Diagonal gates in the Clifford hierarchy

@article{Cui2017DiagonalGI,
  title={Diagonal gates in the Clifford hierarchy},
  author={S. Cui and D. Gottesman and A. Krishna},
  journal={Physical Review A},
  year={2017},
  volume={95},
  pages={012329}
}
  • S. Cui, D. Gottesman, A. Krishna
  • Published 2017
  • Physics
  • Physical Review A
  • The Clifford hierarchy is a set of gates that appears in the theory of fault-tolerant quantum computation, but its precise structure remains elusive. We give a complete characterization of the diagonal gates in the Clifford hierarchy for prime-dimensional qudits. They turn out to be $p^{m}$-th roots of unity raised to polynomial functions of the basis state to which they are applied, and we determine which level of the Clifford hierarchy a given gate sits in based on $m$ and the degree of the… CONTINUE READING
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