@phdthesis(amythesis,
author = {Matthew Amy},
year = {2019},
title = {Formal Methods in Quantum Circuit Design},
school = {University of Waterloo},
)
@inproceedings(Amy18,
author = {Matthew Amy},
year = {2019},
title = {Towards Large-scale Functional Verification of Universal Quantum Circuits},
editor = {Peter Selinger and Giulio Chiribella},
booktitle = {{\rm Proceedings of the 15th International Conference on} Quantum Physics and Logic, {\rm Halifax, Canada, 3-7th June 2018}},
series = {Electronic Proceedings in Theoretical Computer Science},
volume = {287},
publisher = {Open Publishing Association},
pages = {1--21},
doi = {10.4204/EPTCS.287.1},
)
@article(backens1,
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(BK18,
author = {Miriam Backens and Aleks Kissinger},
year = {2019},
title = {ZH: A Complete Graphical Calculus for Quantum Computations Involving Classical Non-linearity},
editor = {Peter Selinger and Giulio Chiribella},
booktitle = {Proceedings of the 15th International Conference on Quantum Physics and Logic, Halifax, Canada, 3-7th June 2018},
series = {Electronic Proceedings in Theoretical Computer Science},
volume = {287},
publisher = {Open Publishing Association},
pages = {23--42},
doi = {10.4204/EPTCS.287.2},
)
@article(backens2021completeness,
author = {Miriam Backens and Aleks Kissinger and Miller-Bakewell, Hector and John van de Wetering and Sal Wolffs},
year = {2021},
title = {{Completeness of the ZH-calculus}},
journal = {arXiv preprint arXiv:2103.06610},
url = {http://arxiv.org/abs/2103.06610},
)
@article(backens2020extraction,
author = {Miriam Backens and Miller-Bakewell, Hector and Giovanni de Felice and Leo Lobski and John van de Wetering},
year = {2021},
title = {{There and back again: A circuit extraction tale}},
journal = {{Quantum}},
volume = {5},
pages = {421},
doi = {10.22331/q-2021-03-25-421},
)
@article(bookatz2012qmacomplete,
author = {Adam D Bookatz},
year = {2012},
title = {{QMA}-complete problems},
journal = {arXiv preprint arXiv:1212.6312},
url = {https://arxiv.org/abs/1212.6312},
)
@article(CD09,
author = {Bob Coecke and Ross Duncan},
year = {2011},
title = {Interacting quantum observables: categorical algebra and diagrammatics},
journal = {New Journal of Physics},
volume = {13},
pages = {043016},
doi = {10.1088/1367-2630/13/4/043016},
)
@book(PQP,
author = {Bob Coecke and Aleks Kissinger},
year = {2018},
title = {Picturing Quantum Processes - {A} First Course on Quantum Theory and Diagrammatic Reasoning},
doi = {10.1007/978-3-319-91376-6\_6},
)
@article(DKPW19,
author = {Ross Duncan and Aleks Kissinger and Simon Pedrix and John van de Wetering},
year = {2020},
title = {{Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus}},
journal = {{Quantum}},
volume = {4},
pages = {279},
doi = {10.22331/q-2020-06-04-279},
)
@inproceedings(DuncanPerdrixGraphStates,
author = {Ross Duncan and Simon Perdrix},
year = {2009},
title = {Graph states and the necessity of {Euler} decomposition},
booktitle = {Conference on Computability in Europe},
organization = {Springer},
pages = {167--177},
doi = {10.1007/978-3-642-03073-4\_18},
)
@inproceedings(duncan2010rewriting,
author = {Ross Duncan and Simon Perdrix},
year = {2010},
title = {Rewriting measurement-based quantum computations with generalised flow},
booktitle = {International Colloquium on Automata, Languages, and Programming},
organization = {Springer},
pages = {285--296},
doi = {10.1007/978-3-642-14162-1\_24},
)
@inproceedings(DP3,
author = {Ross Duncan and Simon Perdrix},
year = {2014},
title = {{Pivoting makes the ZX-calculus complete for real stabilizers}},
booktitle = {Proceedings of the 10th International Workshop on Quantum Physics and Logic (QPL)},
series = {Electronic Proceedings in Theoretical Computer Science},
volume = {171},
publisher = {Open Publishing Association},
pages = {50--62},
doi = {10.4204/EPTCS.171.5},
)
@phdthesis(gachechiladze2019quantum,
author = {Mariami Gachechiladze},
year = {2019},
title = {Quantum hypergraph states and the theory of multiparticle entanglement},
school = {Universit\"at Siegen},
note = {\url{http://141.99.19.133//bitstream/ubsi/1509/2/Dissertation_Mariami_Gachechiladze.pdf}},
)
@article(gachechiladze2019changing,
author = {Mariami Gachechiladze and Otfried G{\"u}hne and Akimasa Miyake},
year = {2019},
title = {Changing the circuit-depth complexity of measurement-based quantum computation with hypergraph states},
journal = {Physical Review A},
