# Solovay–Kitaev theorem

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In the mathematical theory of computation, the **Solovay–Kitaev theorem** says, roughly, that if a set of single-qubit quantum gates generates a dense subset of SU(2) then that set is guaranteed to fill SU(2) quickly, which means good approximations to any desired gate can be created using fairly short sequences of gates from the generating set. It is one of the most important fundamental results in the field of quantum computation.^{[1]} Robert M. Solovay and Alexei Kitaev jointly came up with and proved the theorem.

## References[edit]

**^**Dawson, Christopher M.; Nielsen, Michael A. (2005-05-05). "The Solovay-Kitaev algorithm". arXiv:quant-ph/0505030.

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