The 15-to-1 magic state distillation protocol can be made deterministic and measurement-free with a coherent feedback network, suppressing noise as O(p^2) instead of O(p^3).
Kitaev, Quantum computations: Algorithms and error cor- rection, Russian Mathematical Surveys 52, 1191 (1997)
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Magic state distillation without measurements and post-selection
The 15-to-1 magic state distillation protocol can be made deterministic and measurement-free with a coherent feedback network, suppressing noise as O(p^2) instead of O(p^3).