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This review presents an entry-level introduction to topological quantum computation -- quantum computing with anyons.
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2001
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2002
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M. H. Freedman, A. Kitaev, M. J. Larsen and Z. Wang, Topological Quantum Computation
2003
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A. Kitaev, Fault-tolerant quantum computation by anyons
2003
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Y. Tserkovnyak and S. H. Simon, Monte Carlo Evaluation of Non-Abelian Statistics
2003
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A. Kitaev, Anyons in an exactly solved model and beyond
2005
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M. Levin and X.-G. Wen, String-net condensation: A physical mechanism for topological phases
2005
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N. E. Bonesteel, L. Hormozi, G. Zikos and S. H. Simon, Braid Topologies for Quantum Computation
2005
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S. Bravyi and A. Kitaev, Universal quantum computation with ideal Clifford gates and noisy ancillas
2005
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A. Kitaev and J. Preskill, Topological entanglement entropy
2006
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M. Levin and X.-G. Wen, Detecting Topological Order in a Ground State Wave Function
2006
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A. Micheli, G. K. Brennen and P. Zoller, A toolbox for lattice spin models with polar molecules
2006
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S. Bravyi, Universal quantum computation with the ν = 5 / 2 \nu=5/2 fractional quantum Hall state
2006
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A. Feiguin, S. Trebst, A. W. W. Ludwig, M. Troyer, A. Kitaev, Z. Wang and M. H. Freedman, Interacting Anyons in Topological Quantum Liquids: The Golden Chain
2007
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C. Castelnovo and C. Chamon, Entanglement and topological entropy of the toric code at finite temperature
2007
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C. Nayak, S. H. Simon, A. Stern, M. Freedman and S. Das Sarma, Non-Abelian anyons and topological quantum computation
2008
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A. P. Schnyder, S. Ryu, A. Furusaki and A. W. W. Ludwig, Classification of topological insulators and superconductors in three spatial dimensions
2008
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L. Fu and C. L. Kane, Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator
2008
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S. Trebst, M. Troyer, Z. Wang and A. W.W. Ludwig, A short introduction to Fibonacci anyon models
2008
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H. Xu and X. Wan, Constructing Functional Braids for Low-Leakage Topological Quantum Computing
2008
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P. Bonderson, M. Freedman and C. Nayak, Measurement-Only Topological Quantum Computation
2008
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R. L. Willett, L. N. Pfeiffer and K. W. West, Measurement of filling factor 5 / 2 5/2 quasiparticle interference with observation of charge e / 4 e/4 and e / 2 e/2 period oscillations
2009
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G. Jackeli and G. Khaliullin, Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
2009
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J. K. Pachos, W. Wieczorek, C. Schmid, N. Kiesel, R. Pohlner and H. Weinfurter, Revealing anyonic features in a toric code quantum simulation
2009
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E. Rowell, R. Stong and Z. Wang, On classification of modular tensor categories
2009
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H. Xu and X. Wan, Exploiting Geometric Degrees of Freedom in Topological Quantum Computing
2009
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A. Ahlbrecht, L. S. Georgiev and R. F. Werner, Implementation of Clifford gates in the Ising-anyon topological quantum computer
2009
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P. Bonderson, Splitting the Topological Degeneracy of Non-Abelian Anyons
2009
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M. Cheng, R.M. Lutchyn, V. Galitski and S. Das Sarma, Splitting of Majorana-Fermion Modes due to Intervortex Tunneling in a p x + i p y p_{x}+ip_{y} Superconductor
2009
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M. Baraban, G. Zikos, N. Bonesteel and S.H. Simon, Numerical Analysis of Quasiholes of the Moore-Read Wave Function
2009
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V. Lahtinen and J. K. Pachos, Non-Abelian statistics as a Berry phase in exactly solvable models
2009
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C. Gils, E. Ardonne, S. Trebst, A. W. W. Ludwig, M. Troyer and Z. Wang, Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
2009
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S. Iblisdir, D. Perez-Garcia, M. Aguado and J. K. Pachos, Thermal States of Anyonic Systems
2009
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A. Hamma, C. Castelnovo and C. Chamon, Toric-boson model: Toward a topological quantum memory at finite temperature
2009
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N. Read, Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p x + i p y p_{x}+ip_{y} -paired superfluids
2009
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Z. Wang, Topological Quantum Computation
2010
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M. Z. Hasan and C. L. Kane, Topological Insulators
2010
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L. Balents, Spin liquids in frustrated magnets
2010
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J. D. Sau, R. M. Lutchyn, S. Tewari and S. Das Sarma, Generic New Platform for Topological Quantum Computation Using Semiconductor Heterostructures
2010
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J. Alicea, Majorana fermions in a tunable semiconductor device
2010
Cited alongside, same era.
