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Kitagawa, T. (2012). Topological phenomena in quantum walks: elementary introduction to the physics of topological phases. Quantum Information Processing, 11(5), 1107–1148.

Authors 1
  1. Takuya Kitagawa (first)
References 44 Referenced 131
  1. Aharonov Y., Davidovich L., Zagury N.: Quantum random walks. Phys. Rev. A 48, 1687 (1993) (10.1103/PhysRevA.48.1687) / Phys. Rev. A by Y. Aharonov (1993)
  2. Kempe, J.: Quantum random walks: an introductory overview. Contemp. Phys. 44, 307 (2003). http://www.tandfonline.com/doi/pdf/10.1080/00107151031000110776
  3. Farhi E., Gutmann S.: Quantum computation and decision trees. Phys. Rev. A 58, 915 (1998) (10.1103/PhysRevA.58.915) / Phys. Rev. A by E. Farhi (1998)
  4. Kitagawa T., Rudner M.S., Berg E., Demler E.: Exploring topological phases with quantum walks. Phys. Rev. A 82, 033429 (2010) (10.1103/PhysRevA.82.033429) / Phys. Rev. A by T. Kitagawa (2010)
  5. Kitagawa, T., et al.: Observation of topologically protected bound states in a one dimensional photonic system. arXiv/1105.5334 (2011) (10.1109/CLEOE.2011.5943396)
  6. Zähringer F.: Realization of a quantum walk with one and two trapped ions. Phys. Rev. Lett. 104, 100503 (2010) (10.1103/PhysRevLett.104.100503) / Phys. Rev. Lett. by F. Zähringer (2010)
  7. Karski, M., et al.: Quantum walk in position space with single optically trapped atoms. Science 325, 174 (2009). http://www.sciencemag.org/content/325/5937/174.full.pdf
  8. Schreiber A., et al.: Photons walking the line: a quantum walk with adjustable coin operations. Phys. Rev. Lett. 104, 050502 (2010) (10.1103/PhysRevLett.104.050502) / Phys. Rev. Lett. by A., et al. Schreiber (2010)
  9. Broome M.A. et al.: Discrete single-photon quantum walks with tunable decoherence. Phys. Rev. Lett. 104, 153602 (2010) (10.1103/PhysRevLett.104.153602) / Phys. Rev. Lett. by M.A. Broome (2010)
  10. Biane, P., et al.: Quantum walks. In: Quantum Potential Theory, Lecture Notes in Mathematics, vol. 1954, pp. 309–452. Springer, Berlin, Heidelberg (2008) (10.1007/978-3-540-69365-9_7)
  11. Grimmett G., Janson S., Scudo P.F.: Weak limits for quantum random walks. Phys. Rev. E 69, 026119 (2004) (10.1103/PhysRevE.69.026119) / Phys. Rev. E by G. Grimmett (2004)
  12. Ryu S., Hatsugai Y.: Topological origin of zero-energy edge states in particle-hole symmetric systems. Phys. Rev. Lett. 89, 077002 (2002) (10.1103/PhysRevLett.89.077002) / Phys. Rev. Lett. by S. Ryu (2002)
  13. Oka T., Konno N., Arita R., Aoki H.: Breakdown of an electric-field driven system: a mapping to a quantum walk. Phys. Rev. Lett. 94, 100602 (2005) (10.1103/PhysRevLett.94.100602) / Phys. Rev. Lett. by T. Oka (2005)
  14. Rudner M.S., Levitov L.S.: Topological transition in a non-hermitian quantum walk. Phys. Rev. Lett. 102, 065703 (2009) (10.1103/PhysRevLett.102.065703) / Phys. Rev. Lett. by M.S. Rudner (2009)
  15. von Klitzing K., Dorda G., Pepper M.: New method for high-accuracy determination of the finestructure constant based on quantized hall resistance. Phys. Rev. Lett. 45, 494 (1980) (10.1103/PhysRevLett.45.494) / Phys. Rev. Lett. by K. Klitzing von (1980)
