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The graph state formalism offers strong connections between quantum information processing and graph theory.
A combinatorial equivalence of matrices
Albert W. Tucker · 1960
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Eulerian lines in finite 4-valent graphs and their transformations
Anton Kotzig · 1968
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Local complementation and interlacement graphs
Hubert de Fraysseix · 1981
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Graphic presentations of isotropic systems
André Bouchet · 1987
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Connectivity of isotropic systems
André Bouchet · 1989
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Circle graph obstructions
André Bouchet · 1994
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A generalization of tutte’s characterization of totally unimodular matrices
J. F. Geelen · 1997
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A one-way quantum computer
Robert Raussendorf and Hans J. Briegel · 2001
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Multiparticle entanglement purification for graph states
Wolfgang Dür, Hans Aschauer, and Hans J. Briegel · 2003
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Universal quantum computation using only projective measurement, quantum memory, and preparation of the 0 state
Michael A. Nielsen · 2003
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Measurement-based quantum computation with cluster states
Robert Raussendorf, Daniel E. Browne, and Hans J. Briegel · 2003
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Both toffoli and controlled-not need little help to do universal quantum computation
Yaoyun Shi · 2003
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Quantum computation by measurements
Debbie W. Leung · 2004
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Graphical description of the action of local clifford transformations on graph states
Maarten Van den Nest, Jeroen Dehaene, and Bart De Moor · 2004
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Entanglement in graph states and its applications
Marc Hein, Wolfgang Dür, Jens Eisert, Robert Raussendorf, Maarten Van den Nest, and Hans J. Briegel · 2005
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Rank-width and vertex-minors
Sang-il Oum · 2005
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State transfer instead of teleportation in measurement-based quantum computation
Simon Perdrix · 2005
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Edge-local equivalence of graphs
Maarten Van den Nest and Bart De Moor · 2005
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Experimental one-way quantum computing
Philip Walther, Kevin J. Resch, Terry Rudolph, Emmanuel Schenck, Harald Weinfurter, Vlatko Vedral, Markus Aspelmeyer, and Anton Zeilinger · 2005
Cited alongside, same era.
Determinism in the one-way model
Vincent Danos and Elham Kashefi · 2006
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Finding optimal flows efficiently
Mehdi Mhalla and Simon Perdrix · 2008
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Universal blind quantum computation
Anne Broadbent, Joseph Fitzsimons, and Elham Kashefi · 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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Excluding a bipartite circle graph from line graphs
Sang-il Oum · 2009
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Extended measurement calculus
Vincent Danos, Elham Kashefi, Prakash Panangaden, and Simon Perdrix · 2010
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Graph concatenation for quantum codes
Salman Beigi, Isaac Chuang, Markus Grassl, Peter Shor, and Bei Zeng · 2011
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Resources required for preparing graph states
Peter Høyer, Mehdi Mhalla, and Simon Perdrix · 2006
Cited alongside, same era.
Approximating clique-width and branch-width
Sang-il Oum and Paul Seymour · 2006
Cited alongside, same era.
Universal resources for measurement-based quantum computation
Maarten Van den Nest, Akimasa Miyake, Wolfgang Dür, and Hans J. Briegel · 2006
Cited alongside, same era.
Generalized flow and determinism in measurement-based quantum computation
Daniel E. Browne, Elham Kashefi, Mehdi Mhalla, and Simon Perdrix · 2007
Cited alongside, same era.
The measurement calculus
Vincent Danos, Elham Kashefi, and Prakash Panangaden · 2007
Cited alongside, same era.
Towards minimal resources of measurement-based quantum computation
Simon Perdrix · 2007
Cited alongside, same era.
Daniel E. Browne, Elham Kashefi, and Simon Perdrix · 2011
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Quantum Proofs for Classical Theorems
Andrew Drucker and Ronald de Wolf · 2011
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Optimal accessing and non-accessing structures for graph protocols
Sylvain Gravier, Jérôme Javelle, Mehdi Mhalla, and Simon Perdrix · 2011
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New protocols and lower bound for quantum secret sharing with graph states
Jérôme Javelle, Mehdi Mhalla, and Simon Perdrix · 2011
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Pivot-minors and vertex-minors of trees and paths
Ojoung Kwon and Sang-il Oum · 2011
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Which graph states are useful for quantum information processing?
Mehdi Mhalla, Mio Murao, Simon Perdrix, Masato Someya, and Peter Turner · 2011
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Simple sets of measurements for universal quantum computation and graph state preparation
Yasuhiro Takahashi · 2011
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