New Routes from Topological Materials to Quantum Computing

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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 computing—a 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.