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We reduce the extra qubits needed for two fault-tolerant quantum computing protocols: error correction, specifically syndrome bit measurement, and cat state preparation.
“Topological and subsystem codes on low-degree graphs with flag qubits”
Christopher Chamberland, Guanyu Zhu, Theodore J. Yoder, Jared B. Hertzberg, and Andrew W. Cross · 1907
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“Triangular color codes on trivalent graphs with flag qubits”
Christopher Chamberland, Aleksander Kubica, Theodore J Yoder, and Guanyu Zhu · 1911
Earlier work this paper cites.
“Flag fault-tolerant error correction for any stabilizer code”
Rui Chao and Ben W. Reichardt · 1912
Earlier work this paper cites.
Pulse code communication. U.S. Patent 2632058A
Frank Gray · 1953
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“The Binary Gray Code”
M. Gardner · 1986
Earlier work this paper cites.
Daniel M. Greenberger, Michael A. Horne, and Anton Zeilinger · 1989
Earlier work this paper cites.
“Fault-tolerant quantum computation”
P. W. Shor · 1996
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“Active stabilization, quantum computation, and quantum state synthesis”
A. M. Steane · 1997
Cited alongside, same era.
“Beyond single-shot fault-tolerant quantum error correction”
Nicolas Delfosse, Ben W. Reichardt, and Krysta M. Svore · 2002
Cited alongside, same era.
“Scalable quantum computing in the presence of large detected-error rates”
E. Knill · 2005
Cited alongside, same era.
“Quantum communication”
Nicolas Gisin and Rob Thew · 2007
Cited alongside, same era.
“Effective fault-tolerant quantum computation with slow measurements”
David P. DiVincenzo and Panos Aliferis · 2007
Cited alongside, same era.
“Efficient fault-tolerant decoding of topological color codes” (2014)
Ashley M. Stephens · 2014
Later among the works it cites.
“The surface code with a twist”
Theodore J. Yoder and Isaac H. Kim · 2017
Later among the works it cites.
“Quantum error correction with only two extra qubits”
Rui Chao and Ben W. Reichardt · 2018
Later among the works it cites.
“Fault-tolerant quantum computation with few qubits”
Rui Chao and Ben W. Reichardt · 2018
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“Flag fault-tolerant error correction with arbitrary distance codes”
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Jian-Wei Pan, Zeng-Bing Chen, Chao-Yang Lu, Harald Weinfurter, Anton Zeilinger, and Marek Żukowski · 2012
Cited alongside, same era.
Christopher Chamberland and Michael E. Beverland · 2018
Later among the works it cites.
“Between shor and steane: A unifying construction for measuring error syndromes”
Shilin Huang and Kenneth R. Brown · 2021
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