R. M. Lutchyn, J. D. Sau, and S. Das Sarma, Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
2010
Cited alongside, same era.
Y. Oreg, G. Refael, and F. von Oppen, Helical Liquids and Majorana Bound States in Quantum Wires
2010
Cited alongside, same era.
M. Baraban, N. E. Bonesteel and S. H. Simon, Resources required for topological quantum factoring
2010
Cited alongside, same era.
M. Burrello, H. Xu, G. Mussardo and X. Wan, Quantum hashing with the icosahedral group
2010
Cited alongside, same era.
P. Bonderson, D. J. Clarke, C. Nayak and K. Shtengel, Implementing Arbitrary Phase Gates with Ising Anyons
T. D. Stanescu, R. M. Lutchyn and S. Das Sarma, Dimensional crossover in spin-orbit-coupled semiconductor nanowires with induced superconducting pairing
2013
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D. Rainis, L. Trifunovic, J. Klinovaja and D. Loss, Towards a realistic transport modeling in a superconducting nanowire with Majorana fermions
2013
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M. Barkeshli, C.-M. Jian and X.-L. Qi, Genons, twist defects, and projective non-Abelian braiding statistics
2013
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A. Altland and R. Egger, Multiterminal Coulomb-Majorana Junction
2013
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T. Hyart, B. van Heck, I. C. Fulga, M. Burrello, A. R. Akhmerov and C. W. J. Beenakker, Flux-controlled quantum computation with Majorana fermions
2013
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2010
Cited alongside, same era.
D. J. Clarke and K. Shtengel, Improved phase gate reliability in systems with neutral Ising anyons
2010
Cited alongside, same era.
J. Eisert, M. Cramer, and M. B. Plenio, Area laws for the entanglement entropy
2010
Cited alongside, same era.
A. R. Akhmerov, Topological quantum computation away from the ground state with Majorana fermions
2010
Cited alongside, same era.
X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors
2011
Cited alongside, same era.
L. Fu, Topological Crystalline Insulators
2011
Cited alongside, same era.
N. R. Regnault and B. A. Bernevig, Fractional Chern Insulator
2011
Cited alongside, same era.
