Exact synthesis of multi-qubit Clifford+T circuits

@article{Giles2012ExactSO,
  title={Exact synthesis of multi-qubit Clifford+T circuits},
  author={Brett Giles and Peter Selinger},
  journal={CoRR},
  year={2012},
  volume={abs/1212.0506}
}
We prove that a unitary matrix has an exact representation over the Clifford+T gate set with local ancillas if and only if its entries are in the ring Z[ 1 √ 2 , i]. Moreover, we show that one ancilla always suffices. These facts were conjectured by Kliuchnikov, Maslov, and Mosca. We obtain an algorithm for synthesizing a exact Clifford+T circuit from any such n-qubit operator. We also characterize the Clifford+T operators that can be represented without ancillas. 
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Générateurs et relations pour les circuits booléens réversibles

  • J. Musset
  • Institut de Mathématiques de Luminy,
  • 1997
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