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A web of cohomological facts relates quantum error correction, measurement-based quantum computation, symmetry protected topological order and contextuality.
“Contextuality test of the nonclassicality of variational quantum eigensolvers”
William M. Kirby and Peter J. Love · 1904
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Piers Lillystone and Joseph Emerson · 1904
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“Phase-space-simulation method for quantum computation with magic states on qubits”
Robert Raussendorf, Juani Bermejo-Vega, Emily Tyhurst, Cihan Okay, and Michael Zurel · 1905
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Austin K. Daniel, Rafael N. Alexander, and Akimasa Miyake · 1907
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“On the quantum correction for thermodynamic equilibrium”
Eugene Wigner · 1932
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“On distributions in representation space”
R. L. Stratonovich · 1956
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“On the clifford collineation, transform and similarity groups. ii.”
Beverley Bolt, TG Room, and GE Wall · 1961
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“The problem of hidden variables in quantum mechanics”
Simon Kochen and E. P. Specker · 1968
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“When is the wigner quasi-probability density non-negative?”
R.L. Hudson · 1974
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“Geometry, topology and physics”
Mikio Nakahara · 1990
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“Hidden variables and the two theorems of john bell”
N. David Mermin · 1993
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“Quantum circuit complexity”
A. Chi-Chih Yao · 1993
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“A general theory of phase-space quasiprobability distributions”
C. Brif and A. Mann · 1998
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“The heisenberg representation of quantum computers”
Daniel Gottesman · 1999
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“Quantum computation and quantum information”
Michael A. Nielsen and Isaac L. Chuang · 2000
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“A one-way quantum computer”
Robert Raussendorf and Hans J. Briegel · 2001
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“Topological quantum memory”
Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill · 2002
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“Fault-tolerant quantum computation by anyons”
A. Yu. Kitaev · 2003
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“Negativity of the wigner function as an indicator of non-classicality”
Anatole Kenfack and Karol Zyczkowski · 2004
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“Discrete phase space based on finite fields”
Kathleen S. Gibbons, Matthew J. Hoffman, and William K. Wootters · 2004
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“Hidden variable model for universal quantum computation with magic states on qubits”
Michael Zurel, Cihan Okay, and Robert Raussendorf · 2004
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“Improved simulation of stabilizer circuits”
Scott Aaronson and Daniel Gottesman · 2004
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“Discrete wigner functions and quantum computational speedup”
Ernesto F. Galvao · 2005
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“Universal quantum computation with ideal clifford gates and noisy ancillas”
Sergey Bravyi and Alexei Kitaev · 2005
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“A structure theorem for generalized-noncontextual ontological models” (2020) arXiv:2005.07161
David Schmid, John H. Selby, Matthew F. Pusey, and Robert W. Spekkens · 2005
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“Symmetric informationally complete–positive operator valued measures and the extended clifford group”
D Marcus Appleby · 2005
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“Classicality in discrete wigner functions”
Cecilia Cormick, Ernesto F. Galvão, Daniel Gottesman, Juan Pablo Paz, and Arthur O. Pittenger · 2006
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“A fault-tolerant one-way quantum computer”
R. Raussendorf, J. Harrington, and K. Goyal · 2006
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“Hudson’s theorem for finite-dimensional quantum systems”
David Gross · 2006
Cited alongside, same era.
“Wigner function negativity and contextuality in quantum computation on rebits”
Nicolas Delfosse, Philippe Allard Guerin, Jacob Bian, and Robert Raussendorf · 2015
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“Permutation symmetry determines the discrete wigner function”
Huangjun Zhu · 2016
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“Trading classical and quantum computational resources”
Sergey Bravyi, Graeme Smith, and John A. Smolin · 2016
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“The clifford group forms a unitary 3-design”
Zak Webb · 2016
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Austin K. Daniel and Akimasa Miyake · 2007
Cited alongside, same era.
“Negativity and contextuality are equivalent notions of nonclassicality”
Robert W. Spekkens · 2008
Cited alongside, same era.
“Computational power of quantum many-body states and some results on discrete phase spaces”
David Gross · 2008
Cited alongside, same era.
“Advanced linear algebra”
Steven Roman · 2008
Cited alongside, same era.
Christopher Ferrie and Joseph Emerson · 2008
Cited alongside, same era.
“Computational power of correlations”
Janet Anders and Dan E. Browne · 2009
Cited alongside, same era.
“Quantum computation on the edge of a symmetry-protected topological order”
Akimasa Miyake · 2010
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Ravi Kunjwal · 2016
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“Topological proofs of contextuality in quantum mechanics”
Cihan Okay, Sam Roberts, Stephen D. Bartlett, and Robert Raussendorf · 2017
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“Equivalence between contextuality and negativity of the wigner function for qudits”
Nicolas Delfosse, Cihan Okay, Juan Bermejo-Vega, Dan E Browne, and Robert Raussendorf · 2017
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“Symmetry-protected topological phases with uniform computational power in one dimension”
Robert Raussendorf, Dong-Sheng Wang, Abhishodh Prakash, Tzu-Chieh Wei, and David T. Stephen · 2017
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Lucas Kocia and Peter Love · 2017
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“Contextuality and wigner-function negativity in qubit quantum computation”
Robert Raussendorf, Dan E. Browne, Nicolas Delfosse, Cihan Okay, and Juan Bermejo-Vega · 2017
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“Application of a resource theory for magic states to fault-tolerant quantum computing”
Mark Howard and Earl Campbell · 2017
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“Multiqubit clifford groups are unitary 3-designs”
Huangjun Zhu · 2017
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“Universal quantum computation using fractal symmetry-protected cluster phases”
Trithep Devakul and Dominic J. Williamson · 2018
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Angela Karanjai, Joel J. Wallman, and Stephen D. Bartlett · 2018
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“Cohomological framework for contextual quantum computations”
Robert Raussendorf · 2019
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“Computationally universal phase of quantum matter”
Robert Raussendorf, Cihan Okay, Dong-Sheng Wang, David T. Stephen, and Hendrik Poulsen Nautrup · 2019
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“Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter”
David T. Stephen, Hendrik Poulsen Nautrup, Juani Bermejo-Vega, Jens Eisert, and Robert Raussendorf · 2019
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Lucas Kocia and Peter Love · 2019
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“The stabilizer polytope and contextuality for qubit systems”
Arne Heimendahl · 2020
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“Hidden variable models and classical simulation algorithms for quantum computation with magic states on qubits”
Michael Zurel · 2020
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Jonas Haferkamp and Juani Bermejo-Vega · 2021
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Michael Zurel, Cihan Okay, Robert Raussendorf, and Arne Heimendahl · 2021
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“Contextuality and wigner negativity are equivalent for continuous-variable quantum measurements”
Robert I. Booth, Ulysse Chabaud, and Pierre-Emmanuel Emeriau · 2022
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“Uniqueness of noncontextual models for stabilizer subtheories”
David Schmid, Haoxing Du, John H. Selby, and Matthew F. Pusey · 2022
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