No Access Published Online: 10 August 2021
AIP Conference Proceedings 2382, 020007 (2021); https://doi.org/10.1063/5.0059974
Ettore Majorana, in his short life, unintendedly has uncovered the most profound problem in quantum computation by his discovery of Majorana fermion, a particle which is its own anti-particle. Owing to its non-Abelian exchange statistics, Majorana fermions may act as a qubit for a universal quantum computer which is fault-tolerant. The existence of such particle is predicted in mid-gap states (zero modes) of a topological superconductor as bound states that have a highly entangled degenerate ground state. This introductory overview will focus on the simplest theoretical proposals of Majorana fermions for topological quantum computing in superconducting systems, emphasizing the quest from the scalability problem of quantum computer to its possible solution with topological quantum computer employing non-Abelian anyons on various platforms of certain Majorana fermion ‘signature’ encountered.
  1. 1. R. Jozsa, preprint arXiv:9707034 [quant-ph] (1997). Google Scholar
  2. 2. R. P. Feynman, Int. J. Theor. Physics 21, 467–488 (1982). Google ScholarCrossref
  3. 3. D. Deutsch, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 400, 97–117 (1985). Google ScholarCrossref
  4. 4. A. Steane, Rep. Prog. Physics 61, 117–161 (1998). Google ScholarCrossref
  5. 5. P. W. Shor, SIAM Review 41, 303–332 (1999). Google ScholarCrossref
  6. 6. L. K. Grover, Phys. Rev. Letters 79, 325–328 (1997). Google ScholarCrossref
  7. 7. T. M. Fernández-Caramés, IEEE Internet of Things Journal 7, 6457–6480 (2019). Google ScholarCrossref
  8. 8. C. H. Bennett, E. Bernstein, G. Brassard, and U. Vazirani, SIAM Journal on Computing 26, 1510–1523 (1997). Google ScholarCrossref
  9. 9. A. Aspuru-Guzik, A. D. Dutoi, P. J. Love, and M. Head-Gordon, Science 309, 1704–1707 (2005). Google ScholarCrossref
  10. 10. J. I. Colless, V. V. Ramasesh, D. Dahlen, M. S. Blok, J. R. McClean, J. Carter, W. A. de Jong, and I. Siddiqi, 2017. preprint arXiv:1707.06408 [quant-ph] (2017). Google Scholar
  11. 11. A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J.M. Chow, and J.M. Gambetta, Nature 549, 242–246 (2017). Google ScholarCrossref
  12. 12. J. Preskill, preprint arXiv:1801.00862v3 [quant-ph] (2018). Google Scholar
  13. 13. W. K. Wootters and W.H. Zurek, Nature 299, 802–803 (1982). Google ScholarCrossref
  14. 14. P. W. Shor, Phys. Rev. A 52, R2493–R2496 (1995). Google ScholarCrossref
  15. 15. A. M. Steane, Phys. Rev. Letters 77, 793–796 (1996). Google ScholarCrossref
  16. 16. E. Knill, R. Laflamme, and W. Zurek, preprint arXiv:9610011 [quant-ph] (1996). Google Scholar
  17. 17. D. Gottesman, Journal of Modern Optics 47, 333–345 (2000). Google ScholarCrossref
  18. 18. P. W. Shor, Proc. 37th Annual Symp. on Foundations of Computer Science (IEEE Computer Society Press, Los Alamitos, CA, 1996), pp. 56–65. Google Scholar
  19. 19. A. R. Calderbank and P. W. Shor, Phys. Rev. A 54, 1098–1105 (1996). Google ScholarCrossref
  20. 20. A. Y. Kitaev, Annals of Physics 303, 2–30 (2003). Google ScholarCrossref
  21. 21. A. Y. Kitaev, Physics-Uspekhi 44, 131–136 (2001). Google ScholarCrossref
