New Routes from Topological Materials to Quantum Computing

近年来，拓扑学的概念在室温下的真实材料中得到了显著的应用。存在着一种全新的“拓扑材料”，它们是表面具有强健金属状态的半导体。同样地，如果没有剧烈的变换，球就不能变形成甜甜圈，如果没有相变，这些拓扑材料就不能剥夺其迷人的性质。除了这种拓扑材料之外，理论家们还预测了与原始自由度完全不同的“分步”拓扑相，这些拓扑相包含了与原始自由度完全不同的新兴粒子。这种相包含称为任意子的粒子，它既不是玻色子，也不是费米子。这些成分对于拓扑量子计算来说是必不可少的，这涉及到将这些任意子围绕着彼此移动(“编织”)，以实现计算操作。这种非本地行为对不完美具有很强的抵抗力，使这些系统成为量子计算的一个很有前途的平台，这是一项对科学和社会产生广泛影响的全新技术。然而，一个严重而持久的挑战限制了该领域，那就是预测实现这种细分阶段的新的实验系统。我的长期研究计划将包括开发新的途径，通过使用现有的拓扑材料作为构建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项全新的技术；这项创新的技术既产生了微观模型，也产生了合成量子系统(如超冷原子和超导平台)中的分级相的具体建议。同时，我的研究计划将探索新的技术来操纵由超导拓扑材料产生的被称为“马约拉纳模式”的物体。从拓扑材料到量子计算的这些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增长领域的作用。近年来，凝聚态物质和量子信息理论领域逐渐交织在一起，这笔发现号拨款将大量来自这两个领域，以取得进展。这样的跨学科项目非常有利于培养学生，他们在参与这一计划后将获得全面的技能集和综合视角。因此，发现基金将在实现分步阶段和拓扑量子计算平台这一重要问题上发挥关键作用，并为学生提供基本的研究技能。

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.