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Vast numbers of qubits will be needed for large-scale quantum computing due to the overheads associated with error correction.
Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill, “Topological quantum memory,” Journal of Mathematical Physics 43
2002
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E. Knill, “Scalable quantum computation in the presence of large detected-error rates,” (2003), arXiv:quant-ph/0312190
2003
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Sean D. Barrett and Pieter Kok, “Efficient high-fidelity quantum computation using matter qubits and linear optics,” Phys. Rev. A 71
2005
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Sergey Bravyi and Alexei Kitaev, “Universal quantum computation with ideal clifford gates and noisy ancillas,” Phys. Rev. A 71
2005
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David Poulin, “Stabilizer formalism for operator quantum error correction,” Phys. Rev. Lett. 95
2005
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H. Bombin and M. A. Martin-Delgado, “Topological quantum distillation,” Phys. Rev. Lett. 97
2006
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Dave Bacon, “Operator quantum error-correcting subsystems for self-correcting quantum memories,” Phys. Rev. A 73
2006
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Robert Raussendorf and Jim Harrington, “Fault-tolerant quantum computation with high threshold in two dimensions,” Phys. Rev. Lett. 98
2007
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2008
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2009
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Sergey Bravyi and Barbara Terhal, “A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes,” New Journal of Physics 11
2009
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Sergey Bravyi, David Poulin, and Barbara Terhal, “Tradeoffs for reliable quantum information storage in 2d systems,” Phys. Rev. Lett. 104
2010
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Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland, “Surface codes: Towards practical large-scale quantum computation,” Phys. Rev. A 86
2012
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Clare Horsman, Austin G Fowler, Simon Devitt, and Rodney Van Meter, “Surface code quantum computing by lattice surgery,” New Journal of Physics 14
2012
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Naomi H. Nickerson, Ying Li, and Simon C. Benjamin, “Topological quantum computing with a very noisy network and local error rates approaching one percent,” Nature Communications 4
2013
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Alexey A. Kovalev and Leonid P. Pryadko, “Quantum kronecker sum-product low-density parity-check codes with finite rate,” Phys. Rev. A 88
2013
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Daniel Gottesman, “Fault-tolerant quantum computation with constant overhead,” Quantum Info. Comput. 14
2014
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Dave Wecker, Bela Bauer, Bryan K. Clark, Matthew B. Hastings, and Matthias Troyer, “Gate-count estimates for performing quantum chemistry on small quantum computers,” Phys. Rev. A 90
2014
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Jean-Pierre Tillich and Gilles Zémor, “Quantum ldpc codes with positive rate and minimum distance proportional to the square root of the blocklength,” IEEE Transactions on Information Theory 60
2014
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Matthew B. Hastings, “Decoding in hyperbolic spaces: Quantum ldpc codes with linear rate and efficient error correction,” Quantum Info. Comput. 14
2014
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Anthony Leverrier, Jean-Pierre Tillich, and Gilles Zémor, “Quantum expander codes,” in 2015 IEEE 56th Annual Symposium on Foundations of Computer Science (2015) pp. 810–824
2015
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Héctor Bombín, “Single-shot fault-tolerant quantum error correction,” Phys. Rev. X 5
2015
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Shantanu Debnath, Norbert M Linke, Caroline Figgatt, Kevin A Landsman, Kevin Wright, and Christopher Monroe, “Demonstration of a small programmable quantum computer with atomic qubits,” Nature 536
2016
Cited alongside, same era.
M. B. Hastings, “Weight reduction for quantum codes,” (2016), arXiv:1611.03790 [quant-ph]
2016
Cited alongside, same era.
Nikolas P. Breuckmann and Barbara M. Terhal, “Constructions and noise threshold of hyperbolic surface codes,” IEEE Transactions on Information Theory 62
2016
Cited alongside, same era.
N. Kalb, A. A. Reiserer, P. C. Humphreys, J. J. W. Bakermans, S. J. Kamerling, N. H. Nickerson, S. C. Benjamin, D. J. Twitchen, M. Markham, and R. Hanson, “Entanglement distillation between solid-state quantum network nodes,” Science 356
2017
Cited alongside, same era.
