的平台，这是一项对科学和社会产生广泛影响的全新技术。 ** 然而，限制该领域的一个严峻而持久的挑战是预测实现这种细分阶段的新实验系统。 我的长期研究计划将涉及开发新的路线，通过使用现有的拓扑材料作为构建模块来实现这种细分系统。在拟议的研究中，我将应用我最近开发的一种全新技术;这种创新技术为合成量子系统（如超冷原子和超导平台）中的分数相产生了微观模型和具体建议。 与此同时，我的研究计划将探索新的技术来操纵从超导拓扑材料中产生的被称为“马约拉纳模式”的物体。 这些从拓扑材料到量子计算的新的具体路线图将加强加拿大在凝聚态理论，量子信息和量子计算等快速发展领域的作用。 近年来，凝聚态和量子信息理论的领域已经逐渐交织在一起，而这项发现资助将从这两个领域中获得大量资金，以取得进展。 这样的跨学科项目对于培训学生非常有益，他们在参与该项目后将获得全面的技能和综合视角。 因此，发现补助金将在实现分数阶段和拓扑量子计算平台的重要问题上取得进展，并为学生提供基本的研究技能方面发挥关键作用。

In recent years, concepts from topology have found remarkable applications to real materials at room temperature. There exists an entirely new class of “topological materials” which are semiconductors with robust metallic states on their surfaces. In the same way that a ball cannot be deformed into a donut without a drastic transformation, these topological materials cannot be stripped of their fascinating properties without a phase transition. Beyond such topological materials, theorists have predicted “fractionalized” topological phases which host emergent particles completely different from the original degrees of freedom. Such phases contain particles called anyons which are neither bosons nor fermions. These ingredients are essential for topological quantum computation, which involves moving (“braiding”) these anyons around each other to realize computational operations. Such nonlocal actions are robust against imperfections, making these systems a promising platform for quantum computinga fundamentally new technology with broad repercussions for science and society. ******However, a severe, persistent challenge that has limited the field is predicting new experimental systems realizing such fractionalized phases. My long-term research program will involve developing new routes to achieve such fractionalized systems by using existing topological materials as building blocks. In the proposed research, I will apply a fundamentally new technique that I recently developed; this innovative technique yields both microscopic models and concrete proposals for fractionalized phases in synthetic quantum systems such as ultracold atoms and superconducting platforms. In parallel, my research program will explore new techniques to manipulate objects called “Majorana modes” arising from superconducting topological materials. ******These new concrete roadmaps from topological materials to quantum computing will strengthen Canada's role in the rapidly growing fields of condensed matter theory, quantum information, and quantum computation. The fields of condensed matter and quantum information theory have become progressively intertwined in recent years, and this Discovery grant will draw heavily from both fields to make progress. Such an interdisciplinary program is very beneficial for training students, who will gain a well-rounded skill set and synthetic perspective after working in this initiative. The Discovery grant will thus play a critical role in both enabling progress on the important problem of realizing fractionalized phases and topological quantum computing platforms and providing students with essential research skills.