Physical Platforms for Topological Quantum Computation

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。量子计算机承诺对某些计算任务进行指数级加速，这在现代经典计算机上是不可行的。潜在的好处将从量子化学到设计新的药物和材料，再到密码学应用。构建工作量子计算机的主要障碍之一是退相干：通过与周围环境的相互作用，量子比特或量子位倾向于变得越来越经典。因此，在很短的时间内，基于量子力学定律的计算所产生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状态下编码量子信息来规避这个问题，而不是依赖于单个粒子的量子状态，后者更容易受到通常的退相干源的影响。这种强健的多粒子量子态，被称为拓扑有序态，可能存在于材料中，或者材料可以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。该项目的目标是研究物质的拓扑有序和相关阶段-这是TQC的先决条件。PI旨在解决三个问题：(1)在现实中可能找到具有正确性质的拓扑相的最合适的物理系统是什么？(2)如何操纵候选相以实际方式制备量子力学态并进行逻辑运算？(3)如何从候选状态中恢复信息，特别是因为它们被设计为受环境影响很小，因此不容易测量？这些问题构成了这个项目的核心；回答这些问题涉及到在量子计算和量子信息科学的界面上研究凝聚态物理的许多现代主题。PI将以他之前的工作为基础，开展量子计算的介绍性研讨会，并在加州州立大学校园开展推广工作，部分目的是扩大代表性不足的少数民族的参与。该奖项支持物质拓扑相量子计算实现的理论研究和教育。该项目的主要目标是研究物质的拓扑相，重点是它们在拓扑量子计算中的潜在效用。本项目的一部分旨在进一步研究量子霍尔系统中5/2填充时非阿贝尔任意子的实验特征，为正在进行的实验提供理论支持，并基于这些系统设计现实的量子电路元件。一个相关的活动将涉及在看似不同类型的系统中寻找相似的物理现象，例如手性拓扑超导体或与局部磁矩相互作用的流动电子系统。这个项目的一个重要部分旨在理解如何设计具有非阿贝尔任意子的新型材料系统，例如，将阿贝尔分数量子霍尔系统和传统超导体等“构建块”结合起来——这种方法的灵感来自马约拉纳线的概念设计。PI将在他之前的工作基础上，为这种工程开发一个概念框架，进一步发展它，并设计适合这些系统的新测量和操作技术。虽然许多拟议的活动涉及研究适合拓扑量子计算的系统的物理性质，但本研究旨在推进拓扑量子计算的思想。设计基于这些系统的现实量子电路元件和开发操纵量子信息的新技术是计划研究活动的组成部分。PI将以他之前的工作为基础，开展量子计算的介绍性研讨会，并在加州州立大学校园开展推广工作，部分目的是扩大代表性不足的少数民族的参与。

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.