CAREER: Quantum Frustration, Topological Order in Solids and Topological

University Of California-Riverside, Riverside CA

Investigators

Abstract

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.?