M. Burrello, B. van Heck and A. R. Akhmerov, Braiding of non-Abelian anyons using pairwise interactions
2013
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P. Bonderson, Measurement-only topological quantum computation via tunable interactions
2013
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I. C. Fulga, B. van Heck, M. Burrello and T. Hyart, Effects of disorder on Coulomb-assisted braiding of Majorana zero modes
2013
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L. Mazza, M. Rizzi, M. D. Lukin, and J. I. Cirac, Robustness of quantum memories based on Majorana zero modes
2013
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D. J. Clarke, J. Alicea and K. Shtengel, Exotic non-Abelian anyons from conventional fractional quantum Hall states
2013
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Z.-C. Gu and X.-G. Wen, Symmetry-protected topological orders for interacting fermions – Fermionic topological nonlinear σ \sigma -models and a special group supercohomology theory
2014
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J. Reuther, S.-P. Lee and J. Alicea, Classification of spin liquids on the square lattice with strong spin-orbit coupling
2014
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B. Bauer, L. Cincio, B. P. Keller, M. Dolfi, G. Vidal, S. Trebst and A. W. W. Ludwig, Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator
2014
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S. Nadj-Perge, I. K. Drozdov, J. Li, H. Chen, S. Jeon, J. Seo, A. H. MacDonald, B. A. Bernevig and A. Yazdani, Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor
2014
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G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif and T. Esslinger, Experimental realisation of the topological Haldane model
2014
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A. Bühler, N. Lang, C. V. Kraus, G. Möller, S. D. Huber and H. P. Büchler, Majorana modes and p p -wave superfluids for fermionic atoms in optical lattices
2014
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R. S. K. Mong, D. J. Clarke, J. Alicea, N. H. Lindner, P. Fendley, C. Nayak, Y. Oreg, A. Stern, E. Berg, K. Shtengel and M. P. A. Fisher, Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure
2014
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J. R. Wootton, J. Burri, S. Iblisdir and D. Loss, Error Correction for Non-Abelian Topological Quantum Computation
2014
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V. Lahtinen, A. W. W. Ludwig and S. Trebst, Perturbed vortex lattices and the stability of nucleated topological phases
2014
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G. Kells, V. Lahtinen and J. Vala, Kitaev spin models from topological nanowire networks
2014
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D. Wang, Z. Huang and C. Wu, Fate and remnants of Majorana zero modes in a quantum wire array
2014
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B. J. Brown, A. Al-Shimary and J. K. Pachos, Entropic Barriers for Two-Dimensional Quantum Memories
2014
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Y.-L. Wu, B. Estienne, N. Regnault, B. A. Bernevig, Braiding Non-Abelian Quasiholes in Fractional Quantum Hall States
2014
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F. Maier, J. Klinovaja and D. Loss, Majorana fermions in Ge/Si hole nanowires
2014
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G. Kells, D. Sen, J. K. Slingerland, and S. Vishveshwara, Topological blocking in quantum quench dynamics
2014
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S.-H. Ho, S.-P. Chao, C.-H. Chou and F.-L. Lin, Decoherence patterns of topological qubits from Majorana modes
2014
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S. das Sarma, M. Freedman and C. Nayak, Majorana zero modes and topological quantum computation
2015
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B. M. Terhal, Quantum Error Correction for Quantum Memories
2015
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M. Hermanns, K. O’Brien and S. Trebst, Weyl spin liquids
2015
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S. R. Elliott and M. Franz, Colloquium: Majorana fermions in nuclear, particle, and solid-state physics
2015
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M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J. T. Barreiro, S. Nascimbene, N. R. Cooper, I. Bloch, N. Goldman, Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
2015
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J. M. Murray and O. Vafek, Majorana bands, Berry curvature, and thermal Hall conductivity in the vortex state of a chiral p p -wave superconductor
2015
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T. Liu and M. Franz, Electronic structure of topological superconductors in the presence of a vortex lattice
2015
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Y. Zhang, T. Grover, and A. Vishwanath, General procedure for determining braiding and statistics of anyons using entanglement interferometry