  16. MacDonald, A.H.: Introduction to the physics of the quantum hall regime: quantized hall conductance in a two-dimensional periodic potential. eprint arXiv:cond-mat/9410047 (1994)
  17. Thouless D.J., Kohmoto M., Nightingale M.P., den Nijs M.: Quantized hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405 (1982) (10.1103/PhysRevLett.49.405) / Phys. Rev. Lett. by D.J. Thouless (1982)
  18. Halperin B.I.: Quantized hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential. Phys. Rev. B 25, 2185 (1982) (10.1103/PhysRevB.25.2185) / Phys. Rev. B by B.I. Halperin (1982)
  19. Hasan M.Z., Kane C.L.: Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045 (2010) (10.1103/RevModPhys.82.3045) / Rev. Mod. Phys. by M.Z. Hasan (2010)
  20. Qi X.-L., Zhang S.-C.: Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057 (2011) (10.1103/RevModPhys.83.1057) / Rev. Mod. Phys. by X.-L. Qi (2011)
  21. Su W.P., Schrieffer J.R., Heeger A.J.: Solitons in polyacetylene. Phys. Rev. Lett. 42, 1698 (1979) (10.1103/PhysRevLett.42.1698) / Phys. Rev. Lett. by W.P. Su (1979)
  22. Jackiw R., Rebbi C.: Solitons with fermion number. Phys. Rev. D 13, 3398 (1976) (10.1103/PhysRevD.13.3398) / Phys. Rev. D by R. Jackiw (1976)
  23. Jackiw R., Schrieffer J.: Solitons with fermion number 12 in condensed matter and relativistic field theories. Nuclear Physics B 190, 253 (1981) (10.1016/0550-3213(81)90557-5) / Nuclear Physics B by R. Jackiw (1981)
  24. Kane C.L., Mele E.J.: Quantum spin hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005) (10.1103/PhysRevLett.95.226801) / Phys. Rev. Lett. by C.L. Kane (2005)
  25. Bernevig, B.A., Hughes, T.L., Zhang, S.-C.: Quantum spin hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757 (2006). http://www.sciencemag.org/content/314/5806/1757.full.pdf
  26. Konig, M., et al.: Quantum spin hall insulator state in HgTe quantum wells. Science 318, 766 (2007). http://www.sciencemag.org/content/318/5851/766.full.pdf
  27. Fu L., Kane C.L., Mele E.J.: Topological insulators in three dimensions. Phys. Rev. Lett. 98, 106803 (2007) (10.1103/PhysRevLett.98.106803) / Phys. Rev. Lett. by L. Fu (2007)
  28. Chen, Y.L., et al.: Experimental realization of a three-dimensional topological insulator, Bi2Te3. Science 325, 178 (2009). http://www.sciencemag.org/content/325/5937/178.full.pdf
  29. Xia Y. et al.: Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nat. Phys. 5, 398 (2009) (10.1038/nphys1274) / Nat. Phys. by Y. Xia (2009)
  30. Schnyder A.P., Ryu S., Furusaki A., Ludwig A.W.W.: Classification of topological insulators and superconductors in three spatial dimensions. Phys. Rev. B 78, 195125 (2008) (10.1103/PhysRevB.78.195125) / Phys. Rev. B by A.P. Schnyder (2008)
  31. Qi X.-L., Hughes T.L., Zhang S.-C.: Topological field theory of time-reversal invariant insulators. Phys. Rev. B 78, 195424 (2008) (10.1103/PhysRevB.78.195424) / Phys. Rev. B by X.-L. Qi (2008)
  32. Kitaev, A.: Periodic table for topological insulators and superconductors. In: Lebedev V., Feigel’Man, M. (eds.) American Institute of Physics Conference Series, vol. 1134, pp. 22–30 (2009) (10.1063/1.3149495)
  33. Wang Z., Chong Y., Joannopoulos J.D., Soljacic M.: Observation of unidirectional backscattering–immune topological electromagnetic states. Nature 461, 772 (2009) (10.1038/nature08293) / Nature by Z. Wang (2009)
  34. Kitagawa T., Berg E., Rudner M., Demler E.: Topological characterization of periodically driven quantum systems. Phys. Rev. B 82, 235114 (2010) (10.1103/PhysRevB.82.235114) / Phys. Rev. B by T. Kitagawa (2010)
  35. Jiang L. et al.: Majorana Fermions in equilibrium and in driven cold-atom quantum wires. Phys. Rev. Lett. 106, 220402 (2011) (10.1103/PhysRevLett.106.220402) / Phys. Rev. Lett. by L. Jiang (2011)
  36. Sørensen A.S., Demler E., Lukin M.D.: Fractional quantum hall states of atoms in optical lattices. Phys. Rev. Lett. 94, 086803 (2005) (10.1103/PhysRevLett.94.086803) / Phys. Rev. Lett. by A.S. Sørensen (2005)
  37. Zhu S.-L., Fu H., Wu C.-J., Zhang S.-C., Duan L.-M.: Spin hall effects for cold atoms in a light-induced gauge potential. Phys. Rev. Lett. 97, 240401 (2006) (10.1103/PhysRevLett.97.240401) / Phys. Rev. Lett. by S.-L. Zhu (2006)
  38. Jaksch D., Zoller P.: Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms. N. J. Phys. 5, 56 (2003) (10.1088/1367-2630/5/1/356) / N. J. Phys. by D. Jaksch (2003)
  39. Osterloh K., Baig M., Santos L., Zoller P., Lewenstein M.: Cold atoms in non-abelian gauge potentials: from the hofstadter “Moth” to lattice gauge theory. Phys. Rev. Lett. 95, 010403 (2005) (10.1103/PhysRevLett.95.010403) / Phys. Rev. Lett. by K. Osterloh (2005)
  40. Kitagawa, T.: Wolfram Demonstration: topological phases with quantum walks. http://demonstrations.wolfram.com/TopologicalPhasesWithQuantumWalks/
  41. Thouless D.J.: Quantization of particle transport. Phys. Rev. B 27, 6083 (1983) (10.1103/PhysRevB.27.6083) / Phys. Rev. B by D.J. Thouless (1983)
  42. Obuse H., Kawakami N.: Topological phases and delocalization of quantum walks in random environments. Phys. Rev. B 84, 195139 (2011) (10.1103/PhysRevB.84.195139) / Phys. Rev. B by H. Obuse (2011)
  43. Kitagawa, T., Oka, T., Demler, E.: Photo control of transport properties in disorderd wire; average conductance, conductance statistics, and time-reversal symmetry. WolframDemonstration: topological phases with quantum walks. ArXiv e-prints (2012). 1201.0521
  44. Moore J.E., Ran Y., Wen X.-G.: Topological surface states in three-dimensional magnetic insulators. Phys. Rev. Lett. 101, 186805 (2008) (10.1103/PhysRevLett.101.186805) / Phys. Rev. Lett. by J.E. Moore (2008)
Dates
Type When
Created 13 years ago (Aug. 3, 2012, 5:21 a.m.)
Deposited 6 years, 1 month ago (July 2, 2019, 8:52 a.m.)
Indexed 3 weeks, 5 days ago (Aug. 6, 2025, 9:09 a.m.)
Issued 13 years ago (Aug. 4, 2012)
Published 13 years ago (Aug. 4, 2012)
Published Online 13 years ago (Aug. 4, 2012)
Published Print 12 years, 11 months ago (Oct. 1, 2012)
Funders 0

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@article{Kitagawa_2012, title={Topological phenomena in quantum walks: elementary introduction to the physics of topological phases}, volume={11}, ISSN={1573-1332}, url={http://dx.doi.org/10.1007/s11128-012-0425-4}, DOI={10.1007/s11128-012-0425-4}, number={5}, journal={Quantum Information Processing}, publisher={Springer Science and Business Media LLC}, author={Kitagawa, Takuya}, year={2012}, month=aug, pages={1107–1148} }