Fast and efficient exact synthesis of single-qubit unitaries generated by Clifford and T gates (pp0607-0630)
          Vadym Kliuchnikov, Dmitri Maslov, and Michele Mosca
          doi:https://doi.org/10.26421/QIC13.7-8-4
Abstracts: In this paper, we show the equivalence of the set of unitaries computable by the circuits over the Clifford and T library and the set of unitaries over the ring Z[ √1 2 , i], in the singlequbit case. We report an efficient synthesis algorithm, with an exact optimality guarantee on the number of Hadamard and T gates used. We conjecture that the equivalence of the sets of unitaries implementable by circuits over the Clifford and T library and unitaries over the ring Z[ √1 2 , i] holds in the n-qubit case.
Key words: circuit synthesis; Solovay-Kitaev algorithm