Universal Quantum Computation with Abelian Anyon Models

We consider topological quantum memories for a general class of abelian anyon models defined on spin lattices. These are non-universal for quantum computation when restricting to topological operations alone, such as braiding and fusion. The effects of additional non-topological operations, such as spin measurements, are studied. These are shown to allow universal quantum computation, while still utilizing topological protection. Our work gives an insight into the relation between abelian models and their non-abelian counterparts.

[1]  Sergey Bravyi.  Universal quantum computation with the v=5/2 fractional quantum Hall state , 2006 .

[2]  J I Cirac,et al.  Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices. , 2008, Physical review letters.

[3]  Jiannis K. Pachos,et al.  Universal Quantum Computation with a Non-Abelian Topological Memory , 2009, TCQ.

[4]  Xiao-Gang Wen,et al.  String-net condensation: A physical mechanism for topological phases , 2004, cond-mat/0404617.

[5]  L. Landau.  Fault-tolerant quantum computation by anyons , 2003 .

[6]  Robert Raussendorf,et al.  Topological fault-tolerance in cluster state quantum computation , 2007 .

[7]  Lev B. Ioffe,et al.  Discrete non-Abelian gauge theories in Josephson-junction arrays and quantum computation , 2004 .

[8]  David Olaya,et al.  Superconducting nanocircuits for topologically protected qubits , 2009 .

[9]  G. K. Brennen,et al.  Non-locality of non-Abelian anyons , 2008, 0810.4319.

[10]  Alexander S. Holevo.  On States, Channels, and Purification , 2002, Quantum Inf. Process..

[11]  P. Zoller,et al.  A toolbox for lattice-spin models with polar molecules , 2006 .

[12]  Carlos Mochon.  Anyon computers with smaller groups , 2004 .

[13]  From New States of Matter to a Unification of Light and Electrons(Yukawa International Seminar 2004 (YKIS2004) Physics of Strongly Correlated Electron Systems) , 2005, cond-mat/0508020.

[14]  J. Pachos,et al.  Why should anyone care about computing with anyons? , 2007, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[15]  Gottesman.  Class of quantum error-correcting codes saturating the quantum Hamming bound. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[16]  Sean Clark.  Valence bond solid formalism for d-level one-way quantum computation , 2005, quant-ph/0512155.

[17]  H. Weinfurter,et al.  Revealing anyonic statistics with multiphoton entanglement , 2007 .

[18]  Frank Wilczek,et al.  Quantum Mechanics of Fractional-Spin Particles , 1982 .

[19]  Otfried Gühne,et al.  Demonstrating anyonic fractional statistics with a six-qubit quantum simulator. , 2007, Physical review letters.

[20]  D. Perez-Garcia,et al.  Thermal states of anyonic systems , 2008, 0812.4975.

[21]  J. Cirac,et al.  Simulations of quantum double models , 2009, 0901.1345.

[22]  Jiannis K. Pachos,et al.  QUANTUM COMPUTATION WITH ABELIAN ANYONS ON THE HONEYCOMB LATTICE , 2005, quant-ph/0511273.

[23]  James R. Wootton,et al.  Non-Abelian statistics from an Abelian model , 2008, 0804.0931.

[24]  S. Bravyi.  Universal quantum computation with the nu=5/2 fractional quantum Hall state (16 pages) , 2006 .

[25]  John Preskill,et al.  Lecture Notes for Physics 219: Quantum Computation , 2004 .

[26]  H. Weinfurter,et al.  Revealing anyonic features in a toric code quantum simulation , 2007, 0710.0895.

[27]  Seth Lloyd,et al.  Quantum Computation with Abelian Anyons , 2000, Quantum Inf. Process..

[28]  J. Preskill,et al.  Topological quantum memory , 2001, quant-ph/0110143.