Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2006-07-05
Phys. Rev. B 74 (2006) 235112
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
6 pages, 7 figures, RevTeX; version 3: introduced section names, new reference added; new comment added about the embedding of
Scientific paper
10.1103/PhysRevB.74.235112
We extend the topological quantum computation scheme using the Pfaffian quantum Hall state, which has been recently proposed by Das Sarma et al., 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.
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