References

  1. S. Abramsky & B. Coecke (2004): A categorical semantics of quantum protocols. In: Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science: LICS 2004. IEEE Computer Society, pp. 415–425, doi:10.1109/LICS.2004.1319636.
  2. Miriam Backens (2015): Making the stabilizer ZX-calculus complete for scalars. In: Chris Heunen, Peter Selinger & Jamie Vicary: Proceedings of the 12th International Workshop on Quantum Physics and Logic (QPL 2015), Electronic Proceedings in Theoretical Computer Science 195, pp. 17–32, doi:10.4204/EPTCS.195.2.
  3. Benjamin Balsam & Alexander Kirillov Jr (2012): Kitaev's lattice model and Turaev-Viro TQFTs. ArXiv.org. Available at https://arxiv.org/abs/1206.2308.
  4. Niel de Beaudrap & Dominic Horsman (2020): The ZX calculus is a language for surface code lattice surgery. Quantum 4, pp. 218, doi:10.22331/q-2020-01-09-218.
  5. Yuri Bespalov, Thomas Kerler, Volodymyr Lyubashenko & Vladimir Turaev (2000): Integrals for braided Hopf algebras. Journal of Pure and Applied Algebra 148(2), pp. 113–164, doi:10.1016/S0022-4049(98)00169-8.
  6. Filippo Bonchi, Joshua Holland, Robin Piedeleu, PawełSobociński & Fabio Zanasi (2019): Diagrammatic Algebra: From Linear to Concurrent Systems. Proceedings of the ACM on Programming Languages 3(POPL), pp. 25:1–25:28, doi:10.1145/3290338.
  7. Filippo Bonchi, PawełSobociński & Fabio Zanasi (2017): Interacting Hopf Algebras. Journal of Pure and Applied Algebra 221(1), pp. 144–184, doi:10.1016/j.jpaa.2016.06.002.
  8. Oliver Buerschaper, Juan Martín Mombelli, Matthias Christandl & Miguel Aguado (2013): A hierarchy of topological tensor network states. Journal of Mathematical Physics 54(1), pp. 012201, doi:10.1063/1.4773316.
  9. A. Carboni & R.F.C. Walters (1987): Cartesian bicategories I. Journal of Pure and Applied Algebra 49(1-2), doi:10.1016/0022-4049(87)90121-6.
  10. Hui-Xiang Chen (2000): Quantum doubles in monoidal categories. Communications in Algebra 28(5), pp. 2303–2328, doi:10.1080/00927870008826961.
  11. B. Coecke, D. Pavlovic & J. Vicary (2013): A new description of orthogonal bases. Math. Structures in Comp. Sci. 23(3), pp. 555–567, doi:10.1017/S0960129512000047.
  12. Bob Coecke & Ross Duncan (2011): Interacting Quantum Observables: Categorical Algebra and Diagrammatics. New J. Phys 13(043016), doi:10.1088/1367-2630/13/4/043016. Available at http://iopscience.iop.org/1367-2630/13/4/043016/.
  13. Bob Coecke & Aleks Kissinger (2017): Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning. Cambridge University Press, doi:10.1017/9781316219317.
  14. Yukio Doi & Mitsuhiro Takeuchi (2000): Bi-Frobenius algebras. In: Nicolás Andruskiewitsch, Walter Ricardo Ferrer Santos & Hans-Jürgen Schneider: New trends in Hopf algebra theory, Contemporary Mathematics 267. American Mathematical Society, pp. 67–98, doi:10.1090/conm/267/04265.
  15. Vladimir Gershonovich Drinfeld (1986): Quantum groups. Zapiski Nauchnykh Seminarov POMI 155, pp. 18–49, doi:10.1007/BF01247086.
  16. Ross Duncan & Kevin Dunne (2016): Interacting Frobenius Algebras are Hopf. In: Martin Grohe, Eric Koskinen & Natarajan Shankar: Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS '16, New York, NY, USA, July 5-8, 2016, LICS '16. ACM, pp. 535–544, doi:10.1145/2933575.2934550.
