Limitations of passive protection of quantum information

Quantum Information and Computation

Volumn 10, Issue 7-8, 2010, Pages 580-618

  Fernando, Pastawski ^a   Kay, Alastair ^b   Schuch, Norbert ^a   Cirac, Ignacio ^a  

^a MAX PLANCK INSTITUT FÜR QUANTENOPTIK   (Germany)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; ERROR CORRECTION; GROUND STATE; HAMILTONIANS;

EFFECT OF NOISE; ERROR THRESHOLD; ERROR-CORRECTING; MARKOVIAN APPROXIMATION; N-QUBIT SYSTEMS; OF QUANTUM-INFORMATION; PASSIVE PROTECTION; QUANTUM INFORMATION;

QUANTUM OPTICS;

EID: 77953894124     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (47)

1. D. Bacon (2006), Operator quantum error-correcting subsystems for self-correcting quantum memories, Phys. Rev. A, Vol. 73, p. 012340.
2. P. W. Shor (1997), Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM J. Comput., Vol.26, pp. 1484-1509.
3. A. M. Childs and W. van Dam (2008), Quantum algorithms for algebraic problems, Rev. Mod. Phys., Vol. 82, pp. 1-52.
4. A. W. Harrow, A. Hassidim and S. Lloyd (2009), Quantum algorithm for linear systems of equations., Phys. Rev. Lett., Vol. 103, pp. 150502-4.
5. C. H. Bennet and G. Brassard (1984) Quantum cryptography: Public key distribution and coin tossing, in Proceedings of IEEE International Conference on Computers, Systems & Signal Processing, IEEE Press, New York, Bangalore, India, pp. 175-179.
6. A. K. Ekert (1991), Quantum cryptography based on bells theorem. Phys. Rev. Lett., Vol. 67, p. 661.
7. P. W. Shor (1995), Scheme for reducing decoherence in quantum computer memory, Phys. Rev. A, Vol. 52, p. R2493.
8. D. Aharonov and M. Ben-Or (1996), Fault tolerant quantum computation with constant error, quant-ph/9611025.
9. D. Gottesman (1998), Theory of fault-tolerant quantum computation. Phys. Rev. A, Vol. 57, p. 127.
10. D. Gottesman (2009), An introduction to quantum error correction and Fault-Tolerant quantum computation, arXiv:0904.2557.
11. A. Y. Kitaev (2003), Fault-tolerant quantum computation by anyons, Annals of Physics, Vol. 303, pp. 2-30.
12. E. Dennis, A. Kitaev, A. Landahl and J. Preskill (2002), Topological quantum memory, Jour. Math. Phys., Vol. 43, pp. 4452-4505.
13. S. Bravyi, M. B. Hastings and S. Michalakis (2010), Topological quantum order: stability under local perturbations, arXiv:1001.0344.
14. S. Bravyi and M. B. Hastings (2010), A short proof of stability of topological order under local perturbations, arXiv:1001.4363.
15. M. B. Hastings and X. G. Wen (2005), Quasi-adiabatic continuation of quantum states: The stability of topological ground state degeneracy and emergent gauge invariance, Phys.Rev. B, Vol. 72, p. 45141.
16. A. Hamma and D. A. Lidar (2008), Adiabatic preparation of topological order, Phys. Rev. Lett., Vol. 100, pp. 030502-4.
17. Z. Nussinov and G. Ortiz (2008), Autocorrelations and thermal fragility of anyonic loops in topologically quantum ordered systems, Phys. Rev. B, Vol. 77, p. 064302.
18. Z. Nussinov and G. Ortiz (2009), A symmetry principle for topological quantum order, Annals of Phys., Vol. 324, pp. 977-1057.
19. R. Alicki, M. Fannes, and M. Horodecki (2008), On thermalization in kitaev's 2d model, J. Phys. A: Math. Theor., Vol. 42, pp. 065303-18
20. R. Alicki, M. Horodecki, P. Horodecki and R. Horodecki (2008), On thermal stability of topological qubit in kitaev's 4d model, arXiv:0811.0033.
21. R. Alicki, M. Fannes (2009), Decay of fidelity in terms of correlation functions, Phys. Rev. A, Vol. 79, pp. 012316-4.
