Two-qubit Operation on Majorana Qubits in Ordinary-qubit Chains

  • Yu. MakhlinEmail author
  • S. Backens
  • A. Shnirman


Majorana zero modes can be simulated in structures based on spin or quasi-spin degrees of freedom, e.g., Josephson-qubit chains. Braiding of Majorana degrees of freedom is realized using T -junctions supplied with an auxiliary spin (ancilla). Motivated by prospective experiments, we analyze the braiding in the spin representation, which provides the basis for the analysis of imperfections characteristic to the spin and qubit designs. The result of the braiding operation is straightforwardly found for the initial basis states of the two qubits and the ancilla, up to phase factors. Here we fix these phase factors and thus describe the complete two-qubit operation. This result is relevant for physical simulation of the Majorana qubits in Josephson-qubit chains and other spin or qubit structures.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R.M. Lutchyn, E.P. A.M. Bakkers, L.P. Kouwenhoven, P. Krogstrup, C.M. Marcus, and Y. Oreg, Nat. Rev. Mater. 3, 52 (2018).ADSCrossRefGoogle Scholar
  2. 2.
    C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Rev. Mod. Phys. 80, 1083 (2008).ADSCrossRefGoogle Scholar
  3. 3.
    S. Das Sarma, M. Freedman, and C. Nayak, NJP Quantum Information 1, 15001 (2015).ADSCrossRefGoogle Scholar
  4. 4.
    A.Yu. Kitaev, Ann. Phys. 303, 2 (2003).ADSCrossRefGoogle Scholar
  5. 5.
    A.Yu. Kitaev, Phys. Usp. 44, 131 (2001); Scholar
  6. 6.
    N. Read and D. Green, Phys. Rev. B 61, 10267 (2000).ADSCrossRefGoogle Scholar
  7. 7.
    D. Ivanov, Phys. Rev. Lett. 86, 268 (2001).ADSCrossRefGoogle Scholar
  8. 8.
    J. Alicea, Y. Oreg, G. Refael, F. von Oppen, and M. P.A. Fisher, Nat. Phys. 7, 412 (2011); http: // nphys1915.html.CrossRefGoogle Scholar
  9. 9.
    M. Pino, A.M. Tsvelik, and L.B. Ioffe, Phys. Rev. Lett. 115, 197001 (2015); https: // Scholar
  10. 10.
    S. Backens, A. Shnirman, Yu. Makhlin, Y. Gefen, J. E. Mooij, and G. Schön, Phys. Rev. B 96, 195402 (2017); 10.1103/Phys-RevB.96.195402.ADSCrossRefGoogle Scholar
  11. 11.
    J. Alicea, Rep. Prog. Phys. 75, 076501 (2012).ADSCrossRefGoogle Scholar
  12. 12.
    S. Backens, A. Shnirman, and Yu. Makhlin, e-print arXiv:1810.02590 (2018).Google Scholar
  13. 13.
    A. M. Tsvelik, Phys. Rev. Lett. 110, 147202 (2013); Scholar
  14. 14.
    C. Hutter, A. Shnirman, Yu. Makhlin, and G. Schoen, Europhys. Lett. 74, 1088 (2006).ADSCrossRefGoogle Scholar
  15. 15.
    P. Hauke, D. Marcos, M. Dalmonte, and P. Zoller, Phys. Rev. X 3, 041018 (2013); Scholar
  16. 16.
    N. Crampé and A. Trombettoni, Nucl. Phys. B 871, 526 (2013); Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.Condensed-matter physics LaboratoryNational Research University Higher School of EconomicsMoscowRussia
  2. 2.Landau Institute for Theoretical PhysicsChernogolovkaRussia
  3. 3.Institut für Theorie der Kondensierten MaterieKarlsruhe Institute of TechnologyKarlsruheGermany
  4. 4.Institute of NanotechnologyKarlsruhe Institute of TechnologyEggenstein-LeopoldshafenGermany

Personalised recommendations