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

Abstract

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.

6 pages, 7 figures, RevTeX; version 3: introduced section names, new reference added; new comment added about the embedding of the one- and two- qubit gates into a three-qubit system

References in corpus (1)

• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State

Cited by in corpus (8)

• Non-Abelian Anyons and Topological Quantum Computation
• Implementation of Clifford gates in the Ising-anyon topological quantum computer
• Towards a universal set of topologically protected gates for quantum computation with Pfaffian qubits
• Skein Theory and Topological Quantum Registers: Braiding Matrices and Topological Entanglement Entropy of Non-Abelian Quantum Hall States
• Ultimate braid-group generators for coordinate exchanges of Ising anyons from the multi-anyon Pfaffian wave functions
• Correlated transport of FQHE quasiparticles in a double-antidot system
• Topologically protected qubits as minimal Josephson junction arrays with non trivial boundary conditions: a proposal
• Topological Quantum Computation with the universal R matrix for Ising anyons