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Quantum phases of matter are resources for notions of quantum computation.
“Matrix Product States: Entanglement, symmetries, and state transformations”, 2019
David Sauerwein, Andras Molnar, J. Cirac and Barbara Kraus · 1901
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“Rigorous results on valence-bond ground states in antiferromagnets”
Ian Affleck, Tom Kennedy, Elliott. Lieb and Hal Tasaki · 1987
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“A note on injectivity of additive cellular automata”
Burton Voorhees · 1994
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“Elementary gates for quantum computation”
Adriano Barenco et al · 1995
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“Universality in quantum computation”
David Deutsch, Adriano Barenco and Artur Ekert · 1995
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“The spectral gap for some spin chains with discrete symmetry breaking”
Bruno Nachtergaele · 1996
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“Stabilizer codes and quantum error correction”, 1997
Daniel Gottesman · 1997
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“Fault-Tolerant Quantum Computation with Higher-Dimensional Systems”
Daniel Gottesman · 1998
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“Characters of finite groups”
I Berkovich and EM Zhmud · 1998
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“Unpaired Majorana fermions in quantum wires”
A Kitaev · 2001
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“A One-Way Quantum Computer”
Robert Raussendorf and Hans. Briegel · 2001
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“Practical Scheme for Quantum Computation with Any Two-Qubit Entangling Gate”
Michael. Bremner et al · 2002
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“Fault-tolerant quantum computation by anyons”
A.Yu. Kitaev · 2003
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“Topological quantum computation”
Michael Freedman, Alexei Kitaev, Michael Larsen and Zhenghan Wang · 2003
Earlier work this paper cites.
“Measurement-based quantum computation on cluster states”
Robert Raussendorf, Daniel. Browne and Hans. Briegel · 2003
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“Reversible quantum cellular automata”, 2004
B. Schumacher and R.. Werner · 2004
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“Multiparty entanglement in graph states”
M. Hein, J. Eisert and H.. Briegel · 2004
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“Quantum computation via translation-invariant operations on a chain of qubits”
Robert Raussendorf · 2005
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“Globally Controlled Quantum Wires for Perfect Qubit Transport, Mirroring, and Computing”
Joseph Fitzsimons and Jason Twamley · 2006
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“Matrix product states represent ground states faithfully”
F. Verstraete and J.. Cirac · 2006
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“A fault-tolerant one-way quantum computer”
R. Raussendorf, J. Harrington and K. Goyal · 2006
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“Measurement-based quantum computation beyond the one-way model”
D. Gross, J. Eisert, N. Schuch and D. Perez-Garcia · 2007
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“Quantum Information Processing with Delocalized Qubits under Global Control”
Joseph Fitzsimons, Li Xiao, Simon. Benjamin and Jonathan. Jones · 2007
Earlier work this paper cites.
“Matrix Product State Representations”
D. Perez-Garcia, F. Verstraete, M.. Wolf and J.. Cirac · 2007
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“Novel Schemes for Measurement-Based Quantum Computation”
D. Gross and J. Eisert · 2007
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“Topological fault-tolerance in cluster state quantum computation”
R Raussendorf, J Harrington and K Goyal · 2007
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“Non-Abelian anyons and topological quantum computation”
Chetan Nayak, Steven. Simon, Ady Stern, Michael Freedman and Sankar Das · 2008
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“Family of non-Abelian Kitaev models on a lattice: Topological condensation and confinement”
H. Bombin and M.. Martin-Delgado · 2008
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“A symmetry principle for topological quantum order”
Zohar Nussinov and Gerardo Ortiz · 2008
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“On the structure of Clifford quantum cellular automata”
Dirk-M. Schlingemann, Holger Vogts and Reinhard. Werner · 2008
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“Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems”
F. Verstraete, V. Murg and J.I. Cirac · 2008
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“Entropy Scaling and Simulability by Matrix Product States”
Norbert Schuch, Michael. Wolf, Frank Verstraete and J. Cirac · 2008
Earlier work this paper cites.
