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.?
Quantum computers promise an exponential speedup for certain computational tasks not feasible with modern classical computers. The main obstacle to building a working quantum computer is decoherence: a quantum bit which is not protected from its environment tends to behave classically, losing all potential benefits stemming from it quantum nature. The idea of Topological Quantum Computation (TQC) provides an elegant way of circumventing this problem by encoding quantum information non-locally, in a combined state of a large number of interacting particles. Since the usual sources of decoherence act locally, this approach renders the system immune. This approach relies on the existence in nature of very unusual, topologically-ordered states of matter characterized by such non-local properties. The goal of this award was to advance the field by (i) investigating non-Abelian topological order in condensed matter systems, the conditions under which it may occur and methods of its detection, and (ii) studying the feasibility of using topological phases for fault-tolerant quantum computation by providing conceptual designs for "anyonic" circuitry. The main research highlights along these directions are: 1. Analysis of existing and development of new experiments aiming at probing non-Abelian statistics in the fractional quantum Hall (FQH) systems. Earlier we predicted a distinct signature of non-Abelian anyons – an "even-odd" effect in QH Fabry-Perot interferometers. Similarly to the double-slit interference, tunneling currents through two quantum point contacts would interfere whenever they encircle an even number of localized quasiparticles. However, if this number is odd, no interference should be observed; the currents would add classically. Several experiments produced results consistent with our prediction, yet no incontrovertible proof have been obtained so far. These experiments revealed a number of complications not addressed in our original proposal; we subsequently analyzed them and proposed refinements [Bishara et al., Phys. Rev. B 80, 155303 (2009), Editor's suggestion]. We also considered Coulomb blockade effects as alternative probes [Bonderson et al., Phys. Rev. B 81, 165308 (2010), Editor's suggestion] and concluded that they are inferior to interferometry in providing definitive signatures of non-Abelian statistics. Finally, we proposed specific experiments to test the nature of the FQH state at 5/2 filling; subsequent measurements showed good agreement with our predictions [Willett et al., Phys. Rev. Lett. 111, 186401 (2013)]. 2. Drawing on earlier ideas for creating Majorana zero modes, we have proposed a new route for realizing novel topological states of matter. By replacing a helical edge of a 2D topological insulator by two counter-propagating QH edges, our approach opened a possibility of operating in the fractional quantum Hall regime, leading to new, even more interesting physics [Clarke et al., Nature Commun. 4, 1348 (2013)]. Instead of Majoranas, we found parafermionic zero modes generalizing the former in a very interesting way. A richer Hilbert space associated with them has an important consequence: a unitary transformation produced by braiding two such modes can be used for constructing additional quantum gates. Specifically, while still not computationally universal, braiding of such modes enable two-qubit entangling gates not possible with ‘conventional’ Majoranas. Moreover, we have proposed a blueprint for "engineering" even more computationally powerful anyons by creating an array of such parafermionic modes [Mong et al., Phys. Rev. X 4, 011036 (2014)]. Unlike parafermionic zero modes, the emergent excitations, Fibonacci anyons, are computationally universal. 3. Neither Majorana zero modes nor closely related non-Ablelian quasiholes in the fractional quantum Hall state at ν=5/2 are computationally universal; not all quantum gates can be effected by braiding alone. Yet it seems that anyons of this kind are most likely to be found in nature or engineered, raising questions about their utility for achieving universal quantum computation. We closed this conceptual gap by devising a practical proposal for implementing arbitrary single qubit phase gates for these anyons. Adding such gates to those obtained by braiding and measurement techniques makes it computationally universal. Our original proposal focused on the ν=5/2 QH state [Bonderson et al., Phys. Rev. Lett. 104, 180505 (2010); we further developed it for in systems based on topological superconductivity where standard techniques based on electrostatic gating would not work [Clarke et al., Phys. Rev. B 82, 180519(R) (2010), Editors' Suggestion]. 4. We focused on designing novel quantum devices by utilizing parafermionic zero modes. Such modes can be used to convert edge quasiparticles into oppositely charged quasiholes propagating in the same direction, in contrast with the usual Andreev reflection whereby a hole is reflected back. The key distinction is the chiral nature of the edge; this unusual feature results in reversing the sign of the chiral edge currents and can be used to design several novel circuit elements, including superconducting current and voltage mirrors, transistors for fractional charge currents as well as a flux capacitor – a circuit element which stores magnetic flux energy in response to an applied voltage (while drawing no external current). [To appear in Nature Physics.]
