Universal quantum computing with parafermions assisted by a half-fluxon

We propose a scheme to perform a Non-Clifford gate on a logical qudit encoded in a pair of $Z_N$ parafermionic zero modes via the Aharonov Casher effect. This gate can be implemented by moving a half fluxon around the pair of parafermionic zero modes that can be realized in a two-dimensional set-up via existing proposals. The half fluxon can be created as a part of half fluxon/anti-half fluxon pair in long Josephson junction with chiral superconductors and then moved around the parafermionic zero modes. Supplementing this gate with braiding of parafermions provides the avenue for universal quantum computing with parafermions.

[1]  Earl T Campbell,et al.  Enhanced fault-tolerant quantum computing in d-level systems. , 2014, Physical review letters.

[2]  Y. Maeno,et al.  The superconductivity of Sr2RuO4 and the physics of spin-triplet pairing , 2003 .

[3]  E. Bakkers,et al.  Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices , 2012, Science.

[4]  E. Fradkin,et al.  Charge-4e superconductivity from pair-density-wave order in certain high-temperature superconductors , 2009, 0904.1230.

[5]  M. Cheng.  Superconducting Proximity Effect on the Edge of Fractional Topological Insulators , 2012, 1204.6084.

[6]  Owen P. Leary,et al.  40: PATIENT-SPECIFIC PROGNOSTICATION AFTER TBI IS RELATED TO BLEED PHENOTYPE AND ANATOMIC LOCATION , 2006, Testament d'un patriote exécuté.

[7]  M. Manfra,et al.  Scaling of Majorana Zero-Bias Conductance Peaks. , 2017, Physical review letters.

[8]  Jason Alicea,et al.  Exotic non-Abelian anyons from conventional fractional quantum Hall states , 2012, Nature Communications.

[9]  D. Ivanov.  Non-Abelian statistics of half-quantum vortices in p-wave superconductors. , 2000, Physical review letters.

[10]  N. Read,et al.  Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level , 1998, cond-mat/9809384.

[11]  Liang Jiang,et al.  Measurement-only topological quantum computation without forced measurements , 2016, 1607.07475.

[12]  L. Fu,et al.  Superconducting proximity effect and majorana fermions at the surface of a topological insulator. , 2007, Physical review letters.

[13]  Parsa Bonderson.  Measurement-only topological quantum computation via tunable interactions , 2012, 1210.7929.

[14]  D. Estève,et al.  Evidence for long-lived quasiparticles trapped in superconducting point contacts. , 2011, Physical review letters.

[15]  Mark Howard,et al.  Qudit versions of the qubit "pi-over-eight" gate , 2012, 1206.1598.

[16]  N. Read,et al.  Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect , 1999, cond-mat/9906453.

[17]  A. Kitaev.  Unpaired Majorana fermions in quantum wires , 2000, cond-mat/0010440.

[18]  D. Browne,et al.  Magic-State Distillation in All Prime Dimensions Using Quantum Reed-Muller Codes , 2012, 1205.3104.

[19]  Braiding statistics and congruent invariance of twist defects in bosonic bilayer fractional quantum Hall states , 2013, 1308.5984.

[20]  S. Matsuo.  Half-Fluxon on Long Josephson Junction with Chiral Superconductors , 2013 .

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

[22]  A. Vaezi,et al.  Fractional topological superconductor with fractionalized Majorana fermions , 2012, 1204.6245.

[23]  A. Stern,et al.  Observing Majorana bound states of Josephson vortices in topological superconductors , 2010, Proceedings of the National Academy of Sciences.

[24]  Michael H. Freedman,et al.  Universal Geometric Path to a Robust Majorana Magic Gate , 2015, 1511.05161.

[25]  D. Bohm,et al.  Significance of Electromagnetic Potentials in the Quantum Theory , 1959 .

[26]  C. M. Marcus,et al.  Exponential protection of zero modes in Majorana islands , 2016, Nature.

[27]  Malomed,et al.  Tunnel creation of kink-antikink pairs from an inhomogeneous vacuum by an external field. , 1990, Physical review. B, Condensed matter.

