Coding Theory

Quantum Error-Correcting Codes

See also Quantum Computation

  1. Salah A. Aly, Andreas Klappenecker, and Kiran Sarvepalli Pradeep, Subsystem codes, IEEE International Symposium on Information Theory, Toronto, Canada, 2008 (ISIT 08), IEEE, New York, 2008, pp. 369–373.[doi/arXiv]
  2. Thomas Beth, Christopher Charnes, Markus Grassl, Gernot Alber, Aldo Delgado, and Michael Mussinger, A new class of designs which protect against quantum jumps, Des. Codes Cryptogr. 29 (2003), no. 1-3, 51–70.[MR]
  3. A. Robert Calderbank, Eric M. Rains, P. W. Shor, and Neil J. A. Sloane, Quantum error correction via codes over GF(4), IEEE Trans. Inform. Theory 44 (1998), no. 4, 1369–1387.[MR]
  4. Andrew W. Cross, David P. DiVincenzo, and Barbara M. Terhal, A comparative code study for quantum fault-tolerance, preprint (2007), 33 pages.[arXiv]
  5. G. David Forney, Jr., Markus Grassl, and Saikat Guha, Convolutional and tail-biting quantum error-correcting codes, IEEE Trans. Inform. Theory 53 (2007), no. 3, 865–880.[MR]
  6. David G. Glynn, T. Aaron Gulliver, Johannes G. Maks, and Manish K. Gupta, The geometry of additive quantum codes, Springer, 2006, pp. 219.
  7. M. Grassl, Thomas Beth, and T. Pellizzari, Codes for the quantum erasure channel, Phys. Rev. A (3) 56 (1997), no. 1, 33–38.[MR]
  8. M. Grassl, Thomas Beth, and M. Rötteler, On optimal quantum codes, International Journal of Quantum Information 2 (2004), no. 1, 55-64.
  9. Markus Grassl and Thomas Beth, Quantum BCH codes, in Proceedings X Symposium on Theoretical Electrical Engineering. Magdeburg, Sept. 6–9, 1999, 1999, pp. 207-212.
  10. Markus Grassl and Martin Rötteler, Quantum block and convolutional codes from self-orthogonal product codes, in Proceedings 2005 IEEE International Symposium on Information Theory (ISIT 2005), 2005, pp. 1018-1022.[arXiv]
  11. Markus Grassl and Martin Rötteler, Quantum convolutional codes: Encoders and structural properties, Forty-Fourth Annual Allerton Conference,Allerton House, UIUC, Illinois, USA Sept 27-29, 2006, 2006, pp. 510–519.
  12. Min-Hsiu Hsieh, Igor Devetak, and Todd Brun, General entanglement-assisted quantum error-correcting codes, Physical Review A (Atomic, Molecular, and Optical Physics) 76 (2007), no. 6, 062313.[doi]
  13. A. Klappenecker and M. Rötteler, Remarks on Clifford codes, Quantum Information and Computation 4 (2004), no. 2, 152-160.
  14. A. Klappenecker and P. K. Sarvepalli, Clifford code constructions of operator quantum error-correcting codes, IEEE Transactions on Information Theory 54 (2008), no. 12, 5760-5765.[arXiv]
  15. Andreas Klappenecker and Martin Rötteler, Unitary error bases: Constructions, equivalence, and applications, Applied Algebra, Algebraic Algorithms and Error-correcting Codes (Toulouse, 2003), Lecture Notes in Comput. Sci., vol. 2643, Springer, Berlin, 2003, pp. 139–149.[MR]
  16. Andreas Klappenecker and Martin Rötteler, On the structure of nonstabilizer Clifford codes, Quantum Inf. Comput. 4 (2004), no. 2, 152–160.[MR]
  17. Annika Niehage, Quantum Goppa codes over hypereliptic curves, Master's Thesis, Universität Mannheim, 2004.
  18. Annika Niehage, Nonbinary quantum Goppa codes exceeding the quantum Gilbert-Varshamov bound, Quantum Inf. Process. 6 (2007), no. 3, 143–158.[MR]
  19. Michel Planat, Entangling gates in even Euclidean lattices such as Leech lattice, preprint (2010), 11 pages.[arXiv]
  20. Michel Planat and Philippe Jorrand, Group theory for quantum gates and quantum coherence, J. Phys. A 41 (2008), no. 18, 182001, 8.[MR/arXiv]
  21. Michel Planat and Maurice R. Kibler, Unitary reflection groups for quantum fault tolerance, J. Comput. Theor. Nanosci. 7 (2010), no. 9, 1759–1770.[arXiv]
  22. M. Rötteler, M. Grassl, and Thomas Beth, On quantum MDS codes, in IEEE International Symposium on Information Theory – Proceedings, 2004, pp. 355.
  23. Harold N. Ward, An Introduction to Algebraic Coding Theory, Coding Theory and Quantum Computing, Contemp. Math., vol. 381, Amer. Math. Soc., Providence, RI, 2005, pp. 27–52.[MR]