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The ZH-calculus is a complete graphical calculus for linear maps between qubits that admits a straightforward encoding of hypergraph states and circuits arising from the Toffoli+Hadamard gate set.
arXiv preprint arXiv:1904.07551
Stach Kuijpers, John van de Wetering & Aleks Kissinger (2019): Graphical Fourier Theory and the Cost of Quantum Addition · 1904
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Physical Review A
R. Raussendorf, D.E. Browne & H.J. Briegel (2003): Measurement-based quantum computation on cluster states · 2003
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Physical Review A
M. Van den Nest, J. Dehaene & B. De Moor (2004): Graphical description of the action of local Clifford transformations on graph states · 2004
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In: Conference on Computability in Europe
Ross Duncan & Simon Perdrix (2009): Graph states and the necessity of Euler decomposition · 2009
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In: International Colloquium on Automata, Languages, and Programming
Ross Duncan & Simon Perdrix (2010): Rewriting measurement-based quantum computations with generalised flow · 2010
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New Journal of Physics
Bob Coecke & Ross Duncan (2011): Interacting quantum observables: categorical algebra and diagrammatics · 2011
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arXiv preprint arXiv:1212.6312
Adam D Bookatz (2012): QMA-complete problems · 2012
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In Benedikt Löwe & Glynn Winskel, editors: Proceedings 8th International Workshop on Developments in Computational Models,
Aleks Kissinger, Alex Merry & Matvey Soloviev (2014): Pattern graph rewrite systems · 2012
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Physical Review A
Ri Qu, Juan Wang, Zong-shang Li & Yan-ru Bao (2013): Encoding hypergraphs into quantum states · 2013
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New Journal of Physics
Matteo Rossi, Marcus Huber, Dagmar Bruß & Chiara Macchiavello (2013): Quantum hypergraph states · 2013
Cited alongside, same era.
New Journal of Physics
Miriam Backens (2014): The ZX-calculus is complete for stabilizer quantum mechanics · 2014
Cited alongside, same era.
In: Proceedings of the 10th International Workshop on Quantum Physics and Logic (QPL)
Ross Duncan & Simon Perdrix (2014): Pivoting makes the ZX-calculus complete for real stabilizers · 2014
Cited alongside, same era.
Ph.D. thesis, University of Oxford
Vladimir Zamdzhiev (2016): Rewriting Context-free Families of String Diagrams · 2016
Cited alongside, same era.
Journal of Physics A: Mathematical and Theoretical
Mariami Gachechiladze, Nikoloz Tsimakuridze & Otfried Gühne (2017): Graphical description of unitary transformations on hypergraph states · 2017
Cited alongside, same era.
Journal of Physics A: Mathematical and Theoretical
Ph.D. thesis, University of Waterloo
Matthew Amy (2019): Formal Methods in Quantum Circuit Design · 2019
Later among the works it cites.
Ph.D. thesis, Universität Siegen
Mariami Gachechiladze (2019): Quantum hypergraph states and the theory of multiparticle entanglement · 2019
Later among the works it cites.
Physical Review A
Mariami Gachechiladze, Otfried Gühne & Akimasa Miyake (2019): Changing the circuit-depth complexity of measurement-based quantum computation with hypergraph states · 2019
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In Bob Coecke & Matthew Leifer, editors: Proceedings 16th International Conference on Quantum Physics and Logic,
Aleks Kissinger & John van de Wetering (2020): PyZX: Large Scale Automated Diagrammatic Reasoning · 2019
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Master’s thesis, Radboud University Nijmegen
Louis Lemonnier (2019): Relating high-level frameworks for quantum circuits · 2019
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Scientific reports
Yuki Takeuchi, Tomoyuki Morimae & Masahito Hayashi (2019): Quantum computational universality of hypergraph states with Pauli-X and Z basis measurements · 2019
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Nikoloz Tsimakuridze & Otfried Gühne (2017): Graph states and local unitary transformations beyond local Clifford operations · 2017
Cited alongside, same era.
In Peter Selinger & Giulio Chiribella, editors: Proceedings of the 15th International Conference on Quantum Physics and Logic,
Matthew Amy (2019): Towards Large-scale Functional Verification of Universal Quantum Circuits · 2018
Cited alongside, same era.
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
Cited alongside, same era.
10.1007/978-3-319-91376-6_6
Bob Coecke & Aleks Kissinger (2018): Picturing Quantum Processes - A First Course on Quantum Theory and Diagrammatic Reasoning · 2018
Cited alongside, same era.
Later among the works it cites.
arXiv preprint arXiv:2103.06610
Miriam Backens, Aleks Kissinger, Hector Miller-Bakewell, John van de Wetering & Sal Wolffs (2021): Completeness of the ZH-calculus · 2021
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In Stefan Kiefer & Christine Tasson, editors: Foundations of Software Science and Computation Structures
Renaud Vilmart (2021): The Structure of Sum-Over-Paths, its Consequences, and Completeness for Clifford · 2021
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