On cayley graphs, surface codes, and the limits of homological coding for quantum error correction

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5557 LNCS, Issue , 2009, Pages 259-273

  Zémor, Gilles ^a  

^a UNIVERSITÉ BORDEAUX 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CODES (SYMBOLS); CRYPTOGRAPHY; ERROR CORRECTION; GRAPH DATABASES;

2-DIMENSIONAL CASE; CAYLEY GRAPHS; CYCLE CODES; HIGHER-DIMENSIONAL; MINIMUM DISTANCE; QUANTUM ERROR CORRECTIONS;

GRAPH THEORY;

EID: 69849101595     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-01877-0_21     Document Type: Conference Paper

References (18)

1. Alon, N., Hoory, S., Linial, N.: The Moore bound for irregular graphs. Graphs Combin. 18, 53-57
2. Bombin, H., Martin-Delgado, M.A.: Homological Error Correction: Classical and Quantum Codes. J. Math. Phys. 48, 052105 (2007)
3. Calderbank, A.R., Shor, P.W.: Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098 (1996)
4. Decreusefond, L., Zemor, G.: On the error-correcting capabilities of cycle codes of graphs. Combinatorics, Probability and Computing 6, 27-38 (1997)
5. Dennis, E., Kitaev, A., Landahl, A., Preskill, J.: Topological quantum memory. J. Math. Phys. 43, 4452-4505 (2002)
6. Erdos, P., Sachs, H.: Regulare Graphen gegebener Taillenweite mit minimaler Knotenzahl. Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg, Math.-Naturwiss. Reihe 12, 251-258 (1963)
7. Freedman, M.H., Meyer, D.A., Luo, F.: F2-systolic freedom and quantum codes. In: Mathematics of quantum computation. Comput. Math. Ser., pp. 287-320. Chapman & Hall/CRC, Boca Raton (2002)
8. Hagiwara, M., Imai, H.: Quantum Quasi-Cyclic LDPC Codes. In: Proc. IEEE International Symposium Information Theory (ISIT), Nice 2007, pp. 806-810 (2007)
9. Hatcher, A.: Algebraic Topology. Cambridge University Press, Cambridge (2002)
10. Kim, I.H.: Quantum codes on Hurwitz surfaces, S. B. Thesis, MIT (2007), http://dspace.mit.edu/handle/1721.1/40917
11. Kitaev, A.: Quantum error correction with imperfect gates. In: Proc. 3rd nt. Conf. of Quantum Communication and Measurement (1997)
12. Mackay, D.J.C., Mitchison, G., Mcfadden, P.L.: Sparse Graph Codes for Quantum Error-Correction. IEEE Trans. Inform. Theory 50(10), 2315-2330 (2004)
13. Margulis, G.A.: Explicit constructions of graphs without short cycles and low density codes. Combinatorica 2(1), 71-78 (1982)
14. Preskill, J.: Quantum computation, http://www.theory.caltech.edu/ preskill/ph219
15. Siŕan, J.: Triangle group representations and constructions of regular maps. Proc. London Math. Soc. 82(3), 513-532 (2001) (Pubitemid 33775009)
16. Steane, A.: Multiple particle interference and quantum error correction. Proc. Roy. Soc. Lond. A 452, 2551 (1996)
17. Takeda, K., Nishimori, H.: Self-dual random-plaquette gauge model and the quantum toric code. Nuclear Physics B 686(3), 377-396 (2004)
18. Tillich, J.-P., Zémor, G.: Optimal cycle codes constructed from Ramanujan graphs. Siam J. on Discrete Math. 10(3), 447-459 (1997) (Pubitemid 127647112)