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In order to build a large scale quantum computer, one must be able to correct errors extremely fast.
An improved equivalence algorithm
Bernard A Galler and Michael J Fisher · 1964
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Algorithm 447: efficient algorithms for graph manipulation
John Hopcroft and Robert Tarjan · 1973
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Efficiency of a good but not linear set union algorithm
Robert Endre Tarjan · 1975
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A class of algorithms which require nonlinear time to maintain disjoint sets
Robert Endre Tarjan · 1979
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The cell probe complexity of dynamic data structures
Michael Fredman and Michael Saks · 1989
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Quantum codes on a lattice with boundary
S. B. Bravyi and A. Y. Kitaev · 1998
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Z(2)-Systolic Freedom and Quantum Codes
M.H. Freedman, D.A. Meyer, F. Luo, and Computer Society (IEEE) Washington DC · 1999
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Projective plane and planar quantum codes
M. H. Freedman and D. A. Meyer · 2001
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A scheme for efficient quantum computation with linear optics
Emanuel Knill, Raymond Laflamme, and Gerald J Milburn · 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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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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Analysis of quantum error-correcting codes: symplectic lattice codes and toric codes
James William Harrington · 2004
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Optical quantum computation using cluster states
Michael A Nielsen · 2004
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Resource-efficient linear optical quantum computation
Daniel E Browne and Terry Rudolph · 2005
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Purifying quantum states: Quantum and classical algorithms
Eric Dennis · 2005
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Topological quantum distillation
Hector Bombin and Miguel Angel Martin-Delgado · 2006
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A fault-tolerant one-way quantum computer
Robert Raussendorf, Jim Harrington, and Kovid Goyal · 2006
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Percolation, renormalization, and quantum computing with nondeterministic gates
Konrad Kieling, Terry Rudolph, and Jens Eisert · 2007
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Fault-tolerant quantum computation with high threshold in two dimensions
R. Raussendorf and J. Harrington · 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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Blossom v: a new implementation of a minimum cost perfect matching algorithm
Vladimir Kolmogorov · 2009
Cited alongside, same era.
Thresholds for topological codes in the presence of loss
T.M. Stace, S.D. Barrett, and A.C. Doherty · 2009
Cited alongside, same era.
Graphical algorithms and threshold error rates for the 2d colour code
David S Wang, Austin G Fowler, Charles D Hill, and Lloyd Christopher L Hollenberg · 2009
Cited alongside, same era.
On cayley graphs, surface codes, and the limits of homological coding for quantum error correction
Gilles Zémor · 2009
Cited alongside, same era.
Fast decoders for topological quantum codes
Guillaume Duclos-Cianci and David Poulin · 2010
Cited alongside, same era.
Minimum weight perfect matching of fault-tolerant topological quantum error correction in average o ( 1 ) o(1) parallel time
Austin G Fowler · 2015
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Fault tolerant dynamical decoders for topological quantum memories
Michael Herold, Michael J Kastoryano, Earl T Campbell, and Jens Eisert · 2015
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A surface code quantum computer in silicon
Charles D Hill, Eldad Peretz, Samuel J Hile, Matthew G House, Martin Fuechsle, Sven Rogge, Michelle Y Simmons, and Lloyd CL Hollenberg · 2015
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Improved hdrg decoders for qudit and non-abelian quantum error correction
Adrian Hutter, Daniel Loss, and James R Wootton · 2015
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Fast fault-tolerant decoder for qubit and qudit surface codes
Fern HE Watson, Hussain Anwar, and Dan E Browne · 2015
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Andrew J Landahl, Jonas T Anderson, and Patrick R Rice · 2011
Cited alongside, same era.
Universal topological phase of two-dimensional stabilizer codes
Hector Bombin, Guillaume Duclos-Cianci, and David Poulin · 2012
Cited alongside, same era.
Efficient decoding of topological color codes
Pradeep Sarvepalli and Robert Raussendorf · 2012
Cited alongside, same era.
High threshold error correction for the surface code
James R Wootton and Daniel Loss · 2012
Cited alongside, same era.
Quantum self-correction in the 3d cubic code model
Sergey Bravyi and Jeongwan Haah · 2013
Cited alongside, same era.
Tradeoffs for reliable quantum information storage in surface codes and color codes
Nicolas Delfosse · 2013
Cited alongside, same era.
Kitaev’s z d-code threshold estimates
Guillaume Duclos-Cianci and David Poulin · 2013
Cited alongside, same era.
A simple decoder for topological codes
James Wootton · 2015
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Constructions and noise threshold of hyperbolic surface codes
Nikolas P Breuckmann and Barbara M Terhal · 2016
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Demonstration of a small programmable quantum computer with atomic qubits
S Debnath, NM Linke, C Figgatt, KA Landsman, K Wright, and C Monroe · 2016
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Realization of a scalable shor algorithm
Thomas Monz, Daniel Nigg, Esteban A Martinez, Matthias F Brandl, Philipp Schindler, Richard Rines, Shannon X Wang, Isaac L Chuang, and Rainer Blatt · 2016
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Linear-time maximum likelihood decoding of surface codes over the quantum erasure channel
Nicolas Delfosse and Gilles Zémor · 2017
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Towards sufficiently fast quantum error correction
Austin Fowler · 2017
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Implementing a universal gate set on a logical qubit encoded in an oscillator
Reinier W Heeres, Philip Reinhold, Nissim Ofek, Luigi Frunzio, Liang Jiang, Michel H Devoret, and Robert J Schoelkopf · 2017
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Quantum experience API
IBM · 2017
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Entanglement distillation between solid-state quantum network nodes
Norbert Kalb, Andreas A Reiserer, Peter C Humphreys, Jacob JW Bakermans, Sten J Kamerling, Naomi H Nickerson, Simon C Benjamin, Daniel J Twitchen, Matthew Markham, and Ronald Hanson · 2017
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Blueprint for a microwave trapped ion quantum computer
Bjoern Lekitsch, Sebastian Weidt, Austin G Fowler, Klaus Mølmer, Simon J Devitt, Christof Wunderlich, and Winfried K Hensinger · 2017
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Neural decoder for topological codes
Giacomo Torlai and Roger G Melko · 2017
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Ultra-high error threshold for surface codes with biased noise
David K Tuckett, Stephen D Bartlett, and Steven T Flammia · 2017
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The ABCs of the Color Code: A Study of Topological Quantum Codes as Toy Models for Fault-Tolerant Quantum Computation and Quantum Phases Of Matter
Aleksander Marek Kubica · 2018
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Hyperbolic and semi-hyperbolic surface codes for quantum storage
Nikolas P Breuckmann, Christophe Vuillot, Earl Campbell, Anirudh Krishna, and Barbara M Terhal · 2058
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Decoding small surface codes with feedforward neural networks
Savvas Varsamopoulos, Ben Criger, and Koen Bertels · 2058
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