Computing with Quantum Knots: Non-Abelian Anyons and Topological Quantum Computation

Monday, 25. Februay, 13:00 h, H 0105

Ordinary quantum computation uses simple quantum two level systems (e.g. electron or nuclear spins, atomic hyperfine states, etc.) as quantum bits (’qubits’) with one- and two-qubit unitary operations serving as universal quantum gates. The main problem is quantum decoherence, the inevitable continuous dephasing of a quantum state due to its interaction with the environment. A revolutionary alternative idea is to build a quantum computer which is topologically immune to quantum decoherence. Such an inherently fault tolerant topological quantum computer is completely protected from any local perturbation induced by the environment and uses the time-space braiding (i.e. creating suitable quantum knots) of non-Abelian anyonic quasiparticles for quantum computation. Prospects for topological quantum computation will be discussed in this talk from a combined experimental and theoretical perspective. I will discuss a number of physical systems, mostly the fractional quantum Hall states in high-mobility two-dimensional semiconductor structures, but also chiral p-wave superconductors, p-wave fermionic superfluids, cold atom optical lattices, frustrated quantum magnetic systems, Josephson junction arrays, rotating BEC systems, etc. where the possibility for doing topological quantum computation has been theoretically discussed in the recent literature. I will also provide an elementary introduction to the concepts of topological phase, anyons, and non-Abelian braiding statistics, discussing how the interdisciplinary subject of topological quantum computation brings together topology, conformal field theory, fractional quantum Hall effect, Chern-Simons-Witten theory, and materials science.

Further reading: Charles Day, Physics Today, October 2005; Graham Collins, Scientific American, April 2006; Sankar Das Sarma, Michael Freedman, and Chetan Nayak, Physics Today, July 2006; Sankar Das Sarma, Michael Freedman, Chetan Nayak, Steven Simon, and Ady Stern, http://www.arxiv.org/abs/0707.1889 (to appear in Reviews of Modern Physics 2008).

Sankar Das Sarma
Condensed Matter Theory Center, University of Maryland, USA