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Attaining fault tolerance while maintaining low overhead is one of the main challenges in a practical implementation of quantum circuits.
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A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. Sloane, “Quantum error correction and orthogonal geometry,” Physical Review Letters
1997
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D. Gottesman, Stabilizer Codes and Quantum Error Correction · 1997
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B. M. Terhal and G. Burkard, “Fault-tolerant quantum computation for local non-Markovian noise,” Physical Review A
2005
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M. A. Nielsen and C. M. Dawson, “Fault-tolerant quantum computation with cluster states,” Physical Review A
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E. Knill, “Scalable quantum computing in the presence of large detected-error rates,” Physical Review A
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S. Bravyi and A. Kitaev, “Universal quantum computation with ideal Clifford gates and noisy ancillas,” Physical Review A
2005
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D. Poulin, “Stabilizer formalism for operator quantum error correction,” Physical review letters
2005
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P. Aliferis, D. Gottesman, and J. Preskill, “Quantum accuracy threshold for concatenated distance-3 codes,” Quantum Information and Computation
2006
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2007
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B. Eastin and E. Knill, “Restrictions on transversal encoded quantum gate sets,” Physical review letters
2009
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G. Duclos-Cianci and D. Poulin, “Fast decoders for topological quantum codes,” Physical review letters
2010
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S. Bravyi, “Subsystem codes with spatially local generators,” Physical Review A
2011
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A. Paetznick and B. W. Reichardt, “Fault-tolerant ancilla preparation and noise threshold lower bounds for the 23-qubit Golay code,” Quantum Information and Computation
2012
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A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, “Surface codes: Towards practical large-scale quantum computation,” Physical Review A
2012
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C. Chamberland and M. E. Beverland, “Flag fault-tolerant error correction with arbitrary distance codes,” Quantum
2018
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R. Chao and B. W. Reichardt, “Fault-tolerant quantum computation with few qubits,” npj Quantum Information
2018
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C. Vuillot, “Is error detection helpful on IBM 5q chips?,” Quantum Information and Computation
2018
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C. Chamberland and P. Ronagh, “Deep neural decoders for near term fault-tolerant experiments,” Quantum Science and Technology
2018
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K. Duivenvoorden, N. P. Breuckmann, and B. M. Terhal, “Renormalization group decoder for a four-dimensional toric code,” IEEE Transactions on Information Theory
2018
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S. Bravyi and J. Haah, “Quantum self-correction in the 3d cubic code model,” Physical review letters
2013
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G. Duclos-Cianci and D. Poulin, “Kitaev’s Z d-code threshold estimates,” Physical Review A
2013
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S. Bravyi and R. König, “Classification of topologically protected gates for local stabilizer codes,” Physical review letters
2013
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A. Paetznick and B. W. Reichardt, “Universal fault-tolerant quantum computation with only transversal gates and error correction,” Physical review letters
2013
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H. Anwar, B. J. Brown, E. T. Campbell, and D. E. Browne, “Fast decoders for qudit topological codes,” New Journal of Physics
2014
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S. Bravyi, M. Suchara, and A. Vargo, “Efficient algorithms for maximum likelihood decoding in the surface code,” Physical Review A
2014
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N. Delfosse, “Decoding color codes by projection onto surface codes,” Physical Review A
2014
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A. S. Darmawan and D. Poulin, “Linear-time general decoding algorithm for the surface code,” Physical Review E
2018
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C. Chamberland and A. W. Cross, “Fault-tolerant magic state preparation with flag qubits,” Quantum
2019
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Y. Shi, C. Chamberland, and A. Cross, “Fault-tolerant preparation of approximate GKP states,” New Journal of Physics
2019
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P. Baireuther, M. Caio, B. Criger, C. W. Beenakker, and T. E. O’Brien, “Neural network decoder for topological color codes with circuit level noise,” New Journal of Physics
2019
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A. Bermudez, X. Xu, M. Gutiérrez, S. Benjamin, and M. Müller, “Fault-tolerant protection of near-term trapped-ion topological qubits under realistic noise sources,” Physical Review A
2019
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M. Gutiérrez, M. Müller, and A. Bermúdez, “Transversality and lattice surgery: Exploring realistic routes toward coupled logical qubits with trapped-ion quantum processors,” Physical Review A
2019
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2019
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A. Kubica and J. Preskill, “Cellular-automaton decoders with provable thresholds for topological codes,” Physical review letters
2019
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N. Maskara, A. Kubica, and T. Jochym-O’Connor, “Advantages of versatile neural-network decoding for topological codes,” Physical Review A
2019
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N. H. Nickerson and B. J. Brown, “Analysing correlated noise on the surface code using adaptive decoding algorithms,” Quantum
2019
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M. Vasmer and D. E. Browne, “Three-dimensional surface codes: Transversal gates and fault-tolerant architectures,” Physical Review A
2019
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R. Chao and B. W. Reichardt, “Flag fault-tolerant error correction for any stabilizer code,” PRX Quantum
2020
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T. Tansuwannont, C. Chamberland, and D. Leung, “Flag fault-tolerant error correction, measurement, and quantum computation for cyclic Calderbank-Shor-Steane codes,” Physical Review A
2020
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C. Chamberland, A. Kubica, T. J. Yoder, and G. Zhu, “Triangular color codes on trivalent graphs with flag qubits,” New Journal of Physics
2020
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C. Chamberland, G. Zhu, T. J. Yoder, J. B. Hertzberg, and A. W. Cross, “Topological and subsystem codes on low-degree graphs with flag qubits,” Physical Review X
2020
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L. Lao and C. G. Almudever, “Fault-tolerant quantum error correction on near-term quantum processors using flag and bridge qubits,” Physical Review A
2020
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D. M. Debroy and K. R. Brown, “Extended flag gadgets for low-overhead circuit verification,” Physical Review A
2020
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R. Chao, M. E. Beverland, N. Delfosse, and J. Haah, “Optimization of the surface code design for Majorana-based qubits,” Quantum
2020
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T. Tansuwannont and D. Leung, “Fault-tolerant quantum error correction using error weight parities,” Physical Review A
2021
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A. Rodriguez-Blanco, A. Bermudez, M. Müller, and F. Shahandeh, “Efficient and robust certification of genuine multipartite entanglement in noisy quantum error correction circuits,” PRX Quantum
2021
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M. Vasmer, D. E. Browne, and A. Kubica, “Cellular automaton decoders for topological quantum codes with noisy measurements and beyond,” Scientific reports
2021
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M. E. Beverland, A. Kubica, and K. M. Svore, “Cost of universality: A comparative study of the overhead of state distillation and code switching with color codes,” PRX Quantum
2021
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