New Routes from Topological Materials to Quantum Computing

近年来，拓扑学的概念在室温下的实际材料中得到了显著的应用。存在一种全新的“拓扑材料”，即表面具有坚固金属态的半导体。就像球体不经过剧烈的转变就不能变形成甜甜圈一样，这些拓扑材料不经过相变就不能剥夺其迷人的特性。除了这种拓扑材料之外，理论家还预测了“分块化”拓扑相，其中包含与原始自由度完全不同的涌现粒子。这种相包含一种叫做任意子的粒子，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是必不可少的，这涉及到将这些任意子彼此移动（“编织”）以实现计算操作。这种非局部行为对不完美具有很强的鲁棒性，使这些系统成为量子计算的一个有前途的平台，量子计算是一种对科学和社会具有广泛影响的全新技术。

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.