  22. 22. G. Castagnoli, and M. Rasetti, International Journal of Theoretical Physics 32, 2335–2347 (1993). Google ScholarCrossref
  23. 23. D. P. Arovas, R. Schrieffer, F. Wilczek, and A. Zee, Nuclear Physics B 251, 117–126 (1985). Google ScholarCrossref
  24. 24. F. Wilczek, Phys. Rev. Letters 49, 957–959 (1982). Google ScholarCrossref
  25. 25. J. K. Pachos, Introduction to Topological Quantum Computation (Cambridge University Press, Cambridge, UK, 2012), pp. 55–75. Google ScholarCrossref
  26. 26. P. A. M. Dirac, Proceedings of the Royal Society of London. Series A-Mathematical and Physical Sciences 155, 447–459 (1936). Google ScholarCrossref
  27. 27. E. Majorana, Il Nuovo Cimento (1924-1942) 14, 171–184 (1937). Google ScholarCrossref
  28. 28. C. Jr Cowan, F. Reines, F. Harrison, H. Kruse and A. McGuire, Science 124, 103–104 (1956). Google ScholarCrossref
  29. 29. S. Q. Shen, Topological Insulators (Springer, Berlin, 2012), pp. 13–26. Google ScholarCrossref
  30. 30. R. Jackiw and C. Rebbi, Phys. Rev. D 13, 3398–3409 (1976). Google ScholarCrossref
  31. 31. L. Fu and C. L. Kane, Phys. Rev. Letters 100, 0964071–0964074 (2008). Google Scholar
  32. 32. M. Leijnse and K. Flensberg, Semiconductor Science and Technology 27, 1240031–12400311 (2012). Google ScholarCrossref
  33. 33. J. M. Leinaas and J. Myrheim, Il Nuovo Cimento B (1971-1996) 37, 1–23 (1977). Google ScholarCrossref
  34. 34. D. C. Tsui, H. L. Stormer and A. C. Gossard, Phys. Rev. Letters 48, 1559–1561 (1982). Google ScholarCrossref
  35. 35. R. B. Laughlin, Phys. Rev. Letters 50, 1395–1398 (1983). Google ScholarCrossref
  36. 36. B. I. Halperin, Phys. Rev. Letters 52, 1583–1586 (1984). Google ScholarCrossref
  37. 37. G. Moore and N. Read, Nuclear Physics B 360, 362–396 (1991). Google ScholarCrossref
  38. 38. S. D. Sarma, M. Freedman and C. Nayak, Phys. Rev. Letters 94, 16680232–16680238 (2005). Google Scholar
  39. 39. S. Bravyi, Phys. Rev. A 73, 0423131–04231315 (2006). Google ScholarCrossref
  40. 40. S. Bravyi and A. Y. Kitaev, Phys. Rev. A 71, 0223161–0223162 (2005). Google ScholarCrossref
  41. 41. J. S. Xia, W. Pan, C. Vicente, E. D. Adams, N. S. Sullivan, H. L. Stormer, D. C. Tsui, L. N. Pfeiffer, K. W. Baldwin and K. W. West, Phys. Rev. Letters 93, 1768091–1768094 (2004). Google ScholarCrossref
  42. 42. S. D. Sarma, M. Freedman, and C. Nayak, Physics Today 59, 32–38 (2006). Google ScholarCrossref
  43. 43. A. Stern and N.H. Lindner, Science 339, 1179–1184 (2013). Google ScholarCrossref
  44. 44. C. W. J. Beenakker, preprint arXiv:1907.06497 [cond-mat.mes-hall] (2019). Google Scholar
  45. 45. C. W. J. Beenakker, P. Baireuther, Y. Herasymenko, I. Adagideli, L. Wang and A. R. Akhmerov, Phys. Rev. Letters 122, 1468031–1468034 (2019). Google ScholarCrossref
  46. 46. J. Nakamura, S. Liang, G. C. Gardner and M. J. Manfra, preprint arXiv:2006.14115 [cond-mat.mes-hall] (2020). Google Scholar
  47. 47. N. Read and D. Green, Phys. Rev. B 61, 10267–10268 (2000). Google ScholarCrossref
  48. 48. V. Mourik, K. Zuo, S.M. Frolov, S.R. Plissard, E.P. Bakkers and L.P. Kouwenhoven, Science 336, 1003–1007 (2012). Google ScholarCrossref
  49. 49. X. L. Qi, T. L. Hughes and S. C. Zhang, Phys. Rev. B 82, 1845161–1845165 (2010). Google Scholar
