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The ZX-calculus is a convenient formalism for expressing and reasoning about quantum circuits at a low level, whereas the recently-proposed ZH-calculus yields convenient expressions of mid-level quantum gates such as Toffoli and CCZ.
https://arxiv.org/abs/1902.03178
Ross Duncan, Alex Kissinger, Simon Perdrix & John van de Wetering (2019): Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus · 1902
Earlier work this paper cites.
arXiv preprint arXiv:1903.10477
Aleks Kissinger & John van de Wetering (2019): Reducing T-count with the ZX-calculus · 1903
Earlier work this paper cites.
arXiv preprint arXiv:1904.04735
Aleks Kissinger & John van de Wetering (2019): PyZX: Large Scale Automated Diagrammatic Reasoning · 1904
Earlier work this paper cites.
In: Proceedings of the 37th International Colloquium on Automata, Languages and Programming (ICALP)
B. Coecke & R. Duncan (2008): Interacting quantum observables · 2008
Earlier work this paper cites.
New Journal of Physics
B. Coecke & R. Duncan (2011): Interacting quantum observables: categorical algebra and diagrammatics · 2011
Earlier work this paper cites.
Physical Review A
Cody Jones (2013): Low-overhead constructions for the fault-tolerant Toffoli gate · 2013
Earlier work this paper cites.
Peter Selinger (2013): Quantum circuits of T-depth one · 2013
Earlier work this paper cites.
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Matthew Amy, Dmitri Maslov & Michele Mosca (2014): Polynomial-time T-depth optimization of Clifford+ T circuits via matroid partitioning · 2014
Cited alongside, same era.
Electronic Proceedings in Theoretical Computer Science
Aleks Kissinger, Alex Merry & Matvey Soloviev (2014): Pattern graph rewrite systems · 2014
Cited alongside, same era.
Cambridge University Press, 10.1017/CBO9781139814782
Ryan O’Donnell (2014): Analysis of boolean functions · 2014
Cited alongside, same era.
In Ross Duncan & Chris Heunen, editors: Proceedings 13th International Conference on Quantum Physics and Logic,
Miriam Backens, Simon Perdrix & Quanlong Wang (2017): A Simplified Stabilizer ZX-calculus · 2016
Cited alongside, same era.
arXiv preprint arXiv: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.
Cambridge University Press, 10.1017/9781316219317
B. Coecke & A. Kissinger (2017): Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning · 2017
Later among the works it cites.
arXiv preprint arXiv:1706.09877
Kang Feng Ng & Quanlong Wang (2017): A universal completion of the ZX-calculus · 2017
Later among the works it cites.
In Peter Selinger & Giulio Chiribella, editors: Proceedings of the 15th International Conference on Quantum Physics and Logic, Halifax, Canada, 3-7th June 2018
Miriam Backens & Aleks Kissinger (2019): ZH: A Complete Graphical Calculus for Quantum Computations Involving Classical Non-linearity · 2018
Later among the works it cites.
In: Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science
Emmanuel Jeandel, Simon Perdrix & Renaud Vilmart (2018): A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics · 2018
Later among the works it cites.
IEEE Transactions on Information Theory
Matthew Amy & Michele Mosca (2019): T-count optimization and Reed-Muller codes · 2019
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arXiv preprint arXiv:1704.08670
Niel de Beaudrap & Dominic Horsman (2017): The ZX calculus is a language for surface code lattice surgery · 2017
Cited alongside, same era.
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Quantum Science and Technology
Luke E Heyfron & Earl T Campbell (2018): An efficient quantum compiler that reduces T count · 2058
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