volume = {99},
number = {5},
pages = {052304},
doi = {10.1103/PhysRevA.99.052304},
)
@article(gachechiladze2017graphical,
author = {Mariami Gachechiladze and Nikoloz Tsimakuridze and Otfried G{\"u}hne},
year = {2017},
title = {Graphical description of unitary transformations on hypergraph states},
journal = {Journal of Physics A: Mathematical and Theoretical},
volume = {50},
number = {19},
pages = {19LT01},
doi = {10.1088/1751-8121/aa676a},
)
@inproceedings(KMS12,
author = {Aleks Kissinger and Alex Merry and Matvey Soloviev},
year = {2014},
title = {Pattern graph rewrite systems},
editor = {Benedikt L\"owe and Glynn Winskel},
booktitle = {{\rm Proceedings 8th International Workshop on} Developments in Computational Models, {\rm Cambridge, United Kingdom, 17 June 2012}},
series = {Electronic Proceedings in Theoretical Computer Science},
volume = {143},
publisher = {Open Publishing Association},
pages = {54--66},
doi = {10.4204/EPTCS.143.5},
)
@inproceedings(pyzx,
author = {Aleks Kissinger and John van de Wetering},
year = {2020},
title = {{PyZX: Large Scale Automated Diagrammatic Reasoning}},
editor = {Bob Coecke and Matthew Leifer},
booktitle = {{\rm Proceedings 16th International Conference on} Quantum Physics and Logic, {\rm Chapman University, Orange, CA, USA., 10-14 June 2019}},
series = {Electronic Proceedings in Theoretical Computer Science},
volume = {318},
publisher = {Open Publishing Association},
pages = {229--241},
doi = {10.4204/EPTCS.318.14},
)
@article(KWK19,
author = {Stach Kuijpers and John van de Wetering and Aleks Kissinger},
year = {2019},
title = {Graphical Fourier Theory and the Cost of Quantum Addition},
journal = {arXiv preprint arXiv:1904.07551},
url = {https://arxiv.org/abs/1904.07551},
)
@mastersthesis(lemonnierreport,
author = {Louis Lemonnier},
year = {2019},
title = {Relating high-level frameworks for quantum circuits},
school = {Radboud University Nijmegen},
note = {Available at \url{https://www.cs.ox.ac.uk/people/aleks.kissinger/papers/lemonnier-high-level.pdf}},
)
@article(NestMBQC,
author = {Van den Nest, M. and J. Dehaene and De Moor, B.},
year = {2004},
title = {Graphical description of the action of local {C}lifford transformations on graph states},
journal = {Physical Review A},
volume = {69},
number = {2},
pages = {9422},
doi = {10.1103/physreva.69.022316},
)
@article(qu2013encoding,
author = {Ri Qu and Juan Wang and Zong-shang Li and Yan-ru Bao},
year = {2013},
title = {Encoding hypergraphs into quantum states},
journal = {Physical Review A},
volume = {87},
number = {2},
pages = {022311},
doi = {10.1103/PhysRevA.87.022311},
)
@article(MBQC2,
author = {R. Raussendorf and D.E. Browne and H.J. Briegel},
year = {2003},
title = {Measurement-based quantum computation on cluster states},
journal = {Physical Review A},
volume = {68},
number = {2},
pages = {22312},
doi = {10.1103/physreva.68.022312},
)
@article(rossi2013quantum,
author = {Matteo Rossi and Marcus Huber and Bru{\ss}, Dagmar and Chiara Macchiavello},
year = {2013},
title = {Quantum hypergraph states},
journal = {New Journal of Physics},
volume = {15},
number = {11},
pages = {113022},
doi = {10.1088/1367-2630/15/11/113022},
)
@article(takeuchi2019quantum,
author = {Yuki Takeuchi and Tomoyuki Morimae and Masahito Hayashi},
year = {2019},
title = {Quantum computational universality of hypergraph states with Pauli-X and Z basis measurements},
journal = {Scientific reports},
volume = {9},
number = {1},
pages = {1--14},
doi = {10.1038/s41598-019-49968-3},
)
@article(tsimakuridze2017graph,
author = {Nikoloz Tsimakuridze and Otfried G{\"u}hne},
year = {2017},
title = {Graph states and local unitary transformations beyond local Clifford operations},
journal = {Journal of Physics A: Mathematical and Theoretical},
volume = {50},
number = {19},
pages = {195302},
doi = {10.1088/1751-8121/aa67cd},
)
@inproceedings(vilmart2020structure,
author = {Renaud Vilmart},
year = {2021},
title = {{The Structure of Sum-Over-Paths, its Consequences, and Completeness for Clifford}},
editor = {Stefan Kiefer and Christine Tasson},
booktitle = {Foundations of Software Science and Computation Structures},
publisher = {Springer International Publishing},
address = {Cham},
pages = {531--550},
doi = {10.1007/978-3-030-71995-1\_27},
)
@phdthesis(vladimirthesis,
author = {Vladimir Zamdzhiev},
year = {2016},
title = {Rewriting Context-free Families of String Diagrams},
school = {University of Oxford},
)