The Pfaffian state is an attractive candidate for the observed quantized Hall plateau at a Landau-level filling fraction . This is particularly intriguing because this state has unusual topological properties, including quasiparticle excitations with non-Abelian braiding statistics. In order to determine the nature of the state, one must measure the quasiparticle braiding statistics. Here, we propose an experiment which can simultaneously determine the braiding statistics of quasiparticle excitations and, if they prove to be non-Abelian, produce a topologically protected qubit on which a logical Not operation is performed by quasiparticle braiding. Using the measured excitation gap at , we estimate the error rate to be or lower.
- Received 14 December 2004
- Published 27 April 2005
© 2005 The American Physical Society