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We present a new graphical calculus that is sound and complete for a universal family of quantum circuits, which can be seen as the natural string-diagrammatic extension of the approximately (real-valued) universal family of Hadamard+CCZ circuits.
arXiv: http://arxiv.org/abs/quant-ph/0301040
Dorit Aharonov (2003): A simple proof that Toffoli and Hadamard are quantum universal · 2003
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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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Quantum Info. Comput
Yaoyun Shi (2003): Both Toffoli and controlled-NOT Need Little Help to Do Universal Quantum Computing · 2003
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Electronic Notes in Theoretical Computer Science
P. Selinger (2007): Dagger compact closed categories and completely positive maps · 2006
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In: Proceedings of the 37th International Colloquium on Automata, Languages and Programming (ICALP)
B. Coecke & R. Duncan (2008): Interacting quantum observables · 2008
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Mathematical Theory and Computational Practice
R. Duncan & S. Perdrix (2009): Graph states and the necessity of Euler decomposition · 2009
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In: Proceedings of ICALP
R. Duncan & S. Perdrix (2010): Rewriting measurement-based quantum computations with generalised flow · 2010
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New Journal of Physics
B. Coecke & R. Duncan (2011): Interacting quantum observables: categorical algebra and diagrammatics · 2011
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IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
M. Amy, D. Maslov, M. Mosca & M. Roetteler (2013): A Meet-in-the-Middle Algorithm for Fast Synthesis of Depth-Optimal Quantum Circuits · 2013
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In Chris Heunen, Mehrnoosh Sadrzadeh & Edward Grefenstette, editors: Quantum Physics and Linguistics
Ross Duncan (2013): A graphical approach to measurement-based quantum computing · 2013
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New Journal of Physics
Matteo Rossi, M Huber, D Bruß & C Macchiavello (2013): Quantum hypergraph states · 2013
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IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
M. Amy, D. Maslov & M. Mosca (2014): Polynomial-Time T-Depth Optimization of Clifford+T Circuits Via Matroid Partitioning · 2014
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Electronic Proceedings in Theoretical Computer Science
Aleks Kissinger, Alex Merry & Matvey Soloviev (2014): Pattern graph rewrite systems · 2014
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Physical Review Letters
Mariami Gachechiladze, Costantino Budroni & Otfried Gühne (2016): Extreme violation of local realism in quantum hypergraph states · 2016
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Npj Quantum Information
Jacob Miller & Akimasa Miyake (2016): Hierarchy of universal entanglement in 2D measurement-based quantum computation · 2016
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Cambridge University Press, 10.1017/9781316219317
B. Coecke & A. Kissinger (2017): Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning · 2017
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Phys. Rev. A
Shawn X. Cui, Daniel Gottesman & Anirudh Krishna (2017): Diagonal gates in the Clifford hierarchy · 2017
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arXiv: http://arxiv.org/abs/1706.09877
Kang Feng Ng & Quanlong Wang (2017): A universal completion of the ZX-calculus · 2017
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In: Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science
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Physica Scripta
M Rossi, D Bruß & C Macchiavello (2014): Hypergraph states in Grover’s quantum search algorithm · 2014
Cited alongside, same era.
In: International Conference on Automated Deduction
Aleks Kissinger & Vladimir Zamdzhiev (2015): Quantomatic: A proof assistant for diagrammatic reasoning · 2015
Cited alongside, same era.
arXiv: http://arxiv.org/abs/1601.07363
M. Amy & M. Mosca (2016): T-count optimization and Reed-Muller codes · 2016
Cited alongside, same era.
To appear
Niel de Beaudrap: A toy theory of tensor networks for exact quantum algorithms
Cited in the paper.
PhD thesis, University of Oxford
Amar Hadzihasanovic: The algebra of entanglement and the geometry of composition
Cited in the paper.
Emmanuel Jeandel, Simon Perdrix & Renaud Vilmart (2018): A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics · 2018
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Electronic Proceedings in Theoretical Computer Science
Emmanuel Jeandel, Simon Perdrix & Renaud Vilmart (2018): Y-Calculus: A Language for Real Matrices Derived from the ZX-Calculus · 2018
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Quantum Science and Technology
Luke E Heyfron & Earl T Campbell (2018): An efficient quantum compiler that reduces T count · 2058
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