@article(pi_2-complete, author = {Miriam Backens}, year = {2014}, title = {The ZX-calculus is complete for stabilizer quantum mechanics}, journal = {New Journal of Physics}, volume = {16}, number = {9}, pages = {093021}, doi = {10.1088/1367-2630/16/9/093021}, ) @inproceedings(BernsteinVazirani, author = {E. Bernstein and U. Vazirani}, year = {1993}, title = {{Quantum complexity theory}}, booktitle = {Proceedings of the twenty-fifth annual ACM symposium on Theory of computing}, publisher = {ACM New York, NY, USA}, pages = {11--20}, doi = {10.1145/167088.167097}, ) @inbook(Bonchi2014, author = {Filippo Bonchi and Pawe{\l} Soboci{\'{n}}ski and Fabio Zanasi}, year = {2014}, title = {A Categorical Semantics of Signal Flow Graphs}, pages = {435--450}, publisher = {Springer Berlin Heidelberg}, address = {Berlin, Heidelberg}, doi = {10.1007/978-3-662-44584-6\_30}, ) @article(CSC10, author = {Stephen Clark and Bob Coecke and Mehrnoosh Sadrzadeh}, year = {2010}, title = {Mathematical Foundations for a Compositional Distributional Model of Meaning.}, journal = {Lambek Festschirft, special issue of Linguistic Analysis}, url = {https://arxiv.org/abs/1003.4394}, ) @article(interacting, author = {Bob Coecke and Ross Duncan}, year = {2011}, title = {Interacting quantum observables: categorical algebra and diagrammatics}, journal = {New Journal of Physics}, volume = {13}, number = {4}, pages = {043016}, doi = {10.1088/1367-2630/13/4/043016}, ) @book(coecke2017picturing, author = {Bob Coecke and Aleks Kissinger}, year = {2017}, title = {Picturing quantum processes}, doi = {10.1017/9781316219317}, publisher = {Cambridge University Press}, ) @article(CP12, author = {Bob Coecke and Simon Perdrix}, year = {2012}, title = {{Environment and classical channels in categorical quantum mechanics}}, journal = {{Logical Methods in Computer Science}}, volume = {{Volume 8, Issue 4}}, doi = {10.2168/LMCS-8(4:14)2012}, ) @article(CP-state-transfer, author = {Bob Coecke and Simon Perdrix and {\'E}ric Oliver Paquette}, year = {2008}, title = {Bases in Diagrammatic Quantum Protocols}, journal = {Electronic Notes in Theoretical Computer Science}, volume = {218}, pages = {131 -- 152}, doi = {10.1016/j.entcs.2008.10.009}, note = {Proceedings of the 24th Conference on the Mathematical Foundations of Programming Semantics (MFPS XXIV)}, ) @article(context-rebits, author = {Nicolas Delfosse and Allard Guerin, Philippe and Jacob Bian and Robert Raussendorf}, year = {2015}, title = {Wigner Function Negativity and Contextuality in Quantum Computation on Rebits}, journal = {Phys. Rev. X}, volume = {5}, pages = {021003}, doi = {10.1103/PhysRevX.5.021003}, ) @article(euler-decomp, author = {Ross Duncan and Simon Perdrix}, year = {2009}, title = {Graphs States and the necessity of Euler Decomposition}, journal = {Mathematical Theory and Computational Practice}, volume = {5635}, pages = {167--177}, doi = {10.1007/978-3-642-03073-4}, ) @article(mbqc, author = {Ross Duncan and Simon Perdrix}, year = {2010}, title = {Rewriting measurement-based quantum computations with generalised flow}, journal = {Lecture Notes in Computer Science}, volume = {6199}, pages = {285--296}, doi = {10.1007/978-3-642-14162-1\_24}, url = {http://personal.strath.ac.uk/ross.duncan/papers/gflow.pdf}, ) @article(pivoting, author = {Ross Duncan and Simon Perdrix}, year = {2013}, title = {Pivoting makes