The University of Queensland
Department of Mathematics
Mathematical Physics Seminar
Quantum Error Correction and Topological Degeneracy
Professor Nick Bonesteel
National High Magnetic Field Laboratory and Department of Physics
Florida State University
Friday, August 3, 3pm
Room 641, Priestley (Mathematics) Building
After a review of the basic theory of quantum error correction, the `toric codes' constructed by Kitaev (quant-ph/9707021) using the degenerate ground states of particular spin Hamiltonians realized on finite two-dimensional lattices with periodic boundary conditions will be discussed. These states can only be distinguished by global measurements of topological quantum numbers, it is therefore possible to perform local measurements on encoded states to determine whether and where an error has occurred without disturbing the encoded quantum information. Motivated by this connection between topology and quantum error correction, the possibility of using the topological degeneracy of spin-1/2 chiral spin liquid states on the torus to construct quantum error-correcting codes is investigated. Unlike Kitaev's codes, codes constructed using chiral spin liquids on finite periodic lattices do not meet the necessary and sufficient conditions for correcting even a single qubit error with perfect fidelity. However, for large enough lattice sizes these conditions are approximately satisfied, and the resulting codes may be viewed as approximate quantum error-correcting codes.
Reference: N. E. Bonesteel, Phys. Rev. A 62, 062310 (2000)
All interested are invited to attend.
Enquires to Yao-Zhong Zhang on 3365 2309 or yzz@maths.uq.edu.au