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We introduce the first complete and approximatively universal diagrammatic language for quantum mechanics.
Phys. Rev. A
Scott Aaronson & Daniel Gottesman (2004): Improved simulation of stabilizer circuits · 2004
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Springer
Steven Roman (2006): Field Theory · 2006
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Springer Berlin Heidelberg, Berlin, Heidelberg, doi: 10.1007/978-3-642-14162-1_25
Bob Coecke & Aleks Kissinger (2010): The Compositional Structure of Multipartite Quantum Entanglement , pp. 297–308 · 2010
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Lecture Notes in Computer Science
Ross Duncan & Simon Perdrix (2010): Rewriting measurement-based quantum computations with generalised flow · 2010
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New Journal of Physics
Bob Coecke & Ross Duncan (2011): Interacting quantum observables: categorical algebra and diagrammatics · 2011
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New Journal of Physics
Clare Horsman (2011): Quantum picturalism for topological cluster-state computing · 2011
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Available at https://sites.google.com/site/quantomatic/
A. Kissinger, L. Dixon, R. Duncan, B. Frot, A. Merry, D. Quick, M. Soloviev & V. Zamdzhiev (2011): Quantomatic · 2011
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doi: 10.1093/acprof:oso/9780199646296.003.0003
Ross Duncan (2013): A graphical approach to measurement-based quantum computing · 2013
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In: QPL 2013
Ross Duncan & Simon Perdrix (2013): Pivoting makes the ZX-calculus complete for real stabilizers · 2013
Earlier work this paper cites.
Phys. Rev. A
Brett Giles & Peter Selinger (2013): Exact synthesis of multiqubit Clifford+ T T circuits · 2013
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New Journal of Physics
Miriam Backens (2014): The ZX-calculus is complete for stabilizer quantum mechanics · 2014
Cited alongside, same era.
Electronic Proceedings in Theoretical Computer Science
Miriam Backens (2014): The ZX-calculus is complete for the single-qubit Clifford+T group · 2014
Cited alongside, same era.
Foundations of Physics
Miriam Backens & Ali Nabi Duman (2014): A complete graphical calculus for Spekkens’ toy bit theory · 2014
Cited alongside, same era.
Electronic Proceedings in Theoretical Computer Science
Ross Duncan & Maxime Lucas (2014): Verifying the Steane code with Quantomatic · 2014
Cited alongside, same era.
In: QPL 2014
Christian Schröder de Witt & Vladimir Zamdzhiev (2014): The ZX-calculus is incomplete for quantum mechanics · 2014
Cited alongside, same era.
In: 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science
Amar Hadzihasanovic (2015): A Diagrammatic Axiomatisation for Qubit Entanglement · 2015
Cited alongside, same era.
In: 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)
Simon Perdrix & Quanlong Wang (2016): Supplementarity is Necessary for Quantum Diagram Reasoning · 2016
Later among the works it cites.
Available at https://arxiv.org/abs/1709.08903
Miriam Backens, Simon Perdrix & Quanlong Wang (2017): Towards a Minimal Stabilizer ZX-calculus · 2017
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Niel de Beaudrap & Dominic Horsman (2017): The ZX calculus is a language for surface code lattice surgery · 2017
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Cambridge University Press, doi: 10.1017/9781316219317
Bob Coecke & Aleks Kissinger (2017): Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning · 2017
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Available at https://arxiv.org/abs/1706.02717
Ross Duncan & Liam Garvie (2017): Verifying the Smallest Interesting Colour Code with Quantomatic · 2017
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In Amy P. Felty & Aart Middeldorp, editors: Automated Deduction - CADE-25
Aleks Kissinger & Vladimir Zamdzhiev (2015): Quantomatic: A Proof Assistant for Diagrammatic Reasoning · 2015
Cited alongside, same era.
In: QPL 2016
Miriam Backens, Simon Perdrix & Quanlong Wang (2016): A Simplified Stabilizer ZX-calculus · 2016
Cited alongside, same era.
Available at https://arxiv.org/abs/1611.08012
Nicholas Chancellor, Aleks Kissinger, Joschka Roffe, Stefan Zohren & Dominic Horsman (2016): Graphical Structures for Design and Verification of Quantum Error Correction · 2016
Cited alongside, same era.
In: Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science
Ross Duncan & Kevin Dunne (2016): Interacting Frobenius Algebras Are Hopf · 2016
Cited alongside, same era.
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Ph.D. thesis, University of Oxford
Amar Hadzihasanovic (2017): The algebra of entanglement and the geometry of composition · 2017
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In Kim G. Larsen, Hans L. Bodlaender & Jean-Francois Raskin, editors: 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)
Emmanuel Jeandel, Simon Perdrix, Renaud Vilmart & Quanlong Wang (2017): ZX-Calculus: Cyclotomic Supplementarity and Incompleteness for Clifford+T Quantum Mechanics · 2017
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Available at https://arxiv.org/abs/1706.09877
Kang Feng Ng & Quanlong Wang (2017): A universal completion of the ZX-calculus · 2017
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Available at https://arxiv.org/abs/1801.10142
Emmanuel Jeandel, Simon Perdrix & Renaud Vilmart (2018): Diagrammatic Reasoning beyond Clifford+T Quantum Mechanics · 2018
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Available at https://arxiv.org/abs/1801.07993
Kang Feng Ng & Quanlong Wang (2018): Completeness of the ZX-calculus for Pure Qubit Clifford+T Quantum Mechanics · 2018
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