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The overhead cost of performing universal fault-tolerant quantum computation for large scale quantum algorithms is very high.
Ian D. Kivlichan, Craig Gidney, Dominic W. Berry, Nathan Wiebe, Jarrod McClean, Wei Sun, Zhang Jiang, Nicholas Rubin, Austin Fowler, Alán Aspuru-Guzik, Hartmut Neven, and Ryan Babbush · 1902
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Efficient color code decoders in d ≥ 2 d\geq 2 dimensions from toric code decoders
Aleksander Kubica and Nicolas Delfosse · 1905
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How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits
Craig Gidney and Martin Ekerå · 1905
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Paths, trees, and flowers
Jack Edmonds · 1965
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Threshold accuracy for quantum computation
Emanuel Knill, Raymond Laflamme, and Wojciech H. Zurek · 1996
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Fault-tolerant quantum computation
Peter W. Shor · 1996
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Fault-tolerant error correction with efficient quantum codes
David P. DiVincenzo and Peter W. Shor · 1996
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Quantum computations: algorithms and error correction
Alexei Y. Kitaev · 1997
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The Heisenberg representation of quantum computers
Daniel Gottesman · 1999
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Hierarchical decoding to reduce hardware requirements for quantum computing
Nicolas Delfosse · 2001
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Encoding a qubit in an oscillator
Daniel Gottesman, Alexei Kitaev, and John Preskill · 2001
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Improved simulation of stabilizer circuits
Scott Aaronson and Daniel Gottesman · 2004
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Universal quantum computation with ideal clifford gates and noisy ancillas
Sergey Bravyi and Alexei Kitaev · 2005
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Quantum universality from magic states distillation applied to css codes
Ben W. Reichardt · 2005
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Quantum computing with realistically noisy devices
Emanuel Knill · 2005
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Topological quantum distillation
H. Bombin and M. A. Martin-Delgado · 2006
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The solovay-kitaev algorithm
Christopher M. Dawson and Michael Nielsen · 2006
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Quantum accuracy threshold for concatenated distance-3 codes
Panos Aliferis, Daniel Gottesman, and John Preskill · 2006
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Effective fault-tolerant quantum computation with slow measurements
David P. DiVincenzo and Panos Aliferis · 2007
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Restrictions on transversal encoded quantum gate sets
Bryan Eastin and Emanuel Knill · 2009
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An introduction to quantum error correction and fault-tolerant quantum computation
Daniel Gottesman · 2010
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Fault-tolerant quantum computing with color codes
Andrew J. Landahl, Jonas T. Anderson, and Patrick R. Rice · 2011
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Magic-state distillation with low overhead
Sergey Bravyi and Jeongwan Haah · 2012
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Surface code quantum computing by lattice surgery
Clare Horsman, Austin G Fowler, Simon Devitt, and Rodney Van Meter · 2012
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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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Magic-state distillation with the four-qubit code
Adam M. Meier, Bryan Eastin, and Emanuel Knill · 2013
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Surface code implementation of block code state distillation
Austin G. Fowler, Simon J. Devitt, and Cody Jones · 2013
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Using concatenated quantum codes for universal fault-tolerant quantum gates
Tomas Jochym-O’Connor and Raymond Laflamme · 2014
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Magic state distillation at intermediate size
Jeongwan Haah, Matthew B. Hastings, David Poulin, and Dave Wecker · 2018
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Distillation with sublogarithmic overhead
Matthew B. Hastings and Jeongwan Haah · 2018
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Codes and Protocols for Distilling T T , controlled- S S , and Toffoli Gates
Jeongwan Haah and Matthew B. Hastings · 2018
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Flag fault-tolerant error correction with arbitrary distance codes
Christopher Chamberland and Michael E. Beverland · 2018
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Ben W. Reichardt · 2018
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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
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Phys. Rev. Lett. , 113:080501, Aug 2014
Jonas T. Anderson, Guillaume Duclos-Cianci, and David Poulin · 2014
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Quantum computing by color-code lattice surgery
Andrew J. Landahl and Ciaran Ryan-Anderson · 2014
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Gauge color codes: optimal transversal gates and gauge fixing in topological stabilizer codes
Héctor Bombín · 2015
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Sergey Bravyi and Andrew Cross · 2015
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Universal transversal gates with color codes: A simplified approach
Aleksander Kubica and Michael E. Beverland · 2015
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Quantum error correction for quantum memories
Barbara M. Terhal · 2015
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Aleksander Kubica · 2018
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Fault-Tolerant Quantum Computing in the Pauli or Clifford Frame with Slow Error Diagnostics
Christopher Chamberland, Pavithran Iyer, and David Poulin · 2018
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Lattice Surgery with a Twist: Simplifying Clifford Gates of Surface Codes
Daniel Litinski and Felix von Oppen · 2018
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Low overhead quantum computation using lattice surgery
Austin G. Fowler and Craig Gidney · 2018
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The boundaries and twist defects of the color code and their applications to topological quantum computation
Markus S. Kesselring, Fernando Pastawski, Jens Eisert, and Benjamin J. Brown · 2018
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Performance and structure of single-mode bosonic codes
Victor V. Albert, Kyungjoo Noh, Kasper Duivenvoorden, Dylan J. Young, R. T. Brierley, Philip Reinhold, Christophe Vuillot, Linshu Li, Chao Shen, S. M. Girvin, Barbara M. Terhal, and Liang Jiang · 2018
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High-threshold fault-tolerant quantum computation with analog quantum error correction
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Fault-tolerant magic state preparation with flag qubits
Christopher Chamberland and Andrew W. Cross · 2019
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Fault-tolerant gates via homological product codes
Tomas Jochym-O’Connor · 2019
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Universal logical gates with constant overhead: instantaneous Dehn twists for hyperbolic quantum codes
Ali Lavasani, Guanyu Zhu, and Maissam Barkeshli · 2019
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Magic State Distillation: Not as Costly as You Think
Daniel Litinski · 2019
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Fault-tolerant preparation of approximate GKP states
Yunong Shi, Christopher Chamberland, and Andrew Cross · 2019
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Flag fault-tolerant error correction for any stabilizer code
Rui Chao and Ben W. Reichardt · 2019
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Flag fault-tolerant error correction, measurement, and quantum computation for cyclic calderbank-shor-steane codes
Theerapat Tansuwannont, Christopher Chamberland, and Debbie Leung · 2020
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