“String Order and Symmetries in Quantum Spin Lattices”
D. P“’erez-Garc“’a, M.. Wolf, M. Sanz, F. Verstraete and J.. Cirac · 2008
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“Identifying Phases of Quantum Many-Body Systems That Are Universal for Quantum Computation”
Andrew. Doherty and Stephen. Bartlett · 2009
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“Sufficient symmetry conditions for Topological Quantum Order”
Zohar Nussinov and Gerardo Ortiz · 2009
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“Quantum Computation on the Edge of a Symmetry-Protected Topological Order”
Akimasa Miyake · 2010
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“Quantum Computational Renormalization in the Haldane Phase”
Stephen. Bartlett, Gavin. Brennen, Akimasa Miyake and Joseph. Renes · 2010
Cited alongside, same era.
“Entanglement spectrum of a topological phase in one dimension”
Frank Pollmann, Ari. Turner, Erez Berg and Masaki Oshikawa · 2010
Cited alongside, same era.
“PEPS as ground states: Degeneracy and topology”
Norbert Schuch, Ignacio Cirac and David Perez-Garcia · 2010
Cited alongside, same era.
“Time asymptotics and entanglement generation of Clifford quantum cellular automata”
Johannes G“”utschow, Sonja Uphoff, Reinhard. Werner and Zoltan Zimboras · 2010
Cited alongside, same era.
“Non-Abelian statistics and topological quantum information processing in 1D wire networks”
Jason Alicea, Yuval Oreg, Gil Refael, Felix von Oppen and Matthew P.. Fisher · 2011
Cited alongside, same era.
“Classifying quantum phases using matrix product states and projected entangled pair states”
“Building crystalline topological phases from lower-dimensional states”
Sheng-Jie Huang, Hao Song, Yi-Ping Huang and Michael Hermele · 2017
Later among the works it cites.
“Hand-waving and interpretive dance: an introductory course on tensor networks”
Jacob Bridgeman and Christopher Chubb · 2017
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“Anyons and matrix product operator algebras”
N. Bultinck et al · 2017
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“Entanglement phases as holographic duals of anyon condensates”
Kasper Duivenvoorden, Mohsin Iqbal, Jutho Haegeman, Frank Verstraete and Norbert Schuch · 2017
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“Anyon condensation and a generic tensor-network construction for symmetry-protected topological phases”
Shenghan Jiang and Ying Ran · 2017
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Norbert Schuch, David P“’erez-Garc“’a and Ignacio Cirac · 2011
Cited alongside, same era.
“Classification of gapped symmetric phases in one-dimensional spin systems”
Xie Chen, Zheng-Cheng Gu and Xiao-Gang Wen · 2011
Cited alongside, same era.
“Local stabilizer codes in three dimensions without string logical operators”
Jeongwan Haah · 2011
Cited alongside, same era.
“Symmetry-Protected Phases for Measurement-Based Quantum Computation”
Dominic. Else, Ilai Schwarz, Stephen. Bartlett and Andrew. Doherty · 2012
Cited alongside, same era.
“Symmetry protection of measurement-based quantum computation in ground states”
Dominic Else, Stephen Bartlett and Andrew Doherty · 2012
Cited alongside, same era.
“Detection of symmetry-protected topological phases in one dimension”
Frank Pollmann and Ari. Turner · 2012
Cited alongside, same era.
“Index Theory of One Dimensional Quantum Walks and Cellular Automata”
D. Gross, V. Nesme, H. Vogts and R.. Werner · 2012
Cited alongside, same era.
Dominic. Williamson, Nick Bultinck and Frank Verstraete · 2017
Later among the works it cites.
“Fermionic projected entangled-pair states and topological phases”
Nick Bultinck, Dominic Williamson, Jutho Haegeman and Frank Verstraete · 2017
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“Private quantum computation: an introduction to blind quantum computing and related protocols”
Joseph. Fitzsimons · 2017
Later among the works it cites.