[28]  Yakir Aharonov,et al.  Topological Quantum Effects for Neutral Particles , 1984 .

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

[30]  小谷 正雄.  日本物理学会誌及びJournal of the Physical Society of Japanの月刊について , 1955 .

[31]  M. Freedman,et al.  Majorana zero modes and topological quantum computation , 2015, npj Quantum Information.

[32]  Jason Alicea,et al.  Topological Phases with Parafermions: Theory and Blueprints , 2015, 1504.02476.

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

[34]  D. Vollhardt,et al.  The Superfluid Phases Of Helium 3 , 1990 .

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

[36]  Meng Cheng,et al.  Symmetry fractionalization, defects, and gauging of topological phases , 2014, Physical Review B.

[37]  Y. Gefen,et al.  Measurement and control of a Coulomb-blockaded parafermion box , 2017, 1704.03241.

[38]  Yuri S. Kivshar,et al.  Dynamics of Solitons in Nearly Integrable Systems , 1989 .

[39]  Yi-Zhuang You,et al.  Projective non-Abelian statistics of dislocation defects in a Z N rotor model , 2012, 1204.0113.

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

[41]  Ben-Jacob,et al.  Quantum dynamics of a fluxon in a long circular Josephson junction. , 1994, Physical review. B, Condensed matter.

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

[43]  S. Sarma,et al.  Proposal to stabilize and detect half-quantum vortices in strontium ruthenate thin films: Non-Abelian braiding statistics of vortices in a p x + i p y superconductor , 2005, cond-mat/0510553.

[44]  Peter D. Jarvis,et al.  Group22 : proceedings of the XXII International Colloquium on Group Theoretical Methods in Physics, Hobart, July 13-17, 1998 , 1999 .

[45]  Barbara M. Terhal,et al.  Majorana fermion codes , 2010, 1004.3791.

[46]  C. Nayak,et al.  The Nature and Correction of Diabatic Errors in Anyon Braiding , 2016 .

[47]  Parsa Bonderson,et al.  Topological quantum buses: coherent quantum information transfer between topological and conventional qubits. , 2011, Physical review letters.

[48]  T M Klapwijk,et al.  Evidence of a nonequilibrium distribution of quasiparticles in the microwave response of a superconducting aluminum resonator. , 2013, Physical review letters.

[49]  D. Loss,et al.  Quantum computing with parafermions , 2015, 1511.02704.

[50]  C. Marcus,et al.  Milestones toward Majorana-based quantum computing , 2015, 1511.05153.

[51]  M. Freedman,et al.  Scalable designs for quasiparticle-poisoning-protected topological quantum computation with Majorana zero modes , 2016, 1610.05289.

[52]  Jason Alicea,et al.  Designer non-Abelian anyon platforms: from Majorana to Fibonacci , 2014, 1410.0359.

[53]  Xiao Chen,et al.  Unconventional Fusion and Braiding of Topological Defects in a Lattice Model , 2013, 1306.1538.

[54]  A. Vaezi,et al.  Fibonacci anyons from Abelian bilayer quantum Hall states. , 2014, Physical review letters.

[55]  Maissam Barkeshli,et al.  Twist defects and projective non-Abelian braiding statistics , 2012, 1208.4834.

[56]  Y. Maeno,et al.  Evaluation of Spin-Triplet Superconductivity in Sr2RuO4 , 2011, 1112.1620.

[57]  A. Kitaev,et al.  Universal quantum computation with ideal Clifford gates and noisy ancillas (14 pages) , 2004, quant-ph/0403025.

[58]  A. Altland,et al.  Towards Realistic Implementations of a Majorana Surface Code. , 2015, Physical review letters.

[59]  S. Gopalakrishnan,et al.  Disclination classes, fractional excitations, and the melting of quantum liquid crystals. , 2013, Physical review letters.

[60]  Liang Jiang,et al.  Demonstrating non-Abelian statistics of Majorana fermions using twist defects , 2015, 1508.04166.

[61]  A. Barone,et al.  Physics and Applications of the Josephson Effect , 1982 .

[62]  Liang Fu,et al.  Majorana Fermion Surface Code for Universal Quantum Computation , 2015, 1504.01724.