Das Sarma Sankar, Freedman Michael, Nayak Chetan
Department of Physics, University of Maryland, College Park, Maryland 20742, USA.
Phys Rev Lett. 2005 Apr 29;94(16):166802. doi: 10.1103/PhysRevLett.94.166802. Epub 2005 Apr 27.
The Pfaffian state is an attractive candidate for the observed quantized Hall plateau at a Landau-level filling fraction nu=5/2. 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 nu=5/2 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 nu=5/2, we estimate the error rate to be 10(-30) or lower.
在朗道能级填充因子ν = 5/2时观测到的量子化霍尔平台，其Pfaffian态是一个很有吸引力的候选者。这一点尤其引人关注，因为该态具有非同寻常的拓扑性质，包括具有非阿贝尔编织统计的准粒子激发。为了确定ν = 5/2态的性质，必须测量准粒子的编织统计。在此，我们提出一个实验，它能够同时确定准粒子激发的编织统计，并且，如果事实证明它们是非阿贝尔的，还能产生一个拓扑保护的量子比特，通过准粒子编织在其上执行逻辑非操作。利用在ν = 5/2时测得的激发能隙，我们估计错误率为10^(-30)或更低。
