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We introduce the Scalable ZX-calculus (SZX-calculus for short), a formal and compact graphical language for the design and verification of quantum computations.
Quantum error-correcting codes associated with graphs
D. Schlingemann and R. F. Werner · 2001
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Measurement-based quantum computation on cluster states
Robert Raussendorf, Daniel E. Browne, and Hans J. Briegel · 2003
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Composing props
Stephen Lack · 2004
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Local equivalence of stabilizer states and codes
Maarten Van den Nest · 2005
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Entanglement in graph states and its applications
Marc Hein, Wolfgang Dür, Jens Eisert, Robert Raussendorf, M Nest, and H-J Briegel · 2006
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Generalized flow and determinism in measurement-based quantum computation
Daniel E Browne, Elham Kashefi, Mehdi Mhalla, and Simon Perdrix · 2007
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Graph states for quantum secret sharing
Damian Markham and Barry C. Sanders · 2008
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Graph states and the necessity of euler decomposition
Ross Duncan and Simon Perdrix · 2009
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Information flow in secret sharing protocols
Elham Kashefi, Damian Markham, Mehdi Mhalla, and Simon Perdrix · 2009
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Extended Measurement Calculus
Vincent Danos, Elham Kashefi, Prakash Panangaden, and Simon Perdrix · 2010
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Rewriting measurement-based quantum computations with generalised flow
Ross Duncan and Simon Perdrix · 2010
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Interacting quantum observables: categorical algebra and diagrammatics
Bob Coecke and Ross Duncan · 2011
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A graphical approach to measurement-based quantum computing
Ross Duncan · 2012
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Graph states, pivot minor, and universality of (x, z)-measurements
Mehdi Mhalla and Simon Perdrix · 2012
Earlier work this paper cites.
Verifying the Steane code with Quantomatic
Ross Duncan and Maxime Lucas · 2013
Cited alongside, same era.
Pivoting makes the ZX-calculus complete for real stabilizers
Ross Duncan and Simon Perdrix · 2013
Cited alongside, same era.
New protocols and lower bounds for quantum secret sharing with graph states
Jérôme Javelle, Mehdi Mhalla, and Simon Perdrix · 2013
Cited alongside, same era.
The ZX-calculus is complete for stabilizer quantum mechanics
Miriam Backens · 2014
Cited alongside, same era.
Experimental demonstration of a graph state quantum error-correction code
BA Bell, DA Herrera-Martí, MS Tame, D Markham, WJ Wadsworth, and JG Rarity · 2014
Cited alongside, same era.
Efficient magic state factories with a catalyzed —ccz¿ to 2—t¿ transformation
Craig Gidney and Austin G Fowler · 2018
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Two complete axiomatisations of pure-state qubit quantum computing
Amar Hadzihasanovic, Kang Feng Ng, and Quanlong Wang · 2018
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A complete axiomatisation of the zx-calculus for clifford+ t quantum mechanics
Emmanuel Jeandel, Simon Perdrix, and Renaud Vilmart · 2018
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Pyzx, 2018
A. Kissinger and John van de Wetering · 2018
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Interacting hopf algebras: the theory of linear systems
Fabio Zanasi · 2018
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Aleks Kissinger and David Quick · 2015
Cited alongside, same era.
Quantomatic: A proof assistant for diagrammatic reasoning
Aleks Kissinger and Vladimir Zamdzhiev · 2015
Cited alongside, same era.
Graphical structures for design and verification of quantum error correction
Nicholas Chancellor, Aleks Kissinger, Joschka Roffe, Stefan Zohren, and Dominic Horsman · 2016
Cited alongside, same era.
John C Baez, Brandon Coya, and Franciscus Rebro · 2017
Cited alongside, same era.
Interacting hopf algebras
Filippo Bonchi, Paweł Sobociński, and Fabio Zanasi · 2017
Cited alongside, same era.
The zx calculus is a language for surface code lattice surgery
Niel de Beaudrap and Dominic Horsman · 2017
Cited alongside, same era.
The algebra of entanglement and the geometry of composition
Amar Hadzihasanovic · 2017
Cited alongside, same era.
Miriam Backens and Aleks Kissinger · 2019
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Completeness of graphical languages for mixed states quantum mechanics
Titouan Carette, Emmanuel Jeandel, Simon Perdrix, and Renaud Vilmart · 2019
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Alexander Cowtan, Silas Dilkes, Ross Duncan, Alexandre Krajenbrink, Will Simmons, and Seyon Sivarajah · 2019
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Graph-theoretic simplification of quantum circuits with the zx-calculus
Ross Duncan, Aleks Kissinger, Simon Pedrix, and John van de Wetering · 2019
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A generic normal form for zx-diagrams and application to the rational angle completeness
Emmanuel Jeandel, Simon Perdrix, and Renaud Vilmart · 2019
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CNOT circuit extraction for topologically-constrained quantum memories
Aleks Kissinger and Arianne Meijer-van de Griend · 2019
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Reducing t-count with the zx-calculus
Aleks Kissinger and John van de Wetering · 2019
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Graphical calculus for products and convolutions
Filippo M Miatto · 2019
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A near-optimal axiomatisation of ZX-calculus for pure qubit quantum mechanics
Renaud Vilmart · 2019
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