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, 2004., pp. 415–425, doi:10.1109/LICS.2004.1319636.
  2. Miriam Backens (2014): The ZX-calculus is complete for stabilizer quantum mechanics. New Journal of Physics 16(9), pp. 093021, doi:10.1088/1367-2630/16/9/093021.
  3. Miriam Backens (2016): Completeness and the ZX-calculus. Available at https://arxiv.org/abs/1602.08954.
  4. Mohsen Bahramgiri & Salman Beigi: Graph States Under the Action of Local Clifford Group in Non-Binary Case. arXiv:quant-ph/0610267.
  5. Xiaoning Bian & Quanlong Wang (2015): Graphical Calculus for Qutrit Systems. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E98.A(1), pp. 391–399, doi:10.1587/transfun.E98.A.391.
  6. Alex Bocharov, Martin Roetteler & Krysta M. Svore (2017): Factoring with qutrits: Shor's algorithm on ternary and metaplectic quantum architectures. Phys. Rev. A 96, pp. 012306, doi:10.1103/PhysRevA.96.012306.
  7. Nicholas Chancellor, Aleks Kissinger, Joschka Roffe, Stefan Zohren & Dominic Horsman: Coherent Parity Check Construction for Quantum Error Correction. arXiv:1611.08012.
  8. Bob Coecke & Ross Duncan (2011): Interacting quantum observables: categorical algebra and diagrammatics. New Journal of Physics 13(4), pp. 043016, doi:10.1088/1367-2630/13/4/043016.
  9. Shawn X. Cui & Zhenghan Wang (2015): Universal quantum computation with metaplectic anyons. Journal of Mathematical Physics 56(3), pp. 032202, doi:10.1063/1.4914941.
  10. Ross Duncan & Maxime Lucas (2013): Verifying the Steane code with Quantomatic. In: Proceedings of the 10th International Workshop on Quantum Physics and Logic, QPL 2013, Castelldefels (Barcelona), Spain, July 17-19, 2013., pp. 33–49, doi:10.4204/EPTCS.171.4.
  11. Ross Duncan & Simon Perdrix (2010): Rewriting Measurement-Based Quantum Computations with Generalised Flow. In: Automata, Languages and Programming 6199. Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 285–296, doi:10.1007/978-3-642-14162-1_24.
  12. Xiaoyan Gong & Quanlong Wang: Equivalence of Local Complementation and Euler Decomposition in the Qutrit ZX-calculus. arXiv:1704.05955.
  13. Clare Horsman (2011): Quantum picturalism for topological cluster-state computing. New Journal of Physics 13(9), pp. 095011, doi:10.1088/1367-2630/13/9/095011.
  14. Erik Hostens, Jeroen Dehaene & Bart De Moor (2005): Stabilizer states and Clifford operations for systems of arbitrary dimensions and modular arithmetic. Phys. Rev. A 71, pp. 042315, doi:10.1103/PhysRevA.71.042315.
  15. Mark Howard, Eoin Brennan & Jiri Vala (2013): Quantum Contextuality with Stabilizer States. Entropy 15(6), pp. 2340–2362, doi:10.3390/e15062340.
  16. Dan Hu, Weidong Tang, Meisheng Zhao, Qing Chen, Sixia Yu & C. H. Oh (2008): Graphical nonbinary quantum error-correcting codes. Phys. Rev. A 78, pp. 012306, doi:10.1103/PhysRevA.78.012306.
  17. Emmanuel Jeandel, Simon Perdrix & Renaud Vilmart: A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics. arXiv:1705.11151.
  18. Aleks Kissinger, Alex Merry, Ben Frot, Bob Coecke, David Quick, Lucas Dixon, Matvey Soloviev, Ross Duncan & Vladimir Zamdzhiev: Quantomatic. https://quantomatic.github.io/.
  19. Shiang Yong Looi & Robert B. Griffiths (2011): Tripartite entanglement in qudit stabilizer states and application in quantum error correction. Phys. Rev. A 84, pp. 052306, doi:10.1103/PhysRevA.84.052306.
  20. Shiang Yong Looi, Li Yu, Vlad Gheorghiu & Robert B. Griffiths (2008): Quantum-error-correcting codes using qudit graph states. Phys. Rev. A 78, pp. 042303, doi:10.1103/PhysRevA.78.042303.
  21. Mehul Malik, Manuel Erhard, Marcus Huber, Mario Krenn, Robert Fickler & Anton Zeilinger (2016): Multi-Photon Entanglement in High Dimensions. In: Frontiers in Optics 2016. Optical Society of America, pp. FW3F.1, doi:10.1364/FIO.2016.FW3F.1.
  22. Anne Marin, Damian Markham & Simon Perdrix (2013): Access Structure in Graphs in High Dimension and Application to Secret Sharing. In: Simone Severini & Fernando Brandao: TQC 2013 - 8th Conference on the Theory of Quantum Computation, Communication and Cryptography, Leibniz International Proceedings in Informatics (LIPIcs) 22. Schloss Dagstuhl, Guelph, Canada, pp. 308–324, doi:10.4230/LIPIcs.TQC.2013.308.
  23. Ashok Muthukrishnan & C. R. Stroud (2000): Multivalued logic gates for quantum computation. Phys. Rev. A 62, pp. 052309, doi:10.1103/PhysRevA.62.052309.
  24. Andre Ranchin (2014): Depicting qudit quantum mechanics and mutually unbiased qudit theories. In: Electronic Proceedings in Theoretical Computer Science, EPTCS 172, pp. 68–91, doi:10.4204/EPTCS.172.6.
  25. A. Smith, B. E. Anderson, H. Sosa-Martinez, C. A. Riofrío, Ivan H. Deutsch & Poul S. Jessen (2013): Quantum Control in the Cs 6S_1/2 Ground Manifold Using Radio-Frequency and Microwave Magnetic Fields. Phys. Rev. Lett. 111, pp. 170502, doi:10.1103/PhysRevLett.111.170502.
  26. Quanlong Wang & Xiaoning Bian (2014): Qutrit Dichromatic Calculus and Its Universality. EPTCS, doi:10.4204/EPTCS.172.7.
  27. Christian Schröder de Witt & Vladimir Zamdzhiev (2014): The ZX-calculus is incomplete for quantum mechanics. EPTCS 172, pp. 285–292, doi:10.4204/EPTCS.172.20.

Comments and questions to: eptcs@eptcs.org
For website issues: webmaster@eptcs.org