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We present a completely new approach to quantum circuit optimisation, based on the ZX-calculus.
Eulerian lines in finite 4-valent graphs and their transformations
Anton Kotzig · 1968
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Graphic presentations of isotropic systems
André Bouchet · 1987
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Clifford group, stabilizer states, and linear and quadratic operations over GF(2)
Jeroen Dehaene and Bart De Moor · 2003
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Improved simulation of stabilizer circuits
Scott Aaronson and Daniel Gottesman · 2004
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Determinism in the one-way model
V. Danos and E. Kashefi · 2006
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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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The measurement calculus
Vincent Danos, Elham Kashefi, and Prakash Panangaden · 2007
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Computation at a distance
Samuel A Kutin, David Petrie Moulton, and Lawren M Smithline · 2007
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Optimal synthesis of linear reversible circuits
Ketan Markov, Igor Patel, and John Hayes · 2008
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Graph states and the necessity of Euler decomposition
R. Duncan and S. 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
R. Duncan and S. Perdrix · 2010
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Quantum computation and quantum information
M. A. Nielsen and I. L. Chuang · 2010
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Classical simulation of quantum computation, the gottesman-knill theorem, and slightly beyond
Maarten Van Den Nest · 2010
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Interacting quantum observables: Categorical algebra and diagrammatics
Bob Coecke and Ross Duncan · 2011
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Which graph states are useful for quantum information processing?
Mehdi Mhalla, Mio Murao, Simon Perdrix, Masato Someya, and Peter S Turner · 2011
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Optimization of Clifford circuits
Vadym Kliuchnikov and Dmitri Maslov · 2013
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Quantum circuit optimization by Hadamard gate reduction
Nabila Abdessaied, Mathias Soeken, and Rolf Drechsler · 2014
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Automated optimization of large quantum circuits with continuous parameters
Yunseong Nam, Neil J Ross, Yuan Su, Andrew M Childs, and Dmitri Maslov · 2018
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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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Optimising Clifford Circuits with Quantomatic
Andrew Fagan and Ross Duncan · 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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