Physical Platforms for Topological Quantum Computation

非技术总结该奖项通过操纵由许多电子组成的物质的量子态来支持量子计算的理论研究和教育。量子计算机承诺为某些计算任务提供指数级的加速，而这些任务在现代经典计算机中是不可行的。潜在的好处将从量子化学到设计新的药物和材料，再到密码应用。建造一台工作的量子计算机的主要障碍之一是退相干：通过与周围环境相互作用，量子比特往往会变得越来越经典。因此，在很短的时间内，基于量子力学定律进行计算的所有潜在优势都消失了。拓扑量子计算(TQC)的思想通过在大量相互作用的粒子的组合态中编码量子信息来绕过这个问题，而不是依赖于单个粒子的量子态，后者更容易受到通常的消相干源的影响。这种强健的多粒子量子态，称为拓扑有序态，可能存在于材料中，或者材料可能被设计成支持这种状态。但拓扑量子比特和逻辑元素仍然缺乏。这个项目的目标是研究物质的拓扑有序和相关的相--这是全面质量控制的先决条件。PI旨在解决三个问题：(1)什么是最合适的物理系统，在那里可以现实地找到具有正确性质的拓扑相？(2)如何操作候选相来准备量子力学状态并以实际的方式执行逻辑运算？(3)如何从候选态中恢复信息，特别是因为它们被设计为受环境的弱影响，所以不容易测量？这些问题构成了这个项目的核心；回答这些问题涉及到与量子计算和量子信息科学相结合的许多现代凝聚态物理主题的研究。Pi将在他之前工作的基础上，开发量子计算入门研讨会和加州州立大学的外展工作，部分目的是扩大未被充分代表的少数群体的参与。技术总结该奖项支持关于利用物质的拓扑相实现量子计算的理论研究和教育。这个项目的主要目标是研究物质的拓扑相，并强调它们在拓扑量子计算中的潜在用途。本项目的一部分目的是进一步研究5/2填充的量子霍尔系统中非阿贝尔任意子的实验特征，为正在进行的实验和基于这些系统的实际量子电路元件的设计提供理论支持。一个相关的活动将涉及在看似不同类型的系统中寻找类似的物理，例如手性拓扑超导体或与局部磁矩相互作用的巡回电子系统。该项目的一个重要部分旨在了解如何利用非阿贝尔任意子设计新的材料系统，例如，通过将阿贝尔分数量子霍尔系统和传统超导体等“积木”结合起来--这一方法的灵感来自Majorana导线的概念设计。PI将以他之前的工作为基础，为这类工程开发一个概念性框架，进一步开发它，并设计适用于这些系统的新的测量和操作技术。虽然许多拟议的活动涉及研究适合于拓扑量子计算的系统的物理性质，但这项研究的目的是提出拓扑量子计算的想法。基于这些系统设计现实的量子电路元件，并开发处理量子信息的新技术，是计划中的研究活动的组成部分。PI将在他之前工作的基础上，开发量子计算入门研讨会，并在加利福尼亚州校园开展外联活动，部分目的是扩大未被充分代表的少数族裔的参与。

NONTECHNICAL SUMMARYThis award supports theoretical research and education on quantum computing by manipulating quantum states of matter composed of many electrons. Quantum computers promise an exponential speedup for certain computational tasks which are not feasible with modern classical computers. The potential benefits would have impact from quantum chemistry to designing new medicines and materials to cryptographic applications. One of the main obstacles to building a working quantum computer is decoherence: by interacting with its surroundings, a quantum bit, or qubit, tends to become more and more classical. So, after a short time all potential advantages stemming from computation based on the laws of Quantum Mechanics are gone. The idea of Topological Quantum Computing (TQC) circumvents this problem by encoding quantum information in a combined state of a large number of interacting particles, as opposed to relying on quantum states of an individual particle which are more vulnerable to the usual sources of decoherence. Such robust many particle quantum states, called topologically ordered states, may exist in materials or materials may be engineered to support such states. But topological qubits and logical elements are still lacking. The goal of this project is to study topologically ordered and related phases of matter - a prerequisite for TQC. The PI aims to address three questions: (1) What are the most suitable physical systems where topological phases with the right properties may be realistically found? (2) How can candidate phases be manipulated to prepare quantum mechanical states and perform logical operations in a practical manner? (3) How can information be recovered from the candidate states, particularly since they are designed to be weakly influenced by the environment and so, not easily measured? These questions form the core of this project; answering them involves research across many modern themes of condensed matter physics at the interface with quantum computation and quantum information science. The PI will build on his previous work to develop introductory seminars on quantum computing and an outreach effort to California State campuses with an aim, in part, to broaden participation of underrepresented minorities.TECHNICAL SUMMARYThis award supports theoretical research and education on the realization of quantum computing with topological phases of matter. The main goal of this project is to study topological phases of matter with the emphasis on their potential utility for Topological Quantum Computing. A part of this project aims at further investigating experimental signatures of non-Abelian anyons in quantum Hall systems at 5/2 filling, providing theoretical support for ongoing experiments and designing realistic quantum circuit elements based on these systems. A related activity will involve searching for similar physics in seemingly different types of systems such as chiral topological superconductors or itinerant electron systems interacting with local magnetic moments. A significant part of this project aims to understand how to engineer novel material systems with non-Abelian anyons by, for example, combining such 'building blocks' as Abelian fractional quantum Hall systems and conventional superconductors - an approach inspired by the conceptual designs of Majorana wires. The PI will build on his previous work to develop a conceptual framework for such engineering, further developing it as well as designing new measurement and manipulation techniques suitable for these systems. While much of the proposed activity deals with studying physical properties of the systems suitable for topological quantum computing, this research is aimed to advance the idea of topological quantum computing. Designing realistic quantum circuit elements based on these systems and developing new techniques for manipulating quantum information are integral parts of the planned research activity. The PI will build on his previous work to develop introductory seminars on quantum computing and an outreach effort to California State campuses with an aim, in part, to broaden participation of underrepresented minorities.