the ZX-calculus complete for real stabilizers}, journal = {Electronic Proceedings in Theoretical Computer Science}, doi = {10.4204/EPTCS.171.5}, ) @misc(feynman, author = {Richard P Feynman and Robert B Leighton and Matthew Sands and R Bruce Lindsay}, year = {1966}, title = {The feynman lectures on physics, vol. 3: Quantum mechanics}, ) @article(locality, author = {Lucien Hardy and William K. Wootters}, year = {2012}, title = {Limited Holism and Real-Vector-Space Quantum Theory}, journal = {Foundations of Physics}, volume = {42}, number = {3}, pages = {454--473}, doi = {10.1007/s10701-011-9616-6}, ) @article(complete, author = {Emmanuel Jeandel and Simon Perdrix and Renaud Vilmart}, year = {2017}, title = {A Complete Axiomatisation of the ZX-Calculus for Clifford+ T Quantum Mechanics}, journal = {arXiv preprint arXiv:1705.11151}, ) @inproceedings(gen-supp, author = {Emmanuel Jeandel and Simon Perdrix and Renaud Vilmart and Quanlong Wang}, year = {2017}, title = {ZX-Calculus: Cyclotomic Supplementarity and Incompleteness for Clifford+T quantum mechanics}, booktitle = {42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)}, url = {https://hal.archives-ouvertes.fr/hal-01445707}, ) @article(trichromatic, author = {Alex Lang and Bob Coecke}, year = {2011}, title = {Trichromatic Open Digraphs for Understanding Qubits}, journal = {Electronic Proceedings in Theoretical Computer Science}, volume = {95}, pages = {193--209}, doi = {10.4204/EPTCS.95.14}, ) @article(complexity, author = {Matthew McKague}, year = {2013}, title = {On the power quantum computation over real Hilbert spaces}, journal = {International Journal of Quantum Information}, volume = {11}, number = {01}, pages = {1350001}, doi = {10.1142/S0219749913500019}, ) @article(MP12, author = {Mehdi Mhalla and Simon Perdrix}, year = {2013}, title = {Graph States, Pivot Minor, and Universality of (X, Z)-measurements}, journal = {International Journal of Unconventional Computing}, volume = {9}, number = {1-2}, pages = {153--171}, ) @book(nielsen_chuang_2010, author = {Michael A. Nielsen and Isaac L. Chuang}, year = {2010}, title = {Quantum Computation and Quantum Information: 10th Anniversary Edition}, publisher = {Cambridge University Press}, doi = {10.1017/CBO9780511976667}, ) @conference(perdrix:hal-01377339, author = {Simon Perdrix and Luc Sanselme}, year = {2017}, title = {{Determinism and Computational Power of Real Measurement-based Quantum Computation}}, booktitle = {21st International Symposium on Fundamentals of Computation Theory (FCT'17)}, doi = {10.1007/978-3-662-55751-8\_31}, ) @inproceedings(supplementarity, author = {Simon Perdrix and Quanlong Wang}, year = {2016}, title = {Supplementarity is Necessary for Quantum Diagram Reasoning}, booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, volume = {58}, address = {Krakow, Poland}, pages = {76:1--76:14}, doi = {10.4230/LIPIcs.MFCS.2016.76}, ) @article(clifford+t, author = {Peter Selinger}, year = {2013}, title = {Quantum circuits of $T$-depth one}, journal = {Phys. Rev. A}, volume = {87}, pages = {042302}, doi = {10.1103/PhysRevA.87.042302}, ) @article(incompleteness, author = {Schr\"oder de Witt, Christian and Vladimir Zamdzhiev}, year = {2014}, title = {The ZX-calculus is incomplete for quantum mechanics}, journal = {Electronic Proceedings in Theoretical Computer Science}, doi = {10.4204/EPTCS.172.20}, )