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A method for the implementation of a universal set of fault-tolerant logical gates is presented using homological product codes.
Elementary gates for quantum computation
Adriano Barenco, Charles H. Bennett, Richard Cleve, David P. DiVincenzo, Norman Margolus, Peter Shor, Tycho Sleator, John A. Smolin, and Harald Weinfurter · 1995
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Peter W. Shor · 1996
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Threshold accuracy for quantum computation
Emanuel Knill, Raymond Laflamme, and Wojciech H. Zurek · 1996
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Good quantum error-correcting codes exist
A. Robert Calderbank and Peter W. Shor · 1996
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Sergey Bravyi and Alexei Kitaev · 2005
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Héctor Bombín and Miguel A. Martin-Delgado · 2006
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Sergey Bravyi, Barbara M Terhal, and Bernhard Leemhuis · 2010
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Transversality Versus Universality for Additive Quantum Codes
Bei Zeng, Andrew W. Cross, and Isaac L. Chuang · 2011
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Generating topological order from a two-dimensional cluster state using a duality mapping
Benjamin J Brown, Wonmin Son, Christina V Kraus, Rosario Fazio, and Vlatko Vedral · 2011
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Surface codes: Towards practical large-scale quantum computation
Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland · 2012
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Improved quantum hypergraph-product ldpc codes
Alexey A Kovalev and Leonid P Pryadko · 2012
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Classification of topologically protected gates for local stabilizer codes
Sergey Bravyi and Robert König · 2013
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Quantum ldpc codes with positive rate and minimum distance proportional to the square root of the blocklength
Jean-Pierre Tillich and Gilles Zémor · 2013
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Universal fault-tolerant quantum computation with only transversal gates and error correction
Adam Paetznick and Ben W. Reichardt · 2013
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Universal transversal gates with color codes: A simplified approach
Aleksander Kubica and Michael E. Beverland · 2015
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Fernando Pastawski and Beni Yoshida · 2015
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Aleksander Kubica, Beni Yoshida, and Fernando Pastawski · 2015
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Anthony Leverrier, Jean-Pierre Tillich, and Gilles Zémor · 2015
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Sergey Bravyi and Andrew Cross · 2015
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Demonstration of weight-four parity measurements in the surface code architecture
Maika Takita, Antonio D Córcoles, Easwar Magesan, Baleegh Abdo, Markus Brink, Andrew Cross, Jerry M Chow, and Jay M Gambetta · 2016
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Alexey A. Kovalev and Leonid P. Pryadko · 2013
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Superconducting quantum circuits at the surface code threshold for fault tolerance
R. Barends, J. Kelly, A. Megrant, A. Veitia, D. Sank, E. Jeffrey, T. C. White, J. Mutus, A. G. Fowler, B. Campbell, et al · 2014
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Implementing a strand of a scalable fault-tolerant quantum computing fabric
Jerry M. Chow, Jay M. Gambetta, Easwar Magesan, David W. Abraham, Andrew W. Cross, B. R. Johnson, Nicholas A. Masluk, Colm A. Ryan, John A. Smolin, Srikanth J. Srinivasan, et al · 2014
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Quantum computations on a topologically encoded qubit
Daniel Nigg, Markus Mueller, Esteban A Martinez, Philipp Schindler, Markus Hennrich, Thomas Monz, Miguel A Martin-Delgado, and Rainer Blatt · 2014
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Homological product codes
Sergey Bravyi and Matthew B Hastings · 2014
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Quantum systems on non-k-hyperfinite complexes: a generalization of classical statistical mechanics on expander graphs
Michael H Freedman and Matthew B Hastings · 2014
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Fault-tolerant quantum computation with constant overhead
Daniel Gottesman · 2014
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Stacked codes: Universal fault-tolerant quantum computation in a two-dimensional layout
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Gauge color codes in two dimensions
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Theodore J. Yoder, Ryuji Takagi, and Isaac L. Chuang · 2016
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Thresholds for universal concatenated quantum codes
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Weight reduction for quantum codes
Mathew B. Hastings · 2017
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Overhead analysis of universal concatenated quantum codes
Christopher Chamberland, Tomas Jochym-O’Connor, and Raymond Laflamme · 2017
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Disjointness of stabilizer codes and limitations on fault-tolerant logical gates
Tomas Jochym-O’Connor, Aleksander Kubica, and Theodore J Yoder · 2018
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