22. S. Chesi, D. Loss, S. Bravyi and B. M. Terhal (2010),Thermodynamic stability criteria for a quantum memory based on stabilizer and subsystem codes, New J. Phys., Vol. 12, p. 025013.
23. F. Pastawski, A. Kay, N. Schuch and I. Cirac (2009), How long can a quantum memory withstand depolarizing noise?, Phys. Rev. Lett., Vol. 103, p. 080501.
24. S. Bravyi, D. P. DiVincenzo, D. Loss and B. M. Terhal (2008), Quantum simulation of Many-Body hamiltonians using perturbation theory with Bounded-Strength interactions, Phys. Rev. Lett., Vol. 101, pp. 070503-4.
25. M. M. Wolf (2008), Quantum many-body theory: Divide, perturb and conquer, Nat. Phys., Vol. 4, pp. 834-835.
26. D. Bacon (2008), Stability of quantum concatenated-code hamiltonians, Phys. Rev. A, Vol. 78, pp. 042324-14.
27. S. Chesi, B. Röthlisberger and D. Loss (2009), A Self-Correcting quantum memory in a thermal environment, arXiv:0908.4264.
28. A. Hamma, C. Castelnovo and C. Chamon (2009), Toric-boson model: Toward a topological quantum memory at finite temperature, Phys. Rev. B, Vol. 79, pp. 245122.
29. A. Kay (2009), Nonequilibrium reliability of quantum memories, Phys. Rev. Lett., Vol. 102, p. 070503.
30. C. King (2003), The capacity of the quantum depolarizing channel, Trans. Inform. Theory, Vol. 49, pp. 221-229.
31. P. W. Anderson (1967), Infrared catastrophe in fermi gases with local scattering potentials, Phys. Rev. Lett., Vol. 18, p. 1049.
32. L. C. Venuti and P. Zanardi (2007), Quantum critical scaling of the geometric tensors, Phys. Rev. Lett., Vol. 99, p. 095701.
33. D. Kribs, R. Laflamme and D. Poulin, Unified and generalized approach to quantum error correction, Phys. Rev. Lett., Vol. 94, p. 180501.
34. M. Christandl, N. Datta, A. Ekert and A. J. Landahl (2004), Perfect state transfer in quantum spin networks, Phys. Rev. Lett., Vol. 92, p. 187902.
35. P. Karbach (2005), Spin chains as perfect quantum state mirrors, Phys. Rev. A, Vol. 72, p. 030301.
36. A. Kay (2009), A review of perfect state transfer and its application as a constructive tool, arXiv:0903.4274.
37. S. Bravyi and B. Terhal (2009), A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes, New J. Phys., Vol. 11, p. 043029.
38. A. Kay and R. Colbeck (2008), Quantum self-correcting stabilizer codes, arXiv:0810.3557.
39. P. Vaidya (1988), Geometry helps in matching, STOC '88: Proceedings of the twentieth annual ACM symposium on Theory of computing, ACM Press, New York, Chicago, USA, pp. 422-425.
40. L. H. Richards, S. W. Sides, M. A. Novotny and P. A. Rikvold (1995), Magnetization switching in nanoscale ferromagnetic grains: description by a kinetic ising model, Journal of Magnetism and Magnetic Materials, Vol. 150, pp. 37-50.
41. E. Cirillo and J. Lebowitz (1998), Metastability in the Two-Dimensional ising model with free boundary conditions, Journal of Statistical Physics, Vol. 90, pp. 211-226.
42. G. Grinstein (2004), Can complex structures be generically stable in a noisy world?, IBM J. Res. and Dev., Vol. 48.
43. K. R. Brown (2007), Energy protection arguments fail in the interaction picture, Phys. Rev. A, Vol. 76, p. 022327.
44. D. A. Lidar (2008), Towards fault tolerant adiabatic quantum computation, Phys. Rev. Lett., Vol. 100, p. 160506.
45. S. P. Jordan, E. Farhi and P. W. Shor (2006), Error-correcting codes for adiabatic quantum computation, Phys. Rev. A, Vol. 74, p. 052322.
46. A. Kay and M. Ericsson (2005), Geometric effects and computation in spin networks, New J. Phys., Vol. 7, p. 143.
47. W. Hoeffding (1963), Probability inequalities for sums of bounded random variables, Journal of the American Statistical Association, Vol. 58, pp. 13-30.