Fast and efficient exact synthesis of single-qubit unitaries generated by clifford and T gates

@article{Kliuchnikov2013FastAE,
  title={Fast and efficient exact synthesis of single-qubit unitaries generated by clifford and T gates},
  author={Vadym Kliuchnikov and Dmitri Maslov and Michele Mosca},
  journal={Quantum Information & Computation},
  year={2013},
  volume={13},
  pages={607-630}
}
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… CONTINUE READING
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