  17. Bertfried Fauser (2013): Some Graphical Aspects of Frobenius Algebras. In: Chris Heunen, Mehrnoosh Sadrzadeh & Edward Grefenstette: Quantum Physics and Linguistics: A Compositional, Diagrammatic Discourse. Oxford, doi:10.1093/acprof:oso/9780199646296.003.0002.
  18. Stefano Gogioso & Fabrizio Genovese (2016): Infinite-dimensional Categorical Quantum Mechanics. In: Proceedings of QPL 2016, EPTCS, doi:10.4204/EPTCS.236.4.
  19. Masahito Hasegawa (2010): Bialgebras in rel. Electronic Notes in Theoretical Computer Science 265, pp. 337–350, doi:10.1016/j.entcs.2010.08.020.
  20. Emmanuel Jeandel, Simon Perdrix & Renaud Vilmart (2017): A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics. In: LICS '18- Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science arXiv:1705.11151. ACM, doi:10.1145/3209108.3209131.
  21. Christian Kassel (2012): Quantum groups 155. Springer Science & Business Media, doi:10.4171/047.
  22. G.M. Kelly & M.L. Laplaza (1980): Coherence for Compact Closed Categories. Journal of Pure and Applied Algebra 19, pp. 193–213, doi:10.1016/0022-4049(80)90101-2.
  23. J. Kock (2003): Frobenius Algebras and 2-D Topological Quantum Field Theories. Cambridge University Press, doi:10.1017/cbo9780511615443.
  24. M. Koppinen (1996): On Algebras with Two Multiplications, Including Hopf Algebras and Bose–Mesner Algebras. Journal of Algebra 182(1), pp. 256 – 273, doi:10.1006/jabr.1996.0170. Available at http://www.sciencedirect.com/science/article/pii/S0021869396901702.
  25. Stephen Lack (2004): Composing PROPs. Theory and Applications of Categories 13(9), pp. 147–163.
  26. Richard Gustavus Larson & Moss Eisenberg Sweedler (1969): An Associative Orthogonal Bilinear Form for Hopf Algebras. American Journal of Mathematics 91(1), pp. 75–94, doi:10.2307/2373270. Available at https://www.jstor.org/stable/2373270.
  27. Catherine Meusburger (2017): Kitaev Lattice Models as a Hopf Algebra Gauge Theory. Communications in Mathematical Physics 353(1), pp. 413–468, doi:10.1007/s00220-017-2860-7.
  28. Bodo Pareigis (1971): When Hopf algebras are Frobenius algebras. Journal of Algebra 18(4), pp. 588 – 596, doi:10.1016/0021-8693(71)90141-4. Available at http://www.sciencedirect.com/science/article/pii/0021869371901414.
  29. P. Selinger (2010): Autonomous categories in which A A^*. In: B. Coecke, P. Panangaden & P. Selinger: Proceedings of 7th Workshop on Quantum Physics and Logic (QPL 2010). Available at http://www.mscs.dal.ca/~selinger/papers/halftwist-2up.pdf.
  30. Peter Selinger (2011): A survey of graphical languages for monoidal categories. In: Bob Coecke: New structures for physics, Lecture Notes in Physics 813. Springer, pp. 289–355, doi:10.1007/978-3-642-12821-9_4.
  31. R. Street (2007): Quantum Groups: A Path to Current Algebra. Australian Mathematical Society Lecture Series. Cambridge University Press, doi:10.1017/CBO9780511618505.
  32. Moss E. Sweedler (1969): Hopf Algebras. W. A. Benjamin Inc..
  33. Earl J. Taft (1971): The Order of the Antipode of Finite-dimensional Hopf Algebra. Proceedings of the National Academy of Sciences 68(11), pp. 2631–2633, doi:10.1073/pnas.68.11.2631. Available at https://www.pnas.org/content/68/11/2631.
  34. Mitsuhiro Takeuchi (1999): Finite Hopf algebras in braided tensor categories. Journal of Pure and Applied Algebra 138(1), pp. 59–82, doi:10.1016/s0022-4049(97)00207-7.
Comments and questions to: eptcs@eptcs.org
For website issues: webmaster@eptcs.org