Coulomb-assisted braiding of Majorana fermions in a Josephson junction array

We show how to exchange (braid) Majorana fermions in a network of superconducting nanowires by control over Coulomb interactions rather than tunneling. Even though Majorana fermions are charge-neutral quasiparticles (equal to their own antiparticle), they have an effective long-range interaction through the even–odd electron number dependence of the superconducting ground state. The flux through a split Josephson junction controls this interaction via the ratio of Josephson and charging energies, with exponential sensitivity. By switching the interaction on and off in neighboring segments of a Josephson junction array, the non-Abelian braiding statistics can be realized without the need to control tunnel couplings by gate electrodes.

[1]  K. Kanaya,et al.  ρ meson decay in 2+1 flavor lattice QCD , 2011 .

[2]  C. Beenakker,et al.  Coulomb stability of the 4π-periodic Josephson effect of Majorana fermions , 2011, 1108.1095.

[3]  Martin Leijnse,et al.  Quantum information transfer between topological and spin qubit systems. , 2011, Physical review letters.

[4]  Meng Cheng,et al.  Nonadiabatic effects in the braiding of non-Abelian anyons in topological superconductors , 2011, 1106.2549.

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

[6]  T M Klapwijk,et al.  Number fluctuations of sparse quasiparticles in a superconductor. , 2011, Physical review letters.

[7]  S. Tewari,et al.  Controlling non-Abelian statistics of Majorana fermions in semiconductor nanowires , 2010, 1012.0561.

[8]  Karsten Flensberg,et al.  Non-Abelian operations on Majorana fermions via single-charge control. , 2010, Physical review letters.

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

[10]  John Preskill,et al.  Interface between topological and superconducting qubits. , 2010, Physical review letters.

[11]  G. Refael,et al.  Non-Abelian statistics and topological quantum information processing in 1D wire networks , 2010, 1006.4395.

[12]  S. Das Sarma,et al.  Universal quantum computation in a semiconductor quantum wire network , 2010, 1007.4204.

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

[14]  G. Refael,et al.  Helical liquids and Majorana bound states in quantum wires. , 2010, Physical review letters.

[15]  S. Das Sarma,et al.  Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures. , 2010, Physical review letters.

[16]  Cenke Xu,et al.  Fractionalization in Josephson junction arrays hinged by quantum spin Hall edges , 2009, 0911.1782.

[17]  Liang Fu,et al.  Electron teleportation via Majorana bound states in a mesoscopic superconductor. , 2009, Physical review letters.

[18]  Jens Koch,et al.  Suppressing Charge Noise Decoherence in Superconducting Charge Qubits , 2007, 0712.3581.

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

[20]  S. Girvin,et al.  Charge-insensitive qubit design derived from the Cooper pair box , 2007, cond-mat/0703002.

[21]  S. Bravyi.  Universal quantum computation with the v=5/2 fractional quantum Hall state , 2005, quant-ph/0511178.

[22]  Y. Makhlin,et al.  Quantum-state engineering with Josephson-junction devices , 2000, cond-mat/0011269.

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

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

[25]  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.

[26]  Nazarov,et al.  Single-electron charging of a superconducting island. , 1992, Physical review letters.

[27]  Büttiker.  Zero-current persistent potential drop across small-capacitance Josephson junctions. , 1987, Physical review. B, Condensed matter.

[28]  Frank Wilczek,et al.  Appearance of Gauge Structure in Simple Dynamical Systems , 1984 .

[29]  Michael Tinkham,et al.  Introduction to Superconductivity , 1975 .