Vorlesung (705901 SV/3) im Wintersemester 2007/2008

Grundlagen der Quantenfehlerkorrektur

(Dr. Markus Grassl)

Termine: dienstags, 1100-1230 Uhr   freitags, 900-945 Uhr Seminarraum 2/36, Victor-Franz-Hess-Haus neuer Raum: Erwin-Schrödinger-Saal, IQOQI

Vorlesungsfolien

1. Vorlesung am 09.10.2007
2. Vorlesung am 12.10.2007
3. Vorlesung am 16.10.2007
4. Vorlesung am 19.10.2007
5. Vorlesung am 23.10.2007
6. Vorlesung am 30.10.2007
7. Vorlesung am 06.11.2007
8. Vorlesung am 09.11.2007
9. Vorlesung am 13.11.2007
10. Vorlesung am 16.11.2007
    Konstruktion von endlichen Körpern (siehe auch: Markus Grassl, "Classical Information Theory and Classical Error Correction.", S. 11/12)
11. Vorlesung am 20.11.2007
12. Vorlesung am 23.11.2007
13. Vorlesung am 27.11.2007
14. Vorlesung am 04.12.2007
15. Vorlesung am 07.12.2007
16. Vorlesung am 11.12.2007 (Korrekturen/Ergänzungen in grün)
17. Vorlesung am 14.12.2007
    exemplarische Berechnung eines Codierschaltkreises nach Cleve & Gottesman
18. Vorlesung am 08.01.2008
19. Vorlesung am 11.01.2008
20. Vorlesung am 15.01.2008
21. Vorlesung am 18.01.2008

• Charles H. Bennett, David P. DiVincenzo, and John A. Smolin.
  "Capacities of Quantum Erasure Channels."
  Physical Review Letters, vol. 78, no. 16 , pp. 3217-3220, 1997.
  DOI 10.1103/PhysRevLett.78.3217

• Dagmar Bruß und Gerd Leuchs (Eds.)
  Lectures on Quantum Information
  Weinheim: Wiley-VCH, 2006.
  ISBN 3-527-40527-5

• A. Robert Calderbank, Eric. M. Rains, Peter W. Shor, and Neil J. A. Sloane,
  "Quantum Error Correction Via Codes over GF(4),"
  IEEE Transactions on Information Theory, 44(4):1369-1387, July 1998.
  DOI: 10.1109/18.681315,
  preprint quant-ph/9608006.

• Richard Cleve and Daniel Gottesman.
  "Efficient Computations of Encodings for Quantum Error Correction."
  Physical Review A, vol. 56, no. 1, pp. 76-82, 1997.
  DOI 10.1103/PhysRevA.56.76,
  preprint quant-ph/9607030.

• David P. DiVincenzo, Peter W. Shor, and John A. Smolin.
  "Quantum-channel capacity of very noisy channels."
  Physical Review A, vol. 57, no. 2, pp. 830-839, 1998.
  DOI 10.1103/PhysRevA.57.830

• G. David Forney, Jr., Markus Grassl, and Saikat Guha,
  "Convolutional and tail-biting quantum error-correcting codes",
  IEEE Transactions on Information Theory, vol. 53, no. 3, March 2007, pp. 865-880.
  DOI: 10.1109/TIT.2006.890698
  Preprint quant-ph/0511016.

• Markus Grassl.
  Fehlerkorrigierende Codes für Quantensysteme: Konstruktionen und Algorithmen
  Aachen: Shaker Verlag, August 2002.
  Zugl.: Universität Karlsruhe, Dissertation, Februar 2001.
  ISBN 3-8322-0492-X

• Markus Grassl.
  "Classical Information Theory and Classical Error Correction."
  In: Dagmar Bruß und Gerd Leuchs (Eds.)
  Lectures on Quantum Information
  Weinheim: Wiley-VCH, 2006, pp. 31-16.
  ISBN 3-527-40527-5

• Markus Grassl,
  "Encoding and decoding quantum error-correcting codes",
  in: G. Casati, D. L. Shepelyansky, and P. Zoller,
  Proceedings of the International School of Physics "E. Fermi",
  Course CLXII on "Quantum Computers, Algorithms and Chaos"
  IOS Press, 2006, pp. 33-44.

• Markus Grassl,
  "Quantum Error Correction",
  International School of Physics "Enrico Fermi",
  Course CLXII on Quantum Computers, Algorithms and Chaos,
  Varenna, 12.07.2005.
  Transparencies of the talk.

• Markus Grassl, Andreas Klappenecker, and Martin Rötteler,
  "Graphs, Quadratic Forms, and Quantum Codes",
  in Proceedings 2002 IEEE International Symposium on Information Theory (ISIT 2002),
  Lausanne, Switzerland, June/July 2002, p. 45.
  Preprint quant-ph/0703112,

• Markus Grassl and Martin Rötteler,
  "Non-catastrophic Encoders and Encoder Inverses for Quantum Convolutional Codes",
  in Proceedings 2006 IEEE International Symposium on Information Theory (ISIT 2006),
  Seattle, USA, July 2006, pp. 1109-1113.
  Preprint quant-ph/0602129.

• Markus Grassl, Martin Rötteler, and Thomas Beth,
  "Efficient Quantum Circuits for Non-Qubit Quantum Error-Correcting Codes",
  International Journal of Foundations of Computer Science (IJFCS), Vol. 14, No. 5 (2003), pp. 757-775.
  Preprint quant-ph/0211014.

• Michael Nielsen und Isaac Chuang.
  Quantum Computation and Information Cambridge University Press, 2000.
  DOI 10.2277/0521635039

• Christopher King.
  "The Capacity of the Quantum Depolarizing Channel."
  IEEE Transactions on Information Theory, vol. 49, no.1 , pp. 221-229, 2003.
  DOI 10.1109/TIT.2002.806153

• Emanuel Knill and Raymond Laflamme.
  "Theory of quantum error-correcting codes."
  Physical Review A, vol. 55, no. 2, pp. 900-911, 1997.
  DOI 10.1103/PhysRevA.55.900

• Benjamin Schumacher.
  "Sending entanglement through noisy quantum channels."
  Physical Review A, vol. 54, no.4 , pp. 2614-2628, 1996.
  DOI 10.1103/PhysRevA.54.2614

• Dirk Schlingemann,
  "Stabilizer codes can be realized as graph codes,"
  Quantum Information and Computation, vol. 2, no. 4, 2002, pp. 307-323.
  Preprint quant-ph/0111080.

• Dirk M. Schlingemann and Reinhard F. Werner,
  "Quantum error-correcting codes associated with graphs,"
  Physical Review A, vol. 65, no. 1, 2002, p. 012308.
  DOI: 10.1103/PhysRevA.65.012308.
  Preprint quant-ph/0012111.

Weitere Informationen bei:

Markus Grassl IQOQI, Zimmer 3/12 E-Mail: Markus.Grassl[at]uibk.ac.at Telefon: +43 512/507-4742