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On the Theory of Topological Computation in the Lowest Landau Level of QHE
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Journal of Quantum Information Science·Volume 01 (2011)·Pages 121–126·Published 28 December 2011·DOI10.4236/jqis.2011.13017
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Abstract
We have studied the formation of Hall-qubit in lowest Landau level of (LLL) Quantum Hall effect due to the Aharonov-Bhom oscillation of quasiparticles.The spin echo method plays the key role in the topological entanglement of qubits. The proper ratio of fluxes for maximally entangling qubits has also been pointed out. The generation of higher Quantum Hall state may be possible with the help of quantum teleportation.
KeywordsSpin EchoAharonov-Bohm Phase
- M. V. Berry, “Quantal Phase Factor Accompanying Adi- abatic Changes,” Proceedings of the Royal Society A, Vol. 392, No. 1802, 1984, pp. 45-57. doi:10.1098/rspa.1984.0023
- Y. Aharonov and J. S. Anandan, “Phase Change during a Cyclic Quantum Evolution,” Physical Review Letters, Vol. 58, No. 16, 1987, pp. 1593-1596. doi:10.1103/PhysRevLett.58.1593
- V. Vedral, “Geometric Phase and Topological Quantum Computation,” Physics, Vol. 1, 2002, pp. 1-24.
- R. W. Ogburn and J. Preskill, “Lecture Notes in Computer Science,” Springer-Verlag, New York, 1999.
- A. Y. Kiteav, “Fault Tolarent Quantum Computation by Anyons,” Annals of Physics, Vol. 303, No. 1, 2003, pp. 2-30.
- H. K. Lo and John Preskill, “Non-Abelian Vortices and Non-Abelian Statistics,” Physical Review D, Vol. 48, No. 10, 1993, pp. 4821-4834.
- D. V. Averin and V. J. Goldman, “Quantum Computation with Quasiparticles of the Fractional Quantum Hall Effect,” Solid State Communications, Vol. 121, No. 1, 2001, pp. 25-28. doi:10.1016/S0038-1098(01)00447-1
- A. S. Goldhaber and J. K. Jain, “Characterization of Fractional-Quantum-Hall-Effect Quasiparticles,” Physics Letters A, Vol. 199, No. 3-4, 1995, pp. 267-273. doi:10.1016/0375-9601(95)00101-8
- D. Arovas, J. R. Schrieffer and F. Wilczek, “Fractional Statistics and Quantum Hall Effect,” Physical Review Let- ters, Vol. 53, No. 7, 1984, pp. 722-723. doi:10.1103/PhysRevLett.53.722
- V. Vedral, “Entanglement in Second Quantization formalism,” Central European Journal of Physics, Vol. 1, No. 2, 2003, pp. 289-306.
- D. Banerjee and P. Bandyopadhyay, “Qubit Rotation and Berry Phase,” Physica Scripta, Vol. 73, No. 6, 2006, pp. 571-576. doi:10.1088/0031-8949/73/6/008
- D. Banerjee, “Qubit Rotation in QHE,” Physica Scripta, Vol. 77, No. 6, 2008, pp. 065701-065705. doi:10.1088/0031-8949/77/06/065701
- A. Ekert, M. Ericson, V. Vedral, et al., “Geometric Quantum Computation,” Journal of Modern Optics, Vol. 47, No. 14-15, 2000, pp. 2501-2513.
- R. A. Bertlmann, K. Durstberger, Y. Hasegawa and B. C. Heismayr, “Berry Phase in Entangled Systems: An Experiment with Single Neutrons,” Physical Review A, Vol. 69, No. 3, 2004, pp. 032112-032118. doi:10.1103/PhysRevA.69.032112
- R. Prange and S. Girvin, “The Quantum Hall Effect,” Spinger-Verlag, New York, 1987.