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