CAREER: Quantum Frustration, Topological Order in Solids and Topological

技术概述：该职业奖支持固体中量子挫折和拓扑秩序的理论研究，特别关注拓扑量子计算，并结合教育和推广计划。材料研究部和物理部为该奖项提供资源。两个主要的研究方向是：(i)研究各种凝聚态系统拓扑有序的可能性，如受挫磁体、玻色子和费米子扩展Hubbard模型和相关的Josephson结阵列，以及光学陷阱中的超冷原子系统。特别强调的是非阿贝尔拓扑顺序，它可能发生的条件和它的实验检测的可能方法。（ii）研究在容错量子计算中使用拓扑相位的可行性，特别是那些期望存在于分数量子霍尔系统中的拓扑相位。与其他更“传统”的实现量子计算的方法相比，这种方法具有重要的潜在优势；纠错是自动内置到相关的电子物理的基础固态系统。相关的教育活动包括针对大学新生举办量子计算系列研讨会，主要目的是让他们接触到研究，并激发他们在物理学方面的学习和积极研究。该系列课程将在加州大学河滨分校和加州州立大学洛杉矶分校提供，并将配有一个互动网站。更高级的研究课题和相关的理论工具将被纳入凝聚态物理的现代问题和解决方案的研究生水平的书和一个新的研究生班“凝聚态物理的场论方法”。非技术概述：该职业奖支持凝聚态物理和量子信息科学的理论研究，并结合教育活动，其中一些旨在激发本科生对物理的兴趣。材料研究部和物理部为该奖项提供资源。PI计划研究物质的新状态，这些状态在理论上被预测存在于一个平面内的电子中，并暴露在垂直于平面的高磁场中。这些被称为物质的拓扑状态，具有有趣的量子力学特性。例如，它们对噪音的抵抗力特别强。这破坏了量子力学状态的固有特性，这些特性使得通过操纵量子力学状态来实现高度并行计算成为可能。这些研究活动可能导致发现新的物质拓扑状态。尽管拓扑量子计算具有巨大的潜力，但许多基本的实际问题仍未解决。为了使这个想法成为现实，它们必须被解决，它们与重要的基础物理学有联系。这项研究将涉及这些问题，其中包括：这些拓扑状态是否真的存在于自然界中？如何以一种实用的方式操纵它们来实现计算？那么，如何通过实验来探测这些物质的状态呢？量子力学状态的计算有望极大地加快从密码学到量子化学等重要计算任务的速度。利用拓扑态进行量子计算的概念思想在数学拓扑领域和凝聚态物理领域之间建立了深刻的联系。这项研究还包括通过微软研究院与工业界的合作，并将为参与研究的研究生提供在工业界进行研究的第一手经验。在这里形成的概念和见解将有助于提高美国的竞争力。相关的教育活动包括针对大学新生举办量子计算系列研讨会，主要目的是让他们接触到研究，并激发他们在物理学方面的学习和积极研究。该系列课程将在加州大学河滨分校和加州州立大学洛杉矶分校提供，并将配有一个互动网站。更高级的研究课题和相关的理论工具将被纳入凝聚态物理的现代问题和解决方案的研究生水平的书和一个新的研究生班“凝聚态物理的场论方法”。

TECHNICAL SUMMARY:This CAREER award supports theoretical research on Quantum Frustration and Topological Order in Solids with a special focus on Topological Quantum Computation, combined with educational and outreach programs. The Division of Materials Research and the Physics Division contribute resources to this award.The two main research directions are: (i) Investigating the possibility of topological order in a variety of condensed matter systems such as frustrated magnets, bosonic and fermionic extended Hubbard models and related Josephson junction arrays, as well as ultra-cold atomic systems in optical traps. Special emphasis is placed on non-Abelian topological order, the conditions under which it may occur and possible methods of its experimental detection. (ii) Studying the feasibility of using topological phases for fault-tolerant quantum computation, specifically those expected to exist in Fractional Quantum Hall systems. Such an approach has an important potential advantage over other, more "conventional" proposed ways to realize quantum computing; error correction is automatically built into the correlated electron physics of an underlying solid state system. The related educational activities include developing a seminar series on quantum computation targeting college freshmen with the main goal of exposing them to the research, as well as exciting them about studying and doing active research in Physics. This series will be offered both at University of California, Riverside and California State University, Los Angeles and will be accompanied by an interactive website. More advanced topics of the research and related theoretical tools will be incorporated into a graduate level book of modern problems and solutions in condensed matter physics and a new graduate class "Field Theory Methods in Condensed Matter Physics.? NON-TECHNICAL SUMMARY:This CAREER award supports theoretical research in condensed matter physics and quantum information science combined with educational activities, some designed to stimulate interest in undergraduate students in physics. The Division of Materials Research and the Physics Division contribute resources to this award.The PI plans to study new states of matter that are theoretically predicted to exist in electrons confined to a plane and exposed to a high magnetic field perpendicular to the plane. These topological states of matter, as they are called, have intriguing quantum mechanical properties. For example, they are particularly resistent to ?noise? that disrupts inherent properties of quantum mechanical states that enable the highly parallel computation possible by manipulating quantum mechanical states. The research activities may lead to the discovery of new topological states of matter. Despite the great potential promise of topological quantum computation, many of the basic practical questions remain open. They must be resolved in order for this idea to become a reality, and they have connections to important fundamental physics. This research will engage these questions, among them are: Do these topological states actually exist in nature? How can they be manipulated in a practical way to enable computation? And, how can these states of matter be detected by experiments? Computing with quantum mechanical states holds the promise of formidable speed-up of important computational tasks with implications ranging from cryptography to quantum chemistry. The conceptual idea of using topological states for quantum computation has established deep connections between the fields of topology in mathematics and condensed matter physics. This research also invovles collaboration with industry through Microsoft Research, and will give participating graduate students first-hand experience in research conducted in industry. The concepts and insights developed here will contribute to American competitiveness. The related educational activities include developing a seminar series on quantum computation targeting college freshmen with the main goal of exposing them to the research, as well as exciting them about studying and doing active research in Physics. This series will be offered both at University of California, Riverside and California State University, Los Angeles and will be accompanied by an interactive website. More advanced topics of the research and related theoretical tools will be incorporated into a graduate level book of modern problems and solutions in condensed matter physics and a new graduate class "Field Theory Methods in Condensed Matter Physics.?