Fault-tolerant quantum computation for local non-Markovian noise

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 71, Issue 1, 2005, Pages

  Terhal, Barbara M ^a,b   Burkard, Guido ^b  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

^b IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FAULT-TOLERANCE ANALYSIS; FAULT-TOLERANT QUANTUM COMPUTATION; NON-MARKOVIAN NOISE; QUANTUM CIRCUITRY;

COMPUTATIONAL METHODS; DATA STORAGE EQUIPMENT; DEGREES OF FREEDOM (MECHANICS); FAULT TOLERANT COMPUTER SYSTEMS; FUNCTIONS; HAMILTONIANS; MARKOV PROCESSES; SPURIOUS SIGNAL NOISE; THEOREM PROVING;

QUANTUM THEORY;

EID: 18444391491     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.71.012336     Document Type: Article

References (26)

1. P. W. Shor, in Proceedings of 37th FOCS (IEEE Computer Society Press, Los Alamitos, CA, 1996), p. 56.
2. D. Aharonov and M. Ben-Or, in Proceedings of 29th STOC (1997), p. 56; e-print quant-ph/9611025.
3. E. Knill, R. Laflamme, and W. Zurek, Proc. R. Soc. London, Ser. A 454, 365 (1997); e-print quant-ph/9702058.
4. D. Aharonov and M. Ben-Or, e-print quant-ph/9906129.
5. D. Gottesman, Phys. Rev. A 57, 127 (1998).
6. J. Preskill, in Introduction to Quantum Computation (World Scientific, Singapore, 1998), p. 213.
7. E. Knill, R. Laflamme, and W. Zurek, Science 279, 342 (1998).
8. A. M. Steane, Phys. Rev. A 68, 042322 (2003).
9. W. Dür and H.-J. Briegel, Phys. Rev. Lett. 90, 067901 (2003).
10. E. Knill, e-print quant-ph/0312190.
11. A. Kitaev, Ann. Phys. (N.Y.) 303, 2 (2003); e-print quant-ph/ 9707021.
12. R. Alicki, M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. A 65, 062101 (2002).
13. kl, but this will not make much difference in the analysis.
14. B acting on the bath of qubit q since our analysis (basically Lemma 2) will not depend on the bath dynamics. It is not clear that this extra freedom makes a big difference in the analysis. For example, it can be proven that it does not solve the problems that we face with the norm of the interaction Hamiltonian for the spin-boson bath, see Sec. V.
15. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).
16. E. Knill, R. Laflamme, and L. Viola, Phys. Rev. Lett. 84, 2525 (2000).
17. Introduction to Quantum Computation, edited by H.-K. Lo, S. Popescu, and T. P. Spiller (World Scientific, Singapore, 1998).
18. Codes encoding more than one qubit could also be used, but they will complicate the analysis.
19. R. Alicki, e-print quant-ph/0402139.
20. We could generalize this to c-system local Hamiltonians without much ado.
21. D. J. Wineland, M. Barrett, J. Britton, J. Chiaverini, B. De-Marco, W. M. Itano, B. Jelenkovic, C. Langer, D. Leibfried, V. Meyer, T. Rosenband, and T. Schätz, Proceedings of the Discussion Meeting on Practical Realisations of QIP, held at the Royal Society (to be published), e-print quant-ph/0212079.
22. K. M. Svore, B. M. Terhal, and D. P. DiVmcenzo, e-print quant-ph/0410047.
23. Of course methods also exist for turning off unwanted J-couplings by refocusing.
24. A. Khaetskii, D. Loss, and L. Glazman, Phys. Rev. B 67, 195329 (2003).
25. U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 2000).
26. D. Loss and D. P. DiVincenzo, e-print cond-mat/0304118.