Unified approach to topological quantum computation with anyons: From qubit encoding to Toffoli gate
Abstract
Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasiparticle excitations. We develop an efficient means to map between dense and sparse representations of quantum information (qubits) and a simple construction of multiqubit gates, for all anyon models from ChernSimonsWitten SU(2)_{k} theory that support universal quantum computation by braiding (k⩾3,k≠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⩾3,k≠4, unifying these concepts in a simple framework. Furthermore, we illustrate potential extensions of these ideas to other anyon models outside of ChernSimonsWitten field theory.
 Publication:

Physical Review A
 Pub Date:
 July 2011
 DOI:
 10.1103/PhysRevA.84.012332
 arXiv:
 arXiv:1001.4085
 Bibcode:
 2011PhRvA..84a2332X
 Keywords:

 03.67.Lx;
 03.65.Vf;
 03.67.Pp;
 73.43.f;
 Quantum computation;
 Phases: geometric;
 dynamic or topological;
 Quantum error correction and other methods for protection against decoherence;
 Quantum Hall effects;
 Quantum Physics;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Mathematical Physics
 EPrint:
 4.5 pages, 3 figures, published in PRA