Focus on topological quantum computation

Topological quantum computation started as a niche area of research aimed at employing particles with exotic statistics, called anyons, for performing quantum computation. Soon it evolved to include a wide variety of disciplines. Advances in the understanding of anyon properties inspired new quantum algorithms and helped in the characterisation of topological phases of matter and their experimental realisation. The conceptual appeal of topological systems as well as their promise for building fault-tolerant quantum technologies fuelled the fascination in this field. This `focus on' brings together several of the latest developments in the field and facilitates the synergy between different approaches.

[1]  S. Simon,et al.  Non-Abelian Anyons and Topological Quantum Computation , 2007, 0707.1889.

[2]  S. Tewari,et al.  Topologically non-trivial superconductivity in spin–orbit-coupled systems: bulk phases and quantum phase transitions , 2010, 1012.0057.

[3]  S. Dusuel,et al.  Breakdown of a perturbed topological phase , 2011, 1110.3632.

[4]  H. L. Stormer,et al.  Nobel Lecture: The fractional quantum Hall effect , 1999 .

[5]  B. Friedman,et al.  Entanglement entropy of random fractional quantum Hall systems , 2010, 1007.4202.

[6]  Giuseppe Mussardo,et al.  Topological quantum gate construction by iterative pseudogroup hashing , 2010, 1009.5808.

[7]  L. Huijse,et al.  Charged spin textures over the Moore–Read quantum Hall state , 2010, 1010.0897.

[8]  N. Read Topological phases and quasiparticle braiding , 2012 .

[9]  S. Viefers,et al.  A general approach to quantum Hall hierarchies , 2010, 1011.5365.

[10]  S. Simon,et al.  Phase transitions in topological lattice models via topological symmetry breaking , 2010, 1012.0317.

[11]  F. Bais,et al.  The modular S-matrix as order parameter for topological phase transitions , 2011, 1108.0683.

[12]  C. Beenakker,et al.  Coulomb-assisted braiding of Majorana fermions in a Josephson junction array , 2011, 1111.6001.

[13]  S. Simon,et al.  Aharonov–Bohm-like oscillations in Fabry–Perot interferometers , 2011 .

[14]  C. Kane,et al.  Topological Insulators , 2019, Electromagnetic Anisotropy and Bianisotropy.

[15]  C. Beenakker,et al.  The top-transmon: a hybrid superconducting qubit for parity-protected quantum computation , 2011, 1105.0315.

[16]  Kun Yang,et al.  Scaling and non-Abelian signature in fractional quantum Hall quasiparticle tunneling amplitude , 2010, 1011.4716.

[17]  J. Vala,et al.  Kaleidoscope of topological phases with multiple Majorana species , 2010, 1012.5276.

[18]  H. Bombin,et al.  Nested topological order , 2008, 0803.4299.

[19]  Ville Lahtinen,et al.  Interacting non-Abelian anyons as Majorana fermions in the honeycomb lattice model , 2011, 1103.0238.

[20]  V. Jones A polynomial invariant for knots via von Neumann algebras , 1985 .

[21]  Jiri Vala,et al.  Rigorous calculations of non-Abelian statistics in the Kitaev honeycomb model , 2011, 1103.3061.

[22]  S. Braunstein,et al.  Quantum computation , 1996 .

[23]  Simon J Devitt,et al.  Simulating open quantum systems: from many-body interactions to stabilizer pumping , 2011, 1104.2507.

[24]  M H Freedman,et al.  P/NP, and the quantum field computer , 1998, Proc. Natl. Acad. Sci. USA.

[25]  A. Stern,et al.  Majorana fermions on a disordered triangular lattice , 2011, 1106.6272.

[26]  M. Troyer,et al.  Microscopic models of interacting Yang–Lee anyons , 2010, 1012.1080.

[27]  Jiannis K. Pachos,et al.  Lifetime of topological quantum memories in thermal environment , 2012, 1209.2940.

[28]  Gregory W. Moore,et al.  Nonabelions in the fractional quantum Hall effect , 1991 .

[29]  R. Bhatt,et al.  Stability of the k = 3 Read–Rezayi state in chiral two-dimensional systems with tunable interactions , 2012, 1201.6598.

[30]  S. Simon,et al.  A Wilson line picture of the Levin–Wen partition functions , 2010, 1004.5147.

[31]  A. Kitaev Fault tolerant quantum computation by anyons , 1997, quant-ph/9707021.

[32]  David A. Huse,et al.  Diagnosing deconfinement and topological order , 2010, 1011.4187.

[33]  F. D. M. Haldane,et al.  The hierarchical structure in the orbital entanglement spectrum of fractional quantum Hall systems , 2011, 1105.5907.

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

[35]  Alexei Kitaev,et al.  Anyons in an exactly solved model and beyond , 2005, cond-mat/0506438.

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

[37]  Jason Alicea,et al.  New directions in the pursuit of Majorana fermions in solid state systems , 2012, Reports on progress in physics. Physical Society.

[38]  Vlatko Vedral,et al.  Generating topological order from a two-dimensional cluster state using a duality mapping , 2011, 1105.2111.

[39]  K. B. Whaley,et al.  Loop condensation in the triangular lattice quantum dimer model , 2011, 1106.1882.

[40]  L. Kauffman Topological quantum information, virtual Jones polynomials and Khovanov homology , 2011 .

[41]  S. Simon,et al.  Braiding of Abelian and Non-Abelian Anyons in the Fractional Quantum Hall Effect , 2011, 1112.3400.

[42]  Matthias Troyer,et al.  Two-dimensional quantum liquids from interacting non-Abelian anyons , 2010, 1003.3453.

[43]  J. Pachos,et al.  Fractional quantum Hall effect in a U(1)×SU(2) gauge field , 2010, 1012.3581.

[44]  S. Vishveshwara,et al.  Topological phases, Majorana modes and quench dynamics in a spin ladder system , 2011, 1102.0824.

[45]  F. Bais,et al.  Condensate-induced transitions between topologically ordered phases , 2008, 0808.0627.

[46]  Nonlocal Hanbury?Brown?Twiss interferometry and entanglement generation from Majorana bound states , 2011 .

[47]  Dorit Aharonov,et al.  A Polynomial Quantum Algorithm for Approximating the Jones Polynomial , 2008, Algorithmica.

[48]  C. Beenakker,et al.  Quantum point contact as a probe of a topological superconductor , 2011, 1101.5795.

[49]  K. West,et al.  Magnetic-field-tuned Aharonov-Bohm oscillations and evidence for non-Abelian anyons at ν = 5/2. , 2013, Physical review letters.

[50]  C. W. J. Beenakker,et al.  Anyonic interferometry without anyons: how a flux qubit can read out a topological qubit , 2010, 1005.3423.

[51]  R. Ainsworth,et al.  Topological qubit design and leakage , 2011, 1102.5029.

[52]  B. Estienne,et al.  Particles in non-Abelian gauge potentials: Landau problem and insertion of non-Abelian flux , 2011, 1102.0176.

[53]  D. Clarke,et al.  Edge-induced qubit polarization in systems with Ising anyons , 2011, 1102.2016.

[54]  Dominic Horsman,et al.  Quantum picturalism for topological cluster-state computing , 2011, 1101.4722.

[55]  G. Refael,et al.  Ettingshausen effect due to Majorana modes , 2012, 1203.5793.

[56]  Dorit Aharonov,et al.  The BQP-hardness of approximating the Jones polynomial , 2006, ArXiv.