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The color code is a topological quantum error-correcting code supporting a variety of valuable fault-tolerant logical gates.
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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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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Logical Performance of 9 Qubit Compass Codes in Ion Traps with Crosstalk Errors
Dripto M. Debroy, Muyuan Li, Shilin Huang, and Kenneth R. Brown · 1910
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Paths, trees, and flowers
Jack Edmonds · 1965
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Algorithms for quantum computation: Discrete logarithms and factoring
P.W. Shor · 1994
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Quantum Error Correction via Codes over GF(4)
A. R. Calderbank, E. M Rains, P. W. Shor, and N. J. A. Sloane · 1996
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Stabilizer codes and quantum error correction
Daniel Gottesman · 1997
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Quantum codes on a lattice with boundary
Sergey Bravyi and Alexei Kitaev · 1998
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Topological quantum memory
Eric Dennis, Alexei Kitaev, Andrew Landhal, and John Preskill · 2002
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Fault-tolerant quantum computation by anyons
A.Yu. Kitaev · 2003
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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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Subsystem fault tolerance with the bacon-shor code
Panos Aliferis and Andrew W. Cross · 2007
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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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Error Threshold for Color Codes and Random Three-Body Ising Models
Helmut G. Katzgraber, H. Bombin, and M. A. Martin-Delgado · 2009
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Graphical algorithms and threshold error rates for the 2d colour code
David S. Wang, Austin G. Fowler, Charles D. Hill, and Lloyd C. L. Hollenberg · 2010
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Fully microwave-tunable universal gates in superconducting qubits with linear couplings and fixed transition frequencies
Chad Rigetti and Michel Devoret · 2010
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Np-hardness of decoding quantum error-correction codes
Min-Hsiu Hsieh and Fran çois Le Gall · 2011
Cited alongside, same era.
Transversality versus universality for additive quantum codes
Bei Zeng, Andrew Cross, and Isaac L. Chuang · 2011
Cited alongside, same era.
Fault-tolerant quantum computing with color codes
Andrew J. Landahl, Jonas T. Anderson, and Patrick R. Rice · 2011
Cited alongside, same era.
Simple all-microwave entangling gate for fixed-frequency superconducting qubits
Jerry M. Chow, A. D. Córcoles, Jay M. Gambetta, Chad Rigetti, B. R. Johnson, John A. Smolin, J. R. Rozen, George A. Keefe, Mary B. Rothwell, Mark B. Ketchen, and M. Steffen · 2011
Cited alongside, same era.
Surface code quantum computing with error rates over 1
David S. Wang, Austin G. Fowler, and Lloyd C. L. Hollenberg · 2011
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Toward Realizable Quantum Computers
Michael E. Beverland · 2016
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Almost-linear time decoding algorithm for topological codes
Nicolas Delfosse and Naomi H. Nickerson · 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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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 Kubica · 2018
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Projecting three-dimensional color codes onto three-dimensional toric codes
Arun B. Aloshious and Pradeep Kiran Sarvepalli · 2018
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Efficient decoding of topological color codes
Pradeep Sarvepalli and Robert Raussendorf · 2012
Cited alongside, same era.
Surface codes: Towards practical large-scale quantum computation
Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland · 2012
Cited alongside, same era.
An Introduction to Topological Quantum Codes
H. Bombin · 2013
Cited alongside, same era.
Classification of Topologically Protected Gates for Local Stabilizer Codes
Sergey Bravyi and Robert König · 2013
Cited alongside, same era.
Decoding color codes by projection onto surface codes
Nicolas Delfosse · 2014
Cited alongside, same era.
Low-distance surface codes under realistic quantum noise
Yu Tomita and Krysta M. Svore · 2014
Cited alongside, same era.
Hardness of decoding quantum stabilizer codes
P. Iyer and D. Poulin · 2015
Cited alongside, same era.
Three-dimensional color code thresholds via statistical-mechanical mapping
Aleksander Kubica, Michael E. Beverland, Fernando Brandão, John Preskill, and Krysta M. Svore · 2018
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Tailoring surface codes for highly biased noise
David K. Tuckett, Andrew S. Darmawan, Christopher T. Chubb, Sergey Bravyi, Stephen D. Bartlett, and Steven T. Flammia · 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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Flag fault-tolerant error correction, measurement, and quantum computation for cyclic CSS codes
Theerapat Tansuwannont, Christopher Chamberland, and Debbie Leung · 2018
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Ben W. Reichardt · 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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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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Advantages of versatile neural-network decoding for topological codes
Nishad Maskara, Aleksander Kubica, and Tomas Jochym-O’Connor · 2019
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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 preparation of approximate GKP states
Yunong Shi, Christopher Chamberland, and Andrew Cross · 2019
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Neural network decoder for topological color codes with circuit level noise
P Baireuther, M D Caio, B Criger, C W J Beenakker, and T E O’Brien · 2019
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2d compass codes
Muyuan Li, Daniel Miller, Michael Newman, Yukai Wu, and Kenneth R. Brown · 2019
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Deep neural decoders for near term fault-tolerant experiments
Christopher Chamberland and Pooya Ronagh · 2058
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