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## "Universal quantum computation with ideal Clifford gates and noisy ancillas", Sergey Bravyi, Alexei Kitaev, 2005

*Reviewed August 25, 2023*

*Citation:* Bravyi, Sergey, and Alexei Kitaev. "Universal quantum computation with ideal Clifford gates and noisy ancillas." Physical Review A 71.2 (2005): 022316.

*Web:* https://arxiv.org/abs/quant-ph/0403025

*Tags:* Abelian-anyons, Computer-scientific

This is the paper which introduces magic state distillation. A nice summary of what's left to do is given by the authors:
"From the experimental point of view, an exciting open
problem is to design a physical system in which reliable
storage of quantum information and its processing by
Clifford group operations is possible. Since our simulation scheme tolerates strong decoherence on the ancilla
preparation stage, such a system would be a good candidate for a practical quantum computer."

For the surface codes, this is simple. You can prepare lots of (faulty) physical qubit T-states. Then, physical T-states are turned into logical T-states by state injection. None of this is fault-tolerant, so the result is a noisy ancilla. Magic state distillation can now give a not-noisy ancilla, completing the procedure!