Physics

Quantum Computation

81P68

  1. 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]
  2. 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]
  3. M. Grassl, Thomas Beth, and T. Pellizzari, Codes for the quantum erasure channel, Phys. Rev. A (3) 56 (1997), no. 1, 33–38.[MR]
  4. M. Grassl, Thomas Beth, and M. Rötteler, Computing local invariants of quantum-bit systems, Phys. Rev. A. 58 (1998), no. 3, 833-1839.
  5. Markus Grassl, On SIC-POVMs and MUBs in dimension 6, preprint (2004), 8 pages.[arXiv]
  6. Markus Grassl, Tomography of quantum states in small dimensions, in Proceedings of the Workshop on Discrete Tomography and its Applications, Electron. Notes Discrete Math., vol. 20, Elsevier, Amsterdam, 2005, pp. 151–164 (electronic).[MR]
  7. Russell John Higgs, Nice error bases and Sylow subgroups, IEEE Trans. Inform. Theory 54 (2008), no. 9, 4199–4207.[MR/doi]
  8. 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]
  9. Andreas Klappenecker and Martin Rötteler, Beyond stabilizer codes I: Nice error bases, IEEE Trans. Inform. Theory 48 (2002), no. 8, 2392–2395.[MR/doi]
  10. 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]
  11. Andreas Klappenecker and Martin Rötteler, On the structure of nonstabilizer Clifford codes, Quantum Inf. Comput. 4 (2004), no. 2, 152–160.[MR]
  12. Samuel J. Lomonaco, Jr. and Louis H. Kauffman, Quantum hidden subgroup algorithms: A mathematical perspective, Quantum Computation and Information (Washington, DC, 2000), Contemp. Math., vol. 305, Amer. Math. Soc., Providence, RI, 2002, pp. 139–202.[MR]
  13. Jean-Gabriel Luque, Jean-Yves Thibon, and Frédéric Toumazet, Unitary invariants of qubit systems, Math. Structures Comput. Sci. 17 (2007), no. 6, 1133–1151.[MR/arXiv]
  14. Gabriele Nebe, Eric M. Rains, and Neil J. A. Sloane, Self-dual Codes and Invariant Theory, Algorithms and Computation in Mathematics, vol. 17, Springer-Verlag, Berlin, 2006, pp. xxviii+430.[MR]
  15. Michel Planat, Clifford group dipoles and the enactment of Weyl/Coxeter group W(E8) by entangling gates, preprint (2009).[arXiv]
  16. Michel Planat, Peter Levay, and Metod Saniga, Balanced tripartite entanglement, the alternating group A4 and the Lie algebra sl(3,C)⊕u(1), preprint (2009), 14 pages.[arXiv]
  17. Thomas Schulte-Herbräggen, Uwe Sander, and Robert Zeier, Symmetry principles in quantum system theory of multi-qubit systems made simple, Proceedings of the 4th International Symposium on Communications, Control and Signal Processing, ISCCSP 2010, Limassol, Cyprus, 3–5 March 2010, IEEE, 2010, pp. 1–5.[doi]
  18. Thomas Schulte-Herbriiggen, Uwe Sander, and and Robert Zeier, Symmetry principles in quantum system theory of multi-qubit systems made simple, Communications, Control and Signal Processing, ISCCSP 2010. Proceedings of the 4th International Symposium, IEEE, 2010, pp. 1–5.[doi]
  19. A. J. Scott and M. Grassl, Symmetric informationally complete positive-operator-valued measures: A new computer study, J. Math. Phys. 51 (2010), no. 4, 042203.[arXiv]
  20. Marcus Palmer da Silva, Erasure thresholds for efficient linear optics quantum computation, Master's Thesis, University of Waterloo, 2004.
  21. Barbara M. Terhal, Isaac L. Chuang, David P. Di Vincenzo, Markus Grassl, and John A. Smolin, Simulating quantum operations with mixed environments, Phys. Rev 60 (1999), no. 2, 881-885.[MR]
  22. Pawel Wocjan, Martin Rötteler, Dominik Janzing, and Thomas Beth, Universal simulation of Hamiltonians using a finite set of control operations, Quantum Inf. Comput. 2 (2002), no. 2, 133–150.[MR]
  23. Robert Michael Zeier, Lie-theoretischer zugang zur erzeugung unitärer transformationen auf quantenrechnern, PhD Thesis, Institut für Algorithmen und Kognitive Systeme, Universität Karlsruhe, 2006.