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Measurement-based quantum computing (MBQC) is a promising alternative to traditional circuit-based quantum computing predicated on the construction and measurement of cluster states.
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Ludwig Bieberbach · 1911
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Über die bewegungsgruppen der euklidischen räume (zweite abhandlung.) die gruppen mit einem endlichen fundamentalbereich
Ludwig Bieberbach · 1912
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Andreas WM Dress · 1987
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On tilings of the plane
Andreas WM Dress and Daniel Huson · 1987
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Tilings and Patterns
Branko Grünbaum and Geoffrey Colin Shephard · 1987
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The Classification of Knots and 3-Dimensional Spaces
Geoffery Hemion · 1992
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The generation and classification of tile-k-transitive tilings of the euclidean plane, the sphere and the hyperbolic plane
Daniel H Huson · 1993
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Three-dimensional network topologies
John Nguyen, John Pezaris, Gill Pratt, and Steve Ward · 1994
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Scheme for reducing decoherence in quantum computer memory
Peter W Shor · 1995
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Threshold accuracy for quantum computation
Emanuel Knill, Raymond Laflamme, and W Zurek · 1996
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Fault-tolerant quantum computation
Peter W Shor · 1996
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Good quantum error-correcting codes exist
A Robert Calderbank and Peter W Shor · 1996
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Error correcting codes in quantum theory
Andrew M Steane · 1996
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Two-dimensional groups, orbifolds and tilings
Ludwig Balke and Daniel H Huson · 1996
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Chamber systems, coloured graphs and orbifolds
Ludwig Balke and Alba Valverde · 1996
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Fault-tolerant quantum computation with constant error
Dorit Aharonov and Michael Ben-Or · 1997
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Active stabilization, quantum computation, and quantum state synthesis
Andrew M Steane · 1997
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Stabilizer codes and quantum error correction
Daniel Gottesman · 1997
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Orbifold triangulations and crystallographic groups
Olaf Delgado Friedrichs and Daniel H Huson · 1997
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The Geometry and Topology of Three-Manifolds
William P Thurston, Steve Kerckhoff, WJ Floyd, and John Willard Milnor · 1997
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Systematic enumeration of crystalline networks
Olaf Delgado-Friedrichs, Andreas WM Dress, Daniel H Huson, Jacek Klinowski, and Alan L Mackay · 1999
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Good parameter sets for combined multiple recursive random number generators
Pierre L’Eculier · 1999
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Algebraic Topology
Allen Hatcher · 2000
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A unified formulation of honeycomb and diamond networks
Behrooz Parhami and Ding-Ming Kwai · 2001
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Recognition of flat orbifolds and the classification of tilings in R3
Olaf Delgado-Friedrichs · 2001
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Topological quantum memory
Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill · 2002
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Z2-systolic freedom and quantum codes
Michael H Freedman, David A Meyer, and Feng Luo · 2002
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An objected-oriented random-number package with many long streams and substreams
Pierre L’Eculier, R. Simard, E. J. Chen, and W. D. Kelton · 2002
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Confinement-higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
Chenyang Wang, Jim Harrington, and John Preskill · 2003
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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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Fault-tolerant quantum computation by anyons
A Yu Kitaev · 2003
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Identification of and symmetry computation for crystal nets
Olaf Delgado-Friedrichs and Michael O’Keeffe · 2003
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Barycentric drawings of periodic graphs
Olaf Delgado-Friedrichs · 2003
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Phase structure of the random-plaquette z2 gauge model: accuracy threshold for a toric quantum memory
Takuya Ohno, Gaku Arakawa, Ikuo Ichinose, and Tetsuo Matsui · 2004
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Fault-tolerant quantum computation for local non-markovian noise
Barbara M Terhal and Guido Burkard · 2005
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Quantum computing with realistically noisy devices
Emanuel Knill · 2005
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Long-range quantum entanglement in noisy cluster states
Robert Raussendorf, Sergey Bravyi, and Jim Harrington · 2005
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Crystal nets as graphs: Terminology and definitions
Olaf Delgado-Friedrichs and Michael O’Keeffe · 2005
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Equilibrium placement of periodic graphs and convexity of plane tilings
Olaf Delgado-Friedrichs · 2005
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Single-shot fault-tolerant quantum error correction
Héctor Bombín · 2015
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Reducing the overhead for quantum computation when noise is biased
Paul Webster, Stephen D Bartlett, and David Poulin · 2015
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Leakage suppression in the toric code
Martin Suchara, Andrew W Cross, and Jay M Gambetta · 2015
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Foliated quantum error-correcting codes
A Bolt, G Duclos-Cianci, D Poulin, and TM Stace · 2016
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Quantum codes from high-dimensional manifolds
Matthew B Hastings · 2016
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Constructions and noise threshold of hyperbolic surface codes
Nikolas P Breuckmann and Barbara M Terhal · 2016
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Quantum accuracy threshold for concatenated distance-3 codes
Panos Aliferis, Daniel Gottesman, and John Preskill · 2006
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A fault-tolerant one-way quantum computer
Robert Raussendorf, Jim Harrington, and Kovid Goyal · 2006
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Towards enumeration of crystalline frameworks: the 2D hyperbolic approach
ST Hyde, O Delgado-Friedrichs, SJ Ramsden, and Vanessa Robins · 2006
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Fault-tolerant quantum computation for local leakage faults
Panos Aliferis and Barbara M Terhal · 2007
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Fault-tolerant quantum computation with high threshold in two dimensions
Robert Raussendorf and Jim Harrington · 2007
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Topological fault-tolerance in cluster state quantum computation
Robert Raussendorf, Jim Harrington, and Kovid Goyal · 2007
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Almost-linear time decoding algorithm for topological codes
Nicolas Delfosse and Naomi H Nickerson · 2017
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Jonathan Conrad, Christopher Chamberland, Nikolas P Breuckmann, and Barbara M Terhal · 2017
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Terry Rudolph · 2017
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Decoding schemes for foliated sparse quantum error-correcting codes
A Bolt, D Poulin, and TM Stace · 2018
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Universal fault-tolerant measurement-based quantum computation
Benjamin Brown and Sam Roberts · 2018
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Measurement based fault tolerance beyond foliation
Naomi Nickerson and Héctor Bombín · 2018
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Statistical mechanical models for quantum codes with correlated noise
Christopher T Chubb and Steven T Flammia · 2018
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Ungauging quantum error-correcting codes
Aleksander Kubica and Beni Yoshida · 2018
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Colin J Trout, Muyuan Li, Mauricio Gutiérrez, Yukai Wu, Sheng-Tao Wang, Luming Duan, and Kenneth R Brown · 2018
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Aleksander Kubica, Michael E Beverland, Fernando Brandão, John Preskill, and Krysta M Svore · 2018
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Ultrahigh error threshold for surface codes with biased noise
David K Tuckett, Stephen D Bartlett, and Steven T Flammia · 2018
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Renormalization group decoder for a four-dimensional toric code
Kasper Duivenvoorden, Nikolas P Breuckmann, and Barbara M Terhal · 2018
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