Title | Unified approach to topological quantum computation with anyons: From qubit encoding to Toffoli gate |

Publication Type | Journal Article |

Year of Publication | 2011 |

Authors | Xu, H, Taylor, JM |

Journal | Physical Review A |

Volume | 84 |

Issue | 1 |

Date Published | 2011/7/26 |

Abstract | Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasi-particle excitations. We develop an efficient means to map between dense and sparse representations of quantum information (qubits) and a simple construction of multi-qubit gates, for all anyon models from Chern-Simons-Witten SU(2)$_k$ theory that support universal quantum computation by braiding ($k\geq 3,\ k \neq 4$). In the process, we show how the constructions of topological quantum memory and gates for $k=2,4$ connect naturally to those for $k\geq 3,\ k \neq 4$, unifying these concepts in a simple framework. Furthermore, we illustrate potential extensions of these ideas to other anyon models outside of Chern-Simons-Witten field theory. |

URL | http://arxiv.org/abs/1001.4085v2 |

DOI | 10.1103/PhysRevA.84.012332 |

Short Title | Phys. Rev. A |