Topologically protected gates for quantum computation with non-Abelian anyons in the Pfaffian quantum Hall state

We extend the topological quantum computation scheme using the Pfaffian quantum Hall state, which has been recently proposed by Das Sarma , in a way that might potentially allow for the topologically protected construction of a universal set of quantum gates. We construct, for the first time, a topologically protected controlled-NOT gate, which is entirely based on quasihole braidings of Pfaffian qubits. All single-qubit gates, except for the pi/8 gate, are also explicitly implemented by quasihole braidings. Instead of the pi/8 gate we try to construct a topologically protected Toffoli gate, in terms of the controlled-phase gate and CNOT or by a braid-group-based controlled-controlled-Z precursor. We also give a topologically protected realization of the Bravyi-Kitaev two-qubit gate g(3).