EAGER: BRAIDING: High order non-Abelian excitations for topologically protected qubits

非技术摘要：量子统计是量子力学理解世界的核心。所有已知的粒子都有所谓的阿贝尔统计，这意味着几个连续粒子交换的结果不依赖于交换的顺序。最近有人提出，具有非阿贝尔统计的粒子可以在一些奇异系统中实现，并且已经报道了最简单的这种非阿贝尔粒子-马约拉纳费米子的签名。除了科学好奇心之外，寻找这些难以捉摸的激发的主要驱动力是实现容错量子计算机的可能性。基于马约拉纳费米子的量子比特有其局限性，这项提议的主要目标是开发一种新的系统，在这种系统中可以实现计算上更有用的高阶非阿贝尔激发。技术摘要：提出的研究的主要目标是开发一个系统，高阶非阿贝尔激励可以实现和操纵。非阿贝尔统计（几个相同粒子连续交换的结果取决于交换顺序的概念）是实现容错量子计算机的革命性概念的核心。目前的努力集中在基于马约拉纳的量子比特的开发上，这是最简单的非阿贝尔粒子。然而，基于马约拉纳的量子比特在计算上并不通用，并且需要更高阶的非阿贝尔来实现通用门。具体而言，自旋跃迁的分数量子霍尔效应制度将探讨实现可重构网络的螺旋通道与分数带电激发。在这些通道中诱导超导性的证明将是主要的里程碑。在平凡和拓扑非平凡超导体的边界处形成的激发的量子统计将在多栅极器件中进行研究，其中拓扑通道网络可以在二维平面内重新配置。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

Nontechnical Abstract: Quantum statistics is central to the quantum mechanical understanding of the world. All known particles have so-called Abelian statistics, meaning that result of several consecutive particle exchanges does not depend on the order of the exchanges. Recently it has been proposed that particles with non-Abelian statistics can be realized in some exotic systems, and signatures of simplest such non-Abelian particles - Majorana fermions - have been reported. The main driving force in the search for these elusive excitations, apart from scientific curiosity, is a possibility to realize a fault tolerant quantum computer. Qubits based on Majorana fermions have their limitations, and the main objective on this proposal is to develop a new system where more computationally useful higher order non-Abelian excitations can be realized. Technical Abstract: The main objective of the proposed research is to develop a system where high-order non-Abelian excitations can be realized and manipulated. The non-Abelian statistics (the notion that a result of consecutive exchanges of several identical particles depends on the order of the exchanges) is at the heart of a revolutionary concept to realize a fault-tolerant quantum computer. Current efforts are focused on the development of Majorana-based qubits, the simplest non-Abelian particles. Majorana-based qubits are not computationally universal, though, and higher order non-Abelions are required to realize a universal gate. Specifically, spin transitions in the fractional quantum Hall effect regime will be explored to realize a reconfigurable network of helical channels with fractionalized charged excitations. Demonstration of induced superconductivity in these channels will be the major milestone. Quantum statistics of excitations formed at a boundary of trivial and topologically non-trivial superconductors will be investigated in multi-gate devices, where network of topological channels can be reconfigured within a two-dimensional plane.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.