Accuracy threshold for postselected quantum computation

Quantum Information and Computation

Volumn 8, Issue 3-4, 2008, Pages 181-244

  Aliferis, Panos ^a   Gottesman, Daniel ^b   Preskill, John ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

Author keywords

Accuracy threshold; Fault tolerance; Quantum error correction

Indexed keywords

COMPUTATION THEORY; CONCATENATED CODES; ERROR CORRECTION; ERROR DETECTION; QUANTUM COMPUTERS; QUANTUM NOISE; STOCHASTIC SYSTEMS;

ACCURACY THRESHOLD; ANCILLA; ERROR CORRECTING CODE; ERROR DETECTING CODES; FAULT-TOLERANT QUANTUM COMPUTATION; LOW BOUND; QUANTUM ERROR CORRECTIONS; STOCHASTIC NOISE;

FAULT TOLERANCE;

EID: 43949092940     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: 10.26421/qic8.3-4-1     Document Type: Article

References (26)

1. P. W. Shor, "Fault-tolerant quantum computation," in Proceedings, 37th Annual Symposium on Foundations of Computer Science, pp. 56-65 (Los Alamitos, CA, IEEE Press, 1996), arXiv:quan-ph/9605011.
2. D. Aharonov and M. Ben-Or, "Fault-tolerant quantum computation with constant error," Proc. 29th Ann. ACM Symp. on Theory of Computing, p. 176 (New York, ACM, 1998), arXiv:quan-ph/9611025
3. A. Yu. Kitaev, "Quantum computations: algorithms and error correction," Russian Math. Surveys 52, 1191-1249 (1997). (Pubitemid 127374800)
4. E Knill, R. Laflamme, W. H. Zurek, "Resilient quantum computation: error models and thresholds," Proc. Roy. Soc. London, Ser. A 454, 365 (1998), arXiv:quan-ph/9702058. (Pubitemid 128733168)
5. J. Preskill, "Reliable quantum computers," Proc. Roy. Soc. Lond. A 454, 385-410 (1998), arXiv:quan-ph/9705031. (Pubitemid 128733169)
6. D. Gottesman, "Stabilizer codes and quantum error correction," Caltech Ph.D. thesis (1997), arXiv:quan-ph/9705052.
7. P. Aliferis, D. Gottesman, and J. Preskill, "Quantum accuracy threshold for concatenated distance-3 codes," Quant. Inf. Comp. 6, 97-165 (2006), arXiv:quant-ph/0504218.
8. B. W. Reichardt, "Threshold for the distance three Steane quantum code," arXiv:quant-ph/0509203 (2005).
9. P. Aliferis and A. W. Cross, "Sub-system fault tolerance with the Bacon-Shor code," arXiv:quant- ph/0610063 (2006).
10. E. Knill, "Quantum computing with realistically noisy devices," Nature 434, 39-44 (2005), arXiv:quant-ph/0410199 (2004).
11. A. Steane, "Active stabilisation, quantum computation and quantum state synthesis," Phys. Rev. Lett. 78, 2252-2255 (1997), arXiv:quant-ph/9611027. (Pubitemid 127651854)
12. D. Gottesman and I. Chuang, "Quantum teleportation is a universal computational primitive," Nature 402, 390 (1999), arXiv:quant-ph/9908010.
13. B. W. Reichardt, "Postselection threshold against biased noise," arXiv:quant-ph/0608018 (2006).
14. B. W. Reichardt. "Error-detection-based quantum fault tolerance against discrete Pauli noise," U.C. Berkeley Ph.D. thesis (2006), arXiv:quant-ph/0612004.
15. P. W. Shor, "Scheme for reducing decoherence in quantum computer memory," Phys. Rev. A 52, 2493 (1995).
16. A. Steane, "Error-correcting codes in quantum theory," Phys. Rev. Lett. 77, 793 (1996).
17. 17.E. Knill and R. Laflamme, "Concatenated quantum codes," arXiv:quant-ph/9608012 (1996).
18. P. Aliferis, "Level reduction and the quantum threshold theorem," Caltech Ph.D. thesis (2007), arXiv:quant-ph/0703230.
19. E. Knill, "Fault-tolerant postselected quantum computation: schemes," arXiv:quant-ph/0402171 (2004).
20. B. M. Terhal and G. Burkard, "Fault-tolerant quantum computation for local non-Markovian noise," Phys. Rev. A 71, 012336 (2005), arXiv:quant-ph/0402104.
21. D. Aharonov, A. Kitaev, and J. Preskill, "Fault-tolerant quantum computation with long-range correlated noise," Phys. Rev. Lett. 96, 050504 (2006); arXiv:quant-ph/0510231. (Pubitemid 43270971)
22. D. Bacon, "Operator quantum error correcting subsystems for self-correcting quantum memories," arXiv:quant-ph/0506023 (2005).
23. D. Poulin, "Stabilizer formalism for operator quantum error correction," Phys. Rev. Lett. 95, 230504 (2005). arXiv: quant-ph/0508131.
24. C. H. Bennett, D. P. DiVincenzo, J.A. Smolin, and W. K. Wootters, "Mixed state entanglement and quantum error correction," Phys. Rev. A 54, 3824-3851 (1996), arXiv:quant-ph/9604024. (Pubitemid 126583604)
25. S. Bravyi and A. Kitaev, "Universal quantum computation with ideal Clifford gates and noisy ancillas," Phys. Rev. A 71, 022316 (2005), arXiv:quant-ph/0403025. (Pubitemid 43286554)
26. P. Aliferis and B. M. Terhal, "Fault-tolerant quantum computation for local leakage faults," Quant. Inf. Comp. 7, 139-156 (2007), arXiv:quant-ph/0511065.