Joonho Lee, Dominic W. Berry, Craig Gidney, William J. Huggins, Jarrod R. McClean, Nathan Wiebe, and Ryan Babbush, “Even more efficient quantum computations of chemistry through tensor hypercontraction,” PRX Quantum 2
2021
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2021
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Craig Gidney and Martin Ekerå, “How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits,” Quantum 5
2021
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J. Pablo Bonilla Ataides, David K. Tuckett, Stephen D. Bartlett, Steven T. Flammia, and Benjamin J. Brown, “The XZZX surface code,” Nature Communications 12
2021
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Benjamin J. Brown, Katharina Laubscher, Markus S. Kesselring, and James R. Wootton, “Poking holes and cutting corners to achieve clifford gates with the surface code,” Phys. Rev. X 7
2017
Cited alongside, same era.
Nikolas P Breuckmann, Christophe Vuillot, Earl Campbell, Anirudh Krishna, and Barbara M Terhal, “Hyperbolic and semi-hyperbolic surface codes for quantum storage,” Quantum Science and Technology 2
2017
Cited alongside, same era.
Ali Lavasani and Maissam Barkeshli, “Low overhead clifford gates from joint measurements in surface, color, and hyperbolic codes,” Phys. Rev. A 98
2018
Cited alongside, same era.
Ryan Babbush, Craig Gidney, Dominic W. Berry, Nathan Wiebe, Jarrod McClean, Alexandru Paler, Austin Fowler, and Hartmut Neven, “Encoding electronic spectra in quantum circuits with linear t complexity,” Phys. Rev. X 8
2018
Cited alongside, same era.
Earl Campbell, Ankur Khurana, and Ashley Montanaro, “Applying quantum algorithms to constraint satisfaction problems,” Quantum 3
2019
Cited alongside, same era.
A. R. Mills, D. M. Zajac, M. J. Gullans, F. J. Schupp, T. M. Hazard, and J. R. Petta, “Shuttling a single charge across a one-dimensional array of silicon quantum dots,” Nature Communications 10
2019
Cited alongside, same era.
Daniel Litinski, “A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery,” Quantum 3
2019
Cited alongside, same era.
Christophe Vuillot, Lingling Lao, Ben Criger, Carmen García Almudéver, Koen Bertels, and Barbara M Terhal, “Code deformation and lattice surgery are gauge fixing,” New Journal of Physics 21
2019
Cited alongside, same era.
J. Yoneda, W. Huang, M. Feng, C. H. Yang, K. W. Chan, T. Tanttu, W. Gilbert, R. C. C. Leon, F. E. Hudson, K. M. Itoh, A. Morello, S. D. Bartlett, A. Laucht, A. Saraiva, and A. S. Dzurak, “Coherent spin qubit transport in silicon,” Nature Communications 12
2021
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J. M. Pino, J. M. Dreiling, C. Figgatt, J. P. Gaebler, S. A. Moses, M. S. Allman, C. H. Baldwin, M. Foss-Feig, D. Hayes, K. Mayer, C. Ryan-Anderson, and B. Neyenhuis, “Demonstration of the trapped-ion quantum ccd computer architecture,” Nature 592
2021
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2021
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2021
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2021
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Pavel Panteleev and Gleb Kalachev, “Degenerate Quantum LDPC Codes With Good Finite Length Performance,” Quantum 5
2021
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Antoine Grospellier, Lucien Grouès, Anirudh Krishna, and Anthony Leverrier, “Combining hard and soft decoders for hypergraph product codes,” Quantum 5
2021
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Anirudh Krishna and David Poulin, “Fault-tolerant gates on hypergraph product codes,” Phys. Rev. X 11
2021
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M. B. Hastings, “On quantum weight reduction,” (2021), arXiv:2102.10030 [quant-ph]
2021
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Élie Gouzien and Nicolas Sangouard, “Factoring 2048-bit rsa integers in 177 days with 13 436 qubits and a multimode memory,” Phys. Rev. Lett. 127
2021
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2021
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Oscar Higgott and Nikolas P. Breuckmann, “Subsystem codes with high thresholds by gauge fixing and reduced qubit overhead,” Phys. Rev. X 11
2021
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2021
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2021
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Pavel Panteleev and Gleb Kalachev, “Quantum ldpc codes with almost linear minimum distance,” IEEE Transactions on Information Theory 68
2022
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Nikolas P. Breuckmann and Vivien Londe, “Single-shot decoding of linear rate ldpc quantum codes with high performance,” IEEE Transactions on Information Theory 68
2022
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