@article(toffoli-simple,
author = {Dorit Aharonov},
year = {2003},
title = {A Simple Proof that Toffoli and Hadamard are Quantum Universal},
note = {Arxiv:arXiv:quant-ph/0301040},
)
@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},
)
@article(pi-4-single-qubit,
author = {Miriam Backens},
year = {2014},
title = {The {ZX}-calculus is complete for the single-qubit Clifford+T group},
journal = {Electronic Proceedings in Theoretical Computer Science},
volume = {172},
pages = {293--303},
doi = {10.4204/eptcs.172.21},
)
@inproceedings(simplified-stabilizer,
author = {Miriam Backens and Simon Perdrix and Quanlong Wang},
year = {2016},
title = {A Simplified Stabilizer {ZX}-calculus},
booktitle = {QPL 2016},
series = {Electronic Proceedings in Theoretical Computer Science},
pages = {1--20},
doi = {10.4204/EPTCS.236.1},
)
@article(de2017zx,
author = {Niel de Beaudrap and Dominic Horsman},
year = {2017},
title = {The {ZX} calculus is a language for surface code lattice surgery},
journal = {CoRR},
volume = {arXiv:1704.08670},
)
@unpublished(chancellor2016coherent,
author = {Nicholas Chancellor and Aleks Kissinger and Joschka Roffe and Stefan Zohren and Dominic Horsman},
year = {2016},
title = {Graphical Structures for Design and Verification of Quantum Error Correction},
note = {Last revised Jan. 2018},
)
@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},
)
@incollection(ghz-w,
author = {Bob Coecke and Aleks Kissinger},
year = {2010},
title = {The Compositional Structure of Multipartite Quantum Entanglement},
booktitle = {Automata, Languages and Programming},
publisher = {Springer Berlin Heidelberg},
pages = {297--308},
doi = {10.1007/978-3-642-14162-1_25},
)
@book(picturing-qp,
author = {Bob Coecke and Aleks Kissinger},
year = {2017},
title = {Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning},
publisher = {Cambridge University Press},
doi = {10.1017/9781316219317},
)
@article(category-tof,
author = {Cole Comfort and J. Robin B. Cockett},
year = {2018},
title = {The category {TOF}},
journal = {CoRR},
volume = {arXiv:1804.10360},
)
@article(duncan2014verifying,
author = {Ross Duncan and Maxime Lucas},
year = {2014},
title = {Verifying the Steane code with Quantomatic},
journal = {Electronic Proceedings in Theoretical Computer Science},
volume = {171},
pages = {33--49},
doi = {10.4204/EPTCS.171.4},
)
@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},
)
@inproceedings(pivoting,
author = {Ross Duncan and Simon Perdrix},
year = {2013},
title = {Pivoting makes the {ZX}-calculus complete for real stabilizers},
booktitle = {QPL 2013},
series = {Electronic Proceedings in Theoretical Computer Science},
pages = {50--62},
doi = {10.4204/EPTCS.171.5},
)
@inproceedings(zw,
author = {Amar Hadzihasanovic},
year = {2015},
title = {A Diagrammatic Axiomatisation for Qubit Entanglement},
booktitle = {2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science},
pages = {573--584},
doi = {10.1109/LICS.2015.59},
)
@phdthesis(Amar,
author = {Amar Hadzihasanovic},
year = {2017},
title = {The algebra of entanglement and the geometry of composition},
school = {University of Oxford},
note = {Arxiv:arXiv:1709.08086},
)
@inproceedings(HNW,
author = {Amar Hadzihasanovic and Kang Feng Ng and Quanlong Wang},
year = {2018},
title = {Two Complete Axiomatisations of Pure-state Qubit Quantum Computing},
booktitle = {Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science},
series = {LICS '18},
publisher = {ACM},
address = {New York, NY, USA},
pages = {502--511},
doi = {10.1145/3209108.3209128},
)
@article(horsman2011quantum,
author = {Clare Horsman},
year = {2011},
title = {Quantum picturalism for topological cluster-state computing},
journal = {New Journal of Physics},
volume = {13},
number = {9},
pages = {095011},
doi = {10.1088/1367-2630/13/9/095011},
)
@inproceedings(JPV,
author = {Emmanuel Jeandel and Simon Perdrix and Renaud Vilmart},
year = {2018},
title = {A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics},
booktitle = {Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science},
series = {LICS '18},
publisher = {ACM},
address = {New York, NY, USA},
pages = {559--568},
doi = {10.1145/3209108.3209131},
)
@inproceedings(JPV-universal,
author = {Emmanuel Jeandel and Simon Perdrix and Renaud Vilmart},
year = {2018},
title = {Diagrammatic Reasoning Beyond Clifford+T Quantum Mechanics},
booktitle = {Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science},
series = {LICS '18},
publisher = {ACM},
address = {New York, NY, USA},
pages = {569--578},
doi = {10.1145/3209108.3209139},
)
@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}},
editor = {Kim G. Larsen and Hans L. Bodlaender and Jean-Francois Raskin},
booktitle = {42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {83},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
pages = {11:1--11:13},
doi = {10.4230/LIPIcs.MFCS.2017.11},
)
@misc(quanto,
author = {A. Kissinger and L. Dixon and R. Duncan and B. Frot and A. Merry and D. Quick and M. Soloviev and V. Zamdzhiev},
year = {2011},
title = {Quantomatic},
url = {http://quantomatic.github.io/},
)
@inproceedings(kissinger2015quantomatic,
author = {Aleks Kissinger and Vladimir Zamdzhiev},
year = {2015},
title = {Quantomatic: A Proof Assistant for Diagrammatic Reasoning},
editor = {Amy P. Felty and Aart Middeldorp},
booktitle = {Automated Deduction - CADE-25},
publisher = {Springer International Publishing},
address = {Cham},
pages = {326--336},
doi = {10.1007/978-3-319-21401-6\_22},
)
@unpublished(NgWang,
author = {Kang Feng Ng and Quanlong Wang},
year = {2017},
title = {A universal completion of the ZX-calculus},
note = {Arxiv:arXiv:1706.09877},
)
@unpublished(NgWang-clifford+t,
author = {Kang Feng Ng and Quanlong Wang},
year = {2018},
title = {Completeness of the ZX-calculus for Pure Qubit Clifford+T Quantum Mechanics},
note = {Arxiv:arXiv:1801.07993},
)
@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},
)
@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(toffoli,
author = {Yaoyun Shi},
year = {2003},
title = {Both Toffoli and controlled-NOT need little help to do universal quantum computing},
journal = {Quantum Information {\&} Computation},
volume = {3},
number = {1},
pages = {84--92},
url = {http://portal.acm.org/citation.cfm?id=2011515},
)