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It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal.
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AM Steane, “Space, time, parallelism and noise requirements for reliable quantum computing,” Fortschr. Phys. 46
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Yaoyun Shi, “Both toffoli and controlled-not need little help to do universal quantum computing,” Quantum Inf. Comput. 3
2003
Cited alongside, same era.
Dorit Aharonov, “A simple proof that toffoli and hadamard are quantum universal,” arXiv preprint quant-ph/0301040 (2003)
2003
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Scott Aaronson and Daniel Gottesman, “Improved simulation of stabilizer circuits,” Phys. Rev. A 70
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Sergey Bravyi and Alexei Kitaev, “Universal quantum computation with ideal clifford gates and noisy ancillas,” Phys. Rev. A 71
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Emanuel Knill, “Quantum computing with realistically noisy devices,” Nature 434
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Panos Aliferis, Daniel Gottesman, and John Preskill, “Quantum accuracy threshold for concatenated distance-3 codes,” Quantum Inf. Comput. 6
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Panos Aliferis and Andrew W Cross, “Subsystem fault tolerance with the bacon-shor code,” Physical review letters 98
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2012
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Austin G Fowler, Matteo Mariantoni, John M Martinis, and Andrew N Cleland, “Surface codes: Towards practical large-scale quantum computation,” Physical Review A 86
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Austin G Fowler, Simon J Devitt, and Cody Jones, “Surface code implementation of block code state distillation,” Sci. Rep. 3
2013
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Adam Paetznick and Ben W Reichardt, “Universal fault-tolerant quantum computation with only transversal gates and error correction,” Phys. Rev. Lett. 111
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Tomas Jochym-O’Connor and Raymond Laflamme, “Using concatenated quantum codes for universal fault-tolerant quantum gates,” Phys. Rev. Lett. 112
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Héctor Bombín, “Gauge color codes: optimal transversal gates and gauge fixing in topological stabilizer codes,” New Journal of Physics 17
2015
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Héctor Bombín, “Dimensional jump in quantum error correction,” New Journal of Physics 18
2016
Closest in time.
Hayato Goto, “Minimizing resource overheads for fault-tolerant preparation of encoded states of the steane code,” Scientific reports 6
2016
Closest in time.