Dorit Aharonov (2003):
A Simple Proof that Toffoli and Hadamard are Quantum Universal.
Arxiv:arXiv:quant-ph/0301040.
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.
Miriam Backens (2014):
The ZX-calculus is complete for the single-qubit Clifford+T group.
Electronic Proceedings in Theoretical Computer Science 172,
pp. 293–303,
doi:10.4204/eptcs.172.21.
Miriam Backens, Simon Perdrix & Quanlong Wang (2016):
A Simplified Stabilizer ZX-calculus.
In: QPL 2016,
Electronic Proceedings in Theoretical Computer Science,
pp. 1–20,
doi:10.4204/EPTCS.236.1.
Niel de Beaudrap & Dominic Horsman (2017):
The ZX calculus is a language for surface code lattice surgery.
CoRR arXiv:1704.08670.
Nicholas Chancellor, Aleks Kissinger, Joschka Roffe, Stefan Zohren & Dominic Horsman (2016):
Graphical Structures for Design and Verification of Quantum Error Correction.
Last revised Jan. 2018.
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.
Bob Coecke & Aleks Kissinger (2010):
The Compositional Structure of Multipartite Quantum Entanglement.
In: Automata, Languages and Programming.
Springer Berlin Heidelberg,
pp. 297–308,
doi:10.1007/978-3-642-14162-1_25.
Bob Coecke & Aleks Kissinger (2017):
Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning.
Cambridge University Press,
doi:10.1017/9781316219317.
Cole Comfort & J. Robin B. Cockett (2018):
The category TOF.
CoRR arXiv:1804.10360.
Ross Duncan & Maxime Lucas (2014):
Verifying the Steane code with Quantomatic.
Electronic Proceedings in Theoretical Computer Science 171,
pp. 33–49,
doi:10.4204/EPTCS.171.4.
Ross Duncan & Simon Perdrix (2010):
Rewriting measurement-based quantum computations with generalised flow.
Lecture Notes in Computer Science 6199,
pp. 285–296,
doi:10.1007/978-3-642-14162-1_24.
Ross Duncan & Simon Perdrix (2013):
Pivoting makes the ZX-calculus complete for real stabilizers.
In: QPL 2013,
Electronic Proceedings in Theoretical Computer Science,
pp. 50–62,
doi:10.4204/EPTCS.171.5.
Amar Hadzihasanovic (2015):
A Diagrammatic Axiomatisation for Qubit Entanglement.
In: 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science,
pp. 573–584,
doi:10.1109/LICS.2015.59.
Amar Hadzihasanovic (2017):
The algebra of entanglement and the geometry of composition.
University of Oxford.
Arxiv:arXiv:1709.08086.
Amar Hadzihasanovic, Kang Feng Ng & Quanlong Wang (2018):
Two Complete Axiomatisations of Pure-state Qubit Quantum Computing.
In: Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science,
LICS '18.
ACM,
New York, NY, USA,
pp. 502–511,
doi:10.1145/3209108.3209128.
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.
Emmanuel Jeandel, Simon Perdrix & Renaud Vilmart (2018):
A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics.
In: Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science,
LICS '18.
ACM,
New York, NY, USA,
pp. 559–568,
doi:10.1145/3209108.3209131.
Emmanuel Jeandel, Simon Perdrix & Renaud Vilmart (2018):
Diagrammatic Reasoning Beyond Clifford+T Quantum Mechanics.
In: Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science,
LICS '18.
ACM,
New York, NY, USA,
pp. 569–578,
doi:10.1145/3209108.3209139.
Emmanuel Jeandel, Simon Perdrix, Renaud Vilmart & Quanlong Wang (2017):
ZX-Calculus: Cyclotomic Supplementarity and Incompleteness for Clifford+T Quantum Mechanics.
In: Kim G. Larsen, Hans L. Bodlaender & Jean-Francois Raskin: 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017),
Leibniz International Proceedings in Informatics (LIPIcs) 83.
Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik,
Dagstuhl, Germany,
pp. 11:1–11:13,
doi:10.4230/LIPIcs.MFCS.2017.11.
A. Kissinger, L. Dixon, R. Duncan, B. Frot, A. Merry, D. Quick, M. Soloviev & V. Zamdzhiev (2011):
Quantomatic.
Available at http://quantomatic.github.io/.
Aleks Kissinger & Vladimir Zamdzhiev (2015):
Quantomatic: A Proof Assistant for Diagrammatic Reasoning.
In: Amy P. Felty & Aart Middeldorp: Automated Deduction - CADE-25.
Springer International Publishing,
Cham,
pp. 326–336,
doi:10.1007/978-3-319-21401-6_22.
Kang Feng Ng & Quanlong Wang (2017):
A universal completion of the ZX-calculus.
Arxiv:arXiv:1706.09877.
Kang Feng Ng & Quanlong Wang (2018):
Completeness of the ZX-calculus for Pure Qubit Clifford+T Quantum Mechanics.
Arxiv:arXiv:1801.07993.
Michael A. Nielsen & Isaac L. Chuang (2010):
Quantum Computation and Quantum Information: 10th Anniversary Edition.
Cambridge University Press,
doi:10.1017/CBO9780511976667.
Peter Selinger (2013):
Quantum circuits of T-depth one.
Phys. Rev. A 87,
pp. 042302,
doi:10.1103/PhysRevA.87.042302.
Yaoyun Shi (2003):
Both Toffoli and controlled-NOT need little help to do universal quantum computing.
Quantum Information & Computation 3(1),
pp. 84–92.
Available at http://portal.acm.org/citation.cfm?id=2011515.