Topologically Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State

The Pfaffian state is an attractive candidate for the observed quantized Hall plateau at a Landau-level filling fraction ν=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 ν=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 ν=5/2, we estimate the error rate to be 10^-30 or lower.