“Flow Ambiguity: A Path Towards Classically Driven Blind Quantum Computation”
Atul Mantri, Tommaso. Demarie, Nicolas. Menicucci and Joseph. Fitzsimons · 2017
Later among the works it cites.
“Matrix product unitaries: structure, symmetries, and topological invariants”
J Cirac, David Perez-Garcia, Norbert Schuch and Frank Verstraete · 2017
Later among the works it cites.
“Universality of quantum computation with cluster states and (X, Y)-plane measurements”
Atul Mantri, Tommaso. Demarie and Joseph. Fitzsimons · 2017
Later among the works it cites.
“Symmetry-protected topological entanglement”
Iman Marvian · 2017
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“Colloquium: Zoo of quantum-topological phases of matter”
Xiao-Gang Wen · 2017
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“One-dimensional symmetry protected topological phases and their transitions”
Ruben Verresen, Roderich Moessner and Frank Pollmann · 2017
Later among the works it cites.
“Majorana zero modes in superconductor-semiconductor heterostructures”
R.. Lutchyn et al · 2018
Closest in time.
“Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry”
Jacob Miller and Akimasa Miyake · 2018
Closest in time.
“Universal quantum computation using fractal symmetry-protected cluster phases”
Trithep Devakul and Dominic. Williamson · 2018
Closest in time.
“Universal quantum computing with parafermions assisted by a half fluxon”, 2018
Arpit Dua, Boris Malomed, Meng Cheng and Liang Jiang · 2018
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“Topologically protected braiding in a single wire using Floquet Majorana modes”, 2018
Bela Bauer et al · 2018
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“Gauging Spatial Symmetries and the Classification of Topological Crystalline Phases”
Ryan Thorngren and Dominic. Else · 2018
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“Subsystem symmetry protected topological order”
Yizhi You, Trithep Devakul, F.. Burnell and S.. Sondhi · 2018
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“Classification of subsystem symmetry-protected topological phases”
Trithep Devakul, Dominic. Williamson and Yizhi You · 2018
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“Symmetric Fracton Matter: Twisted and Enriched”, 2018
Yizhi You, Trithep Devakul, F.. Burnell and S.. Sondhi · 2018
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“Ungauging quantum error-correcting codes”, 2018
Aleksander Kubica and Beni Yoshida · 2018
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“Symmetry-protected self-correcting quantum memories”, 2018
Sam Roberts and Stephen. Bartlett · 2018
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“A generalization of the injectivity condition for projected entangled pair states”
Andras Molnar, Yimin Ge, Norbert Schuch and J. Cirac · 2018
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“Projected entangled pair states with continuous virtual symmetries”
Henrik Dreyer, J. Cirac and Norbert Schuch · 2018
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“Architectures for Quantum Simulation Showing a Quantum Speedup”
Juan Bermejo-Vega, Dominik Hangleiter, Martin Schwarz, Robert Raussendorf and Jens Eisert · 2018
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“Anticoncentration theorems for schemes showing a quantum speedup”
Dominik Hangleiter, Juan Bermejo-Vega, Martin Schwarz and Jens Eisert · 2018
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“Normal projected entangled pair states generating the same state”
Andras Molnar, Jos“’e Garre-Rubio, David P“’erez-Garc“’a, Norbert Schuch and J Cirac · 2018
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“Computationally Universal Phase of Quantum Matter”
Robert Raussendorf, Cihan Okay, Dong-Sheng Wang, David. Stephen and Hendrik Nautrup · 2019
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“Fractal Symmetric Phases of Matter”
Trithep Devakul, Yizhi You, F.. Burnell and S.. Sondhi · 2019
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“Foliated fracton order from gauging subsystem symmetries”
Wilbur Shirley, Kevin Slagle and Xie Chen · 2019
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“Twisted fracton models in three dimensions”
Hao Song, Abhinav Prem, Sheng-Jie Huang and M.. Martin-Delgado · 2019
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“Changing the circuit-depth complexity of measurement-based quantum computation with hypergraph states”
Mariami Gachechiladze, Otfried G“”uhne and Akimasa Miyake · 2019
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