2015
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S. Hegde, V. Shivamoggi, S. Vishveshwara and D. Sen, Quench dynamics and parity blocking in Majorana wires
2015
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A. P. Higginbotham, S. M. Albrecht, G. Kirsanskas, W. Chang, F. Kuemmeth, P. Krogstrup, T. S. Jespersen, J. Nygard, K. Flensberg and C. M. Marcus, Parity lifetime of bound states in a proximitized semiconductor nanowire
2015
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D. J. van Woerkom, A. Geresdi and L. P. Kouwenhoven, One minute parity lifetime of a NbTiN Cooper-pair transistor
2015
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B. J. Brown, D. Loss, J. K. Pachos, C. N. Self, J. R. Wootton, Quantum memories at finite temperature
2016
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Z. Wang, A. Alexandradinata, R. J. Cava and B. A. Bernevig, Hourglass Fermions
2016
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B. Bradlyn, J. Cano, Z. Wang, M.G. Vergniory, C. Felser, R. J. Cava and B. A. Bernevig, Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
2016
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A. Bullivant and J. K. Pachos, Entropic Topological Invariants in Three Dimensions
2016
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G. Palumbo and J. K. Pachos, Holographic correspondence in topological superconductors
2016
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P. Nataf, M. Lajko, A. Wietek, K. Penc, F. Mila, A, M. Läuchli, Chiral spin liquids in triangular lattice S U ( N ) SU(N) fermionic Mott insulators with artificial gauge fields
2016
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A. Banerjee, C.A. Bridges, J-Q. Yan, A.A. Aczel, L. Li, M.B. Stone, G.E. Granroth, M.D. Lumsden, Y. Yiu, J. Knolle, D.L. Kovrizhin, S. Bhattacharjee, R. Moessner, D.A. Tennant, D.G. Mandrus, S.E. Nagler, Proximate Kitaev Quantum Spin Liquid Behaviour in α \alpha -RuCl 3
2016
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K. O’Brien, M. Hermanns and S. Trebst, Classification of gapless Z 2 Z_{2} spin liquids in three-dimensional Kitaev models
2016
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S. M. Albrecht, A. P. Higginbotham, M. Madsen, F. Kuemmeth, T. S. Jespersen, J. Nygård, P. Krogstrup and C. M. Marcus, Exponential Protection of Zero Modes in Majorana Islands
2016
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R. Pawlak, M. Kisiel, J. Klinovaja, T. Meier, S. Kawai, T. Glatzel, D. Loss and E. Meyer, Probing atomic structure and Majorana wavefunctions in mono-atomic Fe chains on superconducting Pb surface
2016
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J.-S. Xu, K. Sun, Y.-J. Han, C.-F. Li, J. K. Pachos and G.-C. Guo, Simulating the exchange of Majorana zero modes with a photonic system
2016
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T. Karzig, Y. Oreg, G. Refael and M. H. Freedman, A geometric protocol for a robust Majorana magic gate
2016
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J. Li, T. Neupert, B. A. Bernevig and A. Yazdani, Manipulating Majorana zero modes on atomic rings with an external magnetic field
2016
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D. Aasen, M. Hell, R. V. Mishmash, A. Higginbotham, J. Danon, M. Leijnse, T. S. Jespersen, J. A. Folk, C. M. Marcus, K. Flensberg and J. Alicea, Milestones toward Majorana-based quantum computing
2016
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M. Kjaergaard, F. Nichele, H. J. Suominen, M. P. Nowak, M. Wimmer, A. R. Akhmerov, J. A. Folk, K. Flensberg, J. Shabani, C. J. Palmström and C. M. Marcus, Quantized conductance doubling and hard gap in a two-dimensional semiconductor-superconductor heterostructure
2016
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S. Plugge, L. A. Landau, E. Sela, A. Altland, K. Flensberg and R. Egger, Roadmap to Majorana surface codes
2016
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2016
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A. Roy and D. P. DiVincenzo, Topological Quantum Computing
2017
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S. Plugge, A. Rasmussen, R. Egger and K. Flensberg, Majorana box qubits
2017
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F. Pientka, A. Keselman, E. Berg, A. Yacoby, A. Stern and B. I. Halperin, Topological Superconductivity in a Planar Josephson Junction
2017
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M. Hell, M. Leijnse and K. Flensberg, Two-dimensional platform for networks of Majorana bound states
2017
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T. Karzig, C. Knapp, R. M. Lutchyn, P. Bonderson, M. B. Hastings, C. Nayak, J. Alicea, K. Flensberg, S. Plugge, Y. Oreg, C. M. Marcus and M. H. Freedman, Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes
2017
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