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Double Semion Model as a Quantum Memory

  • Laura Ortiz MartínEmail author
Chapter
Part of the Springer Theses book series (Springer Theses)

Abstract

To carry out a quantum error-correction protocol, we must first encode the quantum information we want to protect, and then repeatedly perform recovery operations that reverse the errors. Standard quantum error correcting codes [1, 2, 3, 4, 5, 6, 7, 8] are based on a special class of codes, called concatenated codes, which enable us to perform longer quantum computations reliably, as we increase the block size.

References

  1. 1.
    Shor Peter W (1995) Scheme for reducing decoherence in quantum computer memory. Phys Rev A 52:R2493–R2496ADSCrossRefGoogle Scholar
  2. 2.
    Steane AM (1996) Error correcting codes in quantum theory. Phys Rev Lett 77:793–797ADSMathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Shor PW (1996) Fault-tolerant quantum computation. arXiv:quantum-phys, 9605011
  4. 4.
    Knill E, Laflamme R, Zurek W (1996) Threshold accuracy for quantum computation. arXiv:quantum-phys, 9610011
  5. 5.
    Kitaev AY (1997) Quantum computations: algorithms and error correction. Russ Math Surv 52:1191MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Aharonov D, Ben-Or M (2008) Fault-tolerant quantum computation with constant error rate. SIAM J Comput 38(4):1207MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Nielsen MA, Chuang IL (2000) Quantum computation and quantum information. University Press, CambridgeGoogle Scholar
  8. 8.
    Galindo A, Martín-Delgado MA (2002) Information and computation: classical and quantum aspects. Rev Mod Phys 74:347–423ADSMathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Kitaev AY (2003) Fault-tolerant quantum computation by anyons. Ann Phys 303(1):2–30ADSMathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Dennis E, Kitaev A, Landahl A, Preskill J (2002) Topological quantum memory. J Math Phys 43(9):4452–4505ADSMathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Bravyi SB, Kitaev AY (1998) Quantum codes on a lattice with boundary. arXiv:9811052
  12. 12.
    Bombin H, Martin-Delgado MA (2006) Topological quantum distillation. Phys Rev Lett 97:180501Google Scholar
  13. 13.
    Bombin H, Martin-Delgado MA (2007) Topological computation without braiding. Phys Rev Lett 98:160502Google Scholar
  14. 14.
    Bombin H, Martin-Delgado MA (2007) Homological error correction: classical and quantum codes. J Math Phys 48(5):052105ADSMathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Bombin H, Martin-Delgado MA (2007) Optimal resources for topological two-dimensional stabilizer codes: comparative study. Phys Rev A 76:012305ADSCrossRefGoogle Scholar
  16. 16.
    Wootton James R, Daniel L (2012) High threshold error correction for the surface code. Phys Rev Lett 109:160503ADSCrossRefGoogle Scholar
  17. 17.
    Sergey B, Jeongwan H (2013) Quantum self-correction in the 3d cubic code model. Phys Rev Lett 111:200501CrossRefGoogle Scholar
  18. 18.
    Sergey B, Martin S, Alexander V (2014) Efficient algorithms for maximum likelihood decoding in the surface code. Phys Rev A 90:032326CrossRefGoogle Scholar
  19. 19.
    Levin Michael A, Xiao-Gang W (2005) String-net condensation: a physical mechanism for topological phases. Phys Rev B 71:045110ADSCrossRefGoogle Scholar
  20. 20.
    Andrej M, Ying R (2013) Classification of symmetry enriched topological phases with exactly solvable models. Phys Rev B 87:155115CrossRefGoogle Scholar
  21. 21.
    von Keyserlingk CW, Burnell FJ, Simon SH (2013) Three-dimensional topological lattice models with surface anyons. Phys Rev B 87:045107Google Scholar
  22. 22.
    Dauphinais G, Ortiz L, Varona S, Martin-Delgado MA (2019) Quantum error correction with the semion code. New J Phys  https://doi.org/10.1088/1367-2630/ab1ed8CrossRefGoogle Scholar
  23. 23.
    Michael L, Xiao-Gang W (2003) Fermion, strings, and gauge fields in lattice spin models. Phys Rev B 67:245316CrossRefGoogle Scholar
  24. 24.
    Chenyang W, Jim H, John P (2003) Confinement-higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory. Ann Phys 303(1):31–58zbMATHCrossRefGoogle Scholar
  25. 25.
    Gregory M, Read N (1991) Nonabelions in the fractional quantum hall effect. Nucl Phys B 360(2):362–396ADSMathSciNetGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Racah Institute of PhysicsThe Hebrew University of JerusalemJerusalemIsrael

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