  50. 50. B. Lian, X. Q. Sun, A. Vaezi, X. L. Qi and S. C. Zhang, Proceedings of the National Academy of Sciences 115, 10938–10942 (2018). Google ScholarCrossref
  51. 51. J. D. Sau, S. Tewari, R. M. Lutchyn, T. D. Stanescu and S. D. Sarma, Phys. Rev. B 82, 2145091–21450923 (2010). Google Scholar
  52. 52. C. W. J. Beenakker, Annu. Rev. Condens. Matter Phys. 4, 113–136 (2013). Google ScholarCrossref
  53. 53. K. T. Law, P. A. Lee and T. K. Ng, Phys. Rev. Letters 103, 2370011–2370014 (2009). Google ScholarCrossref
  54. 54. S. D. Sarma, J. D. Sau and T. D. Stanescu, Phys. Rev. B 86, 2205061–2205064 (2012). Google Scholar
  55. 55. R. M. Lutchyn, J. D. Sau and S. D. Sarma, Phys. Rev. Letters 105, 0770011–0770014 (2010). Google ScholarCrossref
  56. 56. S. Nadj-Perge, I. K. Drozdov, J. Li, H. Chen, S. Jeon, J. Seo, A. H. MacDonald, B. A. Bernevig and A. Yazdani, Science 346, 1–4 (2014). Google ScholarCrossref
  57. 57. J. Wiedenmann, E. Bocquillon, R. S. Deacon, S. Hartinger, O. Herrmann, T. M. Klapwijk, L. Maier, C. Ames, C. Brüne, C. Gould and A. Oiwa, Nature Communications 7, 1–7 (2016). Google ScholarCrossref
  58. 58. H. J. Suominen, M. Kjaergaard, A. R. Hamilton, J. Shabani, C. J Palmstrøm, C. M. Marcus and F. Nichele, Phys. Rev. Letters 119, 1768051–1768055 (2017). Google ScholarCrossref
  59. 59. D. Wang, L. Kong, P. Fan, H. Chen, S. Zhu, W. Liu, L. Cao, Y. Sun, S. Du, J. Schneeloch and R. Zhong, Science 362, 333–335 (2018). Google ScholarCrossref
  60. 60. Q. L. He, L. Pan, A. L. Stern, E. C. Burks, X. Che, G. Yin, J. Wang, B. Lian, Q. Zhou, E. S. Choi and K. Murata, Science 357, 294–299 (2017). Google ScholarCrossref
  61. 61. M. Kayyalha, D. Xiao, R. Zhang, J. Shin, J. Jiang, F. Wang, Y. F. Zhao, R. Xiao, L. Zhang, K. M. Fijalkowski and P. Mandal, Science 367, 64–67 (2020). Google ScholarCrossref
  62. 62. M. T. Deng, S. Vaitiekenas, E. B. Hansen, J. Danon, M. Leijnse, K. Flensberg, J. Nygård, P. Krogstrup and C. M. Marcus, Science 354, 1557–1562 (2016). Google ScholarCrossref
  63. 63. C. X. Liu, J. D. Sau, T. D. Stanescu and S. D. Sarma, Phys. Rev. B 96, 0751611–07516125 (2017). Google Scholar
  64. 64. Y. H. Lai, J. D. Sau and S. D. Sarma, Phys. Rev. B 100, 0453021–0453027 (2019). Google Scholar
  65. 65. H. Zhang, D. E. Liu, M. Wimmer and L. P. Kouwenhoven, Nature Communications 10, 1–7 (2019). Google ScholarCrossref
  66. 66. R. L. O. het Veld, D. Xu, V. Schaller, M. A. Verheijen, S. M. Peters, J. Jung, C. Tong, Q. Wang, M. W. de Moor, B. Hesselmann and K. Vermeulen, Communications Physics 3, 1–7 (2020). Google ScholarCrossref
  67. 67. Y. F. Zhou, Z. Hou and Q. F. Sun, Phys. Rev. B 99, 1951371–1951372 (2019). Google Scholar
  68. 68. W. N. Faugno, J. K. Jain and A. C. Balram, preprint arXiv:2006.00238 [cond-mat.str-el] (2020). Google Scholar
  69. 69. C. Wang, L. Gioia and A. A. Burkov, Phys. Rev. Letters 124, 0966031–0966035 (2020). Google Scholar
  70. 70. A. Bouhon, Q. S. Wu, R. J. Slager, H. Weng, O. V. Yazyev, and T. Bzdušek, Nature Physics 16, 1137–1143 (2020). Google ScholarCrossref
  71. 71. X. Luo, Y. G. Chen, Y. M. Han, B. Chen and Y. Yu, preprint arXiv:2004.03297 [cond-mat.str-el] (2020). Google Scholar
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