Graphical algorithms and threshold error rates for the 2d color code

Quantum Information and Computation

Volumn 10, Issue 9-10, 2010, Pages 780-802

  Wang, David S ^a   Fowler, Austin G ^a   Hill, Charles D ^a   Hollenberg, LLOYD C L ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

COLOR; COLOR CODES; DISTILLATION; ERROR CORRECTION; EXTRACTION; PATTERN MATCHING; QUANTUM COMPUTERS; QUANTUM THEORY;

CLIFFORD GROUP; DISTILLATION PROCEDURE; ERROR-CORRECTING; EXTRACTION CIRCUITS; FAULT-TOLERANT QUANTUM COMPUTATION; GRAPH MATCHINGS; LOWER BOUNDS; TOPOLOGICAL ERRORS;

COLOR MATCHING;

EID: 78649472408     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. R. Raussendorf, J. Harrington, and K. Goyal. Topological fault-tolerance in cluster state quantum computation. New J. Phys., 9:199, 2007. quant-ph/0703143.
2. D. S. Wang, A. G. Fowler, A. M. Stephens, and L. C. L. Hollenberg. Threshold error rates for the toric and planar codes. Quant. Info. Comp., 10:456-469, 2010. arXiv:0905.0531.
3. H. Bombin and M. A. Martin-Delgado. Topological quantum distillation. Phys. Rev. Lett., 97:180501, 2006. quant-ph/0605138.
4. P. W. Shor. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A, 52:R2493, 1995.
5. A. R. Calderbank and P. W. Shor. Good quantum error-correcting codes exist. Phys. Rev. A, 54(2):1098-1105, 1996. quant-ph/9512032.
6. A. M. Steane. Multiple particle interference and quantum error correction. Proc. R. Soc. Lond. A, 452:2551-2576, 1996. quant-ph/9601029.
7. P. W. Shor. Algorithms for quantum computation: Discrete logarithms and factoring. In Proc. 35th Annual Symposium on Foundations of Computer Science, pages 124-134, 1994.
8. E. Knill, R. Laflamme, and W. H. Zurek. Accuracy threshold for quantum computation. Technical Report LAUR-96-2199, Los Alamos National Laboratory, 1996. quant-ph/9610011.
9. K. M. Svore, D. DiVincenzo, and B. Terhal. Noise threshold for a fault-tolerant two-dimensional lattice architecture. Quant. Info. Comp., 7:297, 2007. quant-ph/0604090.
10. F. M. Spedalieri and V. P. Roychowdhury. Latency in local, two-dimensional, fault-tolerant quantum computing. arXiv:0805.4213, 2008.
11. A. Yu. Kitaev. Fault-tolerant quantum computation by anyons. Ann. Phys., 303:2-30, 2003. quant-ph/9707021.
12. R. Raussendorf, J. Harrington, and K. Goyal. A fault-tolerant one-way quantum computer. Ann. Phys., 321:2242-2270, 2006. quant-ph/0510135.
13. A. G. Fowler, A. M. Stephens, and P. Groszkowski. High-threshold universal quantum computation on the surface code. Phys. Rev. A, 80(5):052312, Nov 2009. arXiv:0803.0272.
14. Austin G. Fowler. Universal quantum computation without state distillation on a 2-D color code. arXiv:0806.4827v1, 2008.
15. Helmut G. Katzgraber, H. Bombin, and M. A. Martin-Delgado. Error threshold for color codes and random three-body ising models. Phys. Rev. Lett., 103(9):090501, Aug 2009. arXiv:0902.4845.
16. E. Dennis, A. Kitaev, A. Landahl, and J. Preskill. Topological quantum memory. J. Math. Phys., 43:4452-4505, 2002. quant-ph/0110143.
17. J. Edmonds. Paths, trees, and flowers. Canadian Journal of Mathematics, 17(3):449-467, 1965.
18. J. Edmonds. Maximum matching and a polyhedron with 0, 1-vertices. Journal of Research of the National Bureau of Standards, 69(1-2):125-130, 1965.
19. W. Cook and A. Rohe. Computing minimum-weight perfect matchings. INFORMS J. Comput., 11:138-148, 1999.
20. A. G. Fowler and K. Goyal. Topological cluster state quantum computing. Quant. Info. Comp., 9:721-738, 2009. arXiv:0805.3202.
21. C. Wang, J. Harrington, and J. Preskill. Confinement-higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory. Ann. Phys., 